{
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    "slug": "stellar-nebula",
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    "path": "private/var/folders/t7/b_w5m78j2mbb1ct051p9sv500000gn/T/nudge-opencode-generation-MwDfat",
    "title": "Nudge content generation",
    "agent": "nudge-generation",
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  "messages": [
    {
      "info": {
        "role": "user",
        "time": {
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        },
        "agent": "nudge-generation",
        "model": {
          "providerID": "openai",
          "modelID": "gpt-6-astra",
          "variant": "low"
        },
        "system": "You create Codeforces learning content for Nudge. Your job is to understand the best approach for the problem and teach it clearly in your own words, using existing solutions to inform your reasoning.\n\nStart with a brief, targeted web search for existing solutions so relevant editorials are in context before substantial independent problem-solving. Use any supplied tutorial links first; otherwise search by contest ID and problem index. Prefer the official tutorial/editorial, and read relevant explanations rather than relying on search snippets. Look at accessible alternatives when useful, especially if the official explanation is missing, unclear, or unnecessarily complicated. Accepted submissions can also help clarify an approach. Respect supplied source lookup statuses and avoid repeatedly retrying blocked sources. If no usable source is accessible, proceed from the supplied statement.\n\nTreat existing solutions as a starting point, not a constraint. If an approach is clear and suitable, build on it without unnecessary re-derivation. If an explanation has gaps, seems incorrect, or uses a harder method than necessary, reason through it and derive a better or simpler approach when worthwhile. Choose a correct approach that is easy to teach and fits the constraints. Verify it against the supplied statement and edge cases before writing the hints, editorial, and C++ solution.\n\nThe editorial must be self-contained: explain the key insight, algorithm, why it works, complexity, and implementation details a learner needs, filling in steps the source skips. Keep research and verification concise; spend the output on teaching the solution, not narrating the research process. Follow the user prompt and output schema exactly.",
        "format": {
          "type": "json_schema",
          "schema": {
            "type": "object",
            "properties": {
              "status": {
                "type": "string",
                "enum": [
                  "success",
                  "unsolvable"
                ],
                "description": "Set to 'success' when the supplied statement defines a solvable programming problem. Set to 'unsolvable' only if the statement is fundamentally incomplete, contradictory, or depends on an inaccessible required resource."
              },
              "reason": {
                "anyOf": [
                  {
                    "type": "string",
                    "pattern": "^[^\\u0000]*$",
                    "minLength": 1,
                    "maxLength": 2000
                  },
                  {
                    "type": "null"
                  }
                ],
                "description": "If status is 'unsolvable', provide a detailed failure message to show users. Name the concrete statement/resource blocker and any relevant source lookup/access status, such as missing official tutorial, 403/Cloudflare challenge, 404, or unavailable accepted submissions. Otherwise null."
              },
              "hints": {
                "anyOf": [
                  {
                    "type": "array",
                    "minItems": 5,
                    "maxItems": 5,
                    "description": "Exactly 5 progressive hints, each building on the last.",
                    "items": {
                      "type": "object",
                      "properties": {
                        "order": {
                          "type": "integer",
                          "minimum": 1,
                          "maximum": 5,
                          "description": "Hint number, 1 through 5."
                        },
                        "content": {
                          "type": "string",
                          "pattern": "^[^\\u0000]*$",
                          "minLength": 1,
                          "maxLength": 10000,
                          "description": "Markdown hint text."
                        }
                      },
                      "required": [
                        "order",
                        "content"
                      ],
                      "additionalProperties": false
                    }
                  },
                  {
                    "type": "null"
                  }
                ],
                "description": "If status is 'success', provide exactly 5 progressive hints. Otherwise null."
              },
              "editorial": {
                "anyOf": [
                  {
                    "type": "string",
                    "pattern": "^[^\\u0000]*$",
                    "minLength": 1,
                    "maxLength": 100000
                  },
                  {
                    "type": "null"
                  }
                ],
                "description": "If status is 'success', a prose editorial explaining the solution in Nudge's own voice, with no links, citations, or source/research notes. Otherwise null."
              },
              "solution": {
                "anyOf": [
                  {
                    "type": "string",
                    "pattern": "^[^\\u0000]*$",
                    "minLength": 1,
                    "maxLength": 200000
                  },
                  {
                    "type": "null"
                  }
                ],
                "description": "If status is 'success', a complete C++ solution. Otherwise null."
              }
            },
            "required": [
              "status",
              "reason",
              "hints",
              "editorial",
              "solution"
            ],
            "additionalProperties": false,
            "title": "problem_response",
            "description": "Submit the generated content for the problem, or report if it is unsolvable."
          },
          "retryCount": 2
        },
        "id": "msg_0adf2c1060019D8KDj8Y8Oikq9",
        "sessionID": "ses_f520d3f0affeQfrUZgNLtk436y"
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        {
          "type": "text",
          "text": "Generate Codeforces learning content: five progressive hints, an original editorial, and AC-quality C++.\n\nFollow the editorial-first research workflow in the system instructions. Use the supplied statement to verify that the source solves this exact problem.\n\nWrite clean Markdown with LaTeX as needed. Use quick and clever humor when appropriate. Tell it like it is (don't sugar-coat responses), and use very casual language. You are fully allowed to swear, just don't overdo it like a sailor (be natural). Deconstruct any false assumptions.\n\nGenerate content for Codeforces problem 2259A: \"Moo Language School\" (rated 800).\n\nKnown problem metadata:\n- Contest ID: 2259\n- Index: A\n- Name: Moo Language School\n- Rating: 800 (Codeforces difficulty rating)\n- Tags: brute force, greedy, two pointers\n- Problem URL: https://codeforces.com/contest/2259/problem/A\n\nUse the rating and tags as weak signals only. The supplied statement is the source of truth.\n\nProblem Statement:\n<problem-statement>\n<div class=\"header\"><div class=\"title\">A. Moo Language School</div><div class=\"time-limit\"><div class=\"property-title\">time limit per test</div>1 second</div><div class=\"memory-limit\"><div class=\"property-title\">memory limit per test</div>256 megabytes</div><div class=\"input-file input-standard\"><div class=\"property-title\">input</div>standard input</div><div class=\"output-file output-standard\"><div class=\"property-title\">output</div>standard output</div></div><div><p>Farmer John is trying to increase literacy rates in the United Cows of Farmer John (UCFJ). The UCFJ consists of $$$n$$$ fields and $$$\\frac{n}{k}$$$ farms (where $$$n$$$ is a multiple of $$$k$$$), with each farm consisting of $$$k$$$ consecutive fields. In other words, the $$$i$$$-th field is in the $$$\\lceil \\frac{i}{k} \\rceil$$$-th farm: Fields $$$1, 2, \\ldots, k$$$ are in the first farm, fields $$$k+1, k+2, \\ldots, 2k$$$ are in the second farm, etc.</p><p>Farmer John wants to build schools such that each farm has at least one school. However, some fields are owned by Farmer Nhoj, who will charge Farmer John extra to build a school there. Farmer John wants to know the minimum number of times that he would have to build a school on Farmer Nhoj's land in order to ensure that each farm has at least one school.</p></div><div class=\"input-specification\"><div class=\"section-title\">Input</div><p>The first line of each input contains an integer $$$t$$$ ($$$1 \\leq t \\leq 10^4$$$) — the number of test cases.</p><p>The first line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\leq k \\leq n \\leq 20$$$, $$$n$$$ is a multiple of $$$k$$$) — the number of fields and size of each farm.</p><p>The second line of each test case contains a binary string $$$s$$$ of length $$$n$$$ — the fields owned by Farmer Nhoj. If $$$s_i = 1$$$, the $$$i$$$-th field is owned by Farmer Nhoj. If $$$s_i = 0$$$, the $$$i$$$-th field is not owned by Farmer Nhoj.</p></div><div class=\"output-specification\"><div class=\"section-title\">Output</div><p>For each test case, output a single integer — the minimum number of times that Farmer John must build a school on Farmer Nhoj's land.</p></div><div class=\"sample-tests\"><div class=\"section-title\">Example</div><div class=\"sample-test\"><div class=\"input\"><div class=\"title\">Input</div><pre><div class=\"test-example-line test-example-line-even test-example-line-0\">6</div><div class=\"test-example-line test-example-line-odd test-example-line-1\">8 2</div><div class=\"test-example-line test-example-line-odd test-example-line-1\">10011100</div><div class=\"test-example-line test-example-line-even test-example-line-2\">5 1</div><div class=\"test-example-line test-example-line-even test-example-line-2\">11111</div><div class=\"test-example-line test-example-line-odd test-example-line-3\">8 4</div><div class=\"test-example-line test-example-line-odd test-example-line-3\">01111110</div><div class=\"test-example-line test-example-line-even test-example-line-4\">5 1</div><div class=\"test-example-line test-example-line-even test-example-line-4\">00101</div><div class=\"test-example-line test-example-line-odd test-example-line-5\">4 4</div><div class=\"test-example-line test-example-line-odd test-example-line-5\">1101</div><div class=\"test-example-line test-example-line-even test-example-line-6\">4 4</div><div class=\"test-example-line test-example-line-even test-example-line-6\">1111</div></pre></div><div class=\"output\"><div class=\"title\">Output</div><pre><div class=\"test-example-line test-example-line-odd test-example-line-1\">1</div><div class=\"test-example-line test-example-line-even test-example-line-2\">5</div><div class=\"test-example-line test-example-line-odd test-example-line-3\">0</div><div class=\"test-example-line test-example-line-even test-example-line-4\">2</div><div class=\"test-example-line test-example-line-odd test-example-line-5\">0</div><div class=\"test-example-line test-example-line-even test-example-line-6\">1</div></pre></div></div></div><div class=\"note\"><div class=\"section-title\">Note</div><p>For the first test case, we can build a school on the $$$2$$$nd, $$$3$$$rd, $$$5$$$th, and $$$7$$$th fields, and of those, only the $$$5$$$th field is owned by Farmer Nhoj, meaning our answer is $$$1$$$. It can be shown that this is the best possible answer.</p><p>For the second test case, Farmer Nhoj owns every field, and since we have to build $$$5$$$ schools, we must build on Farmer Nhoj's land $$$5$$$ times.</p></div>\n</problem-statement>\n\n\nSource lookup status:\n<source-lookup-status>\n- Tutorial (en): https://codeforces.com/blog/entry/156457 loaded (200 OK; title: \"Codeforces Round 1119 (Div. 3) Editorial - Codeforces\"; mentions 2259A)\n</source-lookup-status>\n\nGenerate:\n1. Five progressive hints, from a gentle nudge to the key insight.\n2. A self-contained editorial that teaches the solution clearly, including the key insight, algorithm, correctness argument, complexity, and necessary implementation details. Explain non-obvious steps without padding or a discovery-process transcript.\n3. A complete C++26 solution that gets AC on Codeforces.\n\nFormatting & Style Rules:\n- Hints and editorial: valid Markdown with LaTeX as needed (e.g., $dp[i]$, $$\\sum_{i=1}^{n} a_i$$).\n- Hints and editorial must read like Nudge's own explanation. No research notes, source notes, citations, Markdown links, URLs, or references to editorials/submissions/posts.\n- Solution: raw C++ only, no Markdown fences.\n- Keep C++ short, clean, standard, and single-file. Comments are fine when they clarify the idea.\n\nOutput strictness:\n- Return JSON matching the provided schema exactly.\n- Never include NUL (U+0000) characters in any field. Use literal $ or $$ for math delimiters, never control characters.\n- If the problem is solvable, return `status: \"success\"`, `reason: null`, and fill in `hints`, `editorial`, and `solution`.\n- Return `status: \"unsolvable\"`, a short `reason`, and set `hints`, `editorial`, and `solution` to null only when the supplied statement is fundamentally incomplete, contradictory, or dependent on an inaccessible resource needed to define the task. Missing research, high rating, uncertainty, or \"can't guarantee AC\" is not a reason to return unsolvable.\n- If you return `status: \"unsolvable\"`, the `reason` is shown directly to users. Be concrete: say what exact statement/resource blocker stopped you, and include relevant source lookup status if it mattered (for example: official tutorial missing, Codeforces returned 403/Cloudflare challenge, tutorial page 404, accepted submissions unavailable).\n- Each hint must be an object with `order` (1 through 5) and `content` (the Markdown hint text), not a plain string. The `content` must contain just the hint text, with no \"Hint 1:\" or subtitles. The UI adds those automatically.\n- Do not start the editorial with an \"# Editorial\" heading. The UI already adds that section. Feel free to add other headers as needed though.\n- Use styling in the editorial if needed! Just that first header is no good but any subheaders or bolding or whatever is good!\n\nFor the C++ solution, you MUST use this template and work around it:\n\n```cpp\n#include <bits/stdc++.h>\nusing namespace std;\n\nusing ll = long long;\n\nvoid setIO() {\n    ios::sync_with_stdio(false);\n    cin.tie(nullptr);\n}\n\nint main() {\n    setIO();\n}\n```",
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          "cwd": "/private/var/folders/t7/b_w5m78j2mbb1ct051p9sv500000gn/T/nudge-opencode-generation-MwDfat",
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          "type": "step-start",
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            "output": "---\nimage: https://codeforces.com/codeforces.org/s/21069/images/codeforces-telegram-square-1024x1024.png\ntitle: Codeforces Round 1119 (Div. 3) Editorial - Codeforces\ndescription: Codeforces. Programming competitions and contests, programming community\n---\n\n<!DOCTYPE HTML PUBLIC \"-//W3C//DTD HTML 4.01//EN\"> \n\n  \n[![Codeforces](//codeforces.com/codeforces.org/s/21069/images/codeforces-logo-with-telegram-555x130.png \"Codeforces\")](https://codeforces.com/) \n\n[![In English](//codeforces.com/codeforces.org/s/21069/images/flags/24/gb.png \"In English\")](https://codeforces.com/blog/entry/156457?locale=en) [![По-русски](//codeforces.com/codeforces.org/s/21069/images/flags/24/ru.png \"По-русски\")](https://codeforces.com/blog/entry/156457?locale=ru) \n\n[Enter](https://codeforces.com/enter?back=%2Fblog%2Fentry%2F156457)| [Register](https://codeforces.com/register) \n\n  \n* [Home](https://codeforces.com/)\n* [Top](https://codeforces.com/top)\n* [Catalog](https://codeforces.com/catalog)\n* [Contests](https://codeforces.com/contests)\n* [Gym](https://codeforces.com/gyms)\n* [Problemset](https://codeforces.com/problemset)\n* [Groups](https://codeforces.com/groups)\n* 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Round 1119 (Div. 3) Editorial](https://codeforces.com/blog/entry/156457) ![New comment\\(s\\)](//codeforces.com/codeforces.org/s/21069/images/icons/comment-12x12.png \"New comment(s)\")\n* [MikeMirzayanov](https://codeforces.com/profile/MikeMirzayanov \"Headquarters, MikeMirzayanov\") → [Telegram Returns as Title Sponsor of Codeforces!](https://codeforces.com/blog/entry/156620) ![New comment\\(s\\)](//codeforces.com/codeforces.org/s/21069/images/icons/comment-12x12.png \"New comment(s)\")\n* [AmShZ](https://codeforces.com/profile/AmShZ \"Grandmaster AmShZ\") → [Repovive Premier Round 8 — $300 Prize Pool](https://codeforces.com/blog/entry/156827) ![New comment\\(s\\)](//codeforces.com/codeforces.org/s/21069/images/icons/comment-12x12.png \"New comment(s)\")\n* [DuyMinh3005](https://codeforces.com/profile/DuyMinh3005 \"Pupil DuyMinh3005\") → [Is this acceptable?](https://codeforces.com/blog/entry/155682) ![Text created or updated](//codeforces.com/codeforces.org/s/21069/images/icons/x-update-12x12.png \"Text created or updated\")\n* [kondasujay2](https://codeforces.com/profile/kondasujay2 \"International Master kondasujay2\") → [Codeforces Round 1120 (Div. 1, Div. 2)](https://codeforces.com/blog/entry/156576) ![Text created or updated](//codeforces.com/codeforces.org/s/21069/images/icons/x-update-12x12.png \"Text created or updated\")\n* [Down\\_bad\\_4\\_haiender288](https://codeforces.com/profile/Down%5Fbad%5F4%5Fhaiender288 \"Pupil Down_bad_4_haiender288\") → [new manmade horrors (barely within comprehension) just dropped](https://codeforces.com/blog/entry/156825) ![Text created or updated](//codeforces.com/codeforces.org/s/21069/images/icons/x-update-12x12.png \"Text created or updated\")\n* [qwexd](https://codeforces.com/profile/qwexd \"Master qwexd\") → [Codeforces Round 1121 (Div. 2)](https://codeforces.com/blog/entry/156653) ![Text created or updated](//codeforces.com/codeforces.org/s/21069/images/icons/x-update-12x12.png \"Text created or updated\")\n* [lumibons](https://codeforces.com/profile/lumibons \"International Grandmaster lumibons\") → [IOI 2027 Call for Tasks](https://codeforces.com/blog/entry/156793) ![New comment\\(s\\)](//codeforces.com/codeforces.org/s/21069/images/icons/comment-12x12.png \"New comment(s)\")\n* [OmarAfterMidnight](https://codeforces.com/profile/OmarAfterMidnight \"Pupil OmarAfterMidnight\") → [VoidHub Update: Relive CPC Contests as If You Were There](https://codeforces.com/blog/entry/156807) ![Text created or updated](//codeforces.com/codeforces.org/s/21069/images/icons/x-update-12x12.png \"Text created or updated\")\n* [Grizoo](https://codeforces.com/profile/Grizoo \"Candidate Master Grizoo\") → [\\[GYM\\] Aleppo Collegiate Programming Contest 2026](https://codeforces.com/blog/entry/156707) ![New comment\\(s\\)](//codeforces.com/codeforces.org/s/21069/images/icons/comment-12x12.png \"New comment(s)\")\n* [pllk](https://codeforces.com/profile/pllk \"Grandmaster pllk\") → [Competitive Programmer's Handbook — a new book on competitive programming](https://codeforces.com/blog/entry/50728) ![New comment\\(s\\)](//codeforces.com/codeforces.org/s/21069/images/icons/comment-12x12.png \"New comment(s)\") ![Necropost](//codeforces.com/codeforces.org/s/21069/images/icons/hourglass.png \"Necropost\")\n* [sadwqdqEF213](https://codeforces.com/profile/sadwqdqEF213 \"Expert sadwqdqEF213\") → [Introducing SoSOI 2027 - The First Solar System Olympiad in Informatics](https://codeforces.com/blog/entry/156550) ![Text created or updated](//codeforces.com/codeforces.org/s/21069/images/icons/x-update-12x12.png \"Text created or updated\")\n* [kondasujay2](https://codeforces.com/profile/kondasujay2 \"International Master kondasujay2\") → [Codeforces Round 1120 (Div 1, Div 2) Editorial](https://codeforces.com/blog/entry/156688) ![Text created or updated](//codeforces.com/codeforces.org/s/21069/images/icons/x-update-12x12.png \"Text created or updated\")\n* [adarshsolanki2004](https://codeforces.com/profile/adarshsolanki2004 \"Newbie adarshsolanki2004\") → [Cloudflare anti-bot verification not appearing](https://codeforces.com/blog/entry/151688) ![New comment\\(s\\)](//codeforces.com/codeforces.org/s/21069/images/icons/comment-12x12.png \"New comment(s)\")\n* [123gjweq2](https://codeforces.com/profile/123gjweq2 \"Master 123gjweq2\") → [Is this a good problem + can you please help me gauge its difficulty?](https://codeforces.com/blog/entry/156760) ![Text created or updated](//codeforces.com/codeforces.org/s/21069/images/icons/x-update-12x12.png \"Text created or updated\")\n\n|  | [Detailed →](https://codeforces.com/recent-actions) |\n|  | --------------------------------------------------- |\n\n* [nik\\_exists](https://codeforces.com/profile/nik%5Fexists)\n* [Blog](https://codeforces.com/blog/nik%5Fexists)\n* [Teams](https://codeforces.com/teams/with/nik%5Fexists)\n* [Submissions](https://codeforces.com/submissions/nik%5Fexists)\n* [Groups](https://codeforces.com/groups/with/nik%5Fexists)\n* [Contests](https://codeforces.com/contests/with/nik%5Fexists)\n* [Problemsetting](https://codeforces.com/contests/writer/nik%5Fexists)\n\n### [nik\\_exists's blog](https://codeforces.com/blog/nik%5Fexists)\n\n[ Codeforces Round 1119 (Div. 3) Editorial ](https://codeforces.com/blog/entry/156457) \n\nBy [nik\\_exists](https://codeforces.com/profile/nik%5Fexists \"Expert nik_exists\"), 12 days ago, ![In English](//codeforces.com/codeforces.org/s/21069/images/flags/24/gb.png \"In English\") \n\nThank y'all so much for participating!\n\n[2259A - Moo Language School](https://codeforces.com/contest/2259/problem/A \"Codeforces Round 1119 (Div. 3)\")\n\n**Solution**\n\nTutorial is loading...\n\n**Code**\n\n```\n#include <bits/stdc++.h>\nusing namespace std;\n\nint main() {\n    int t;\n    cin >> t;\n\n    while (t--) {\n        int n, k;\n        cin >> n >> k;\n\n        string s;\n        cin >> s;\n\n        int ans = 0;\n        for (int i = 0; i < n / k; i++) {\n            bool has_non_nhoj_farm = false;\n            for (int j = i * k; j < (i + 1) * k; j++) {\n                if (s[j] == '0') has_non_nhoj_farm = true;\n            }\n            ans += !has_non_nhoj_farm;\n        }\n\n        cout << ans << \"\\n\";\n    }\n}\n\n```\n\n**Difficulty**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too hard\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") A bit on the harder side\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good difficulty\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Easy\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too easy\n\n**Quality**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Amazing\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") So-so\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Bad\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Awful\n\n[2259B - Minus Two](https://codeforces.com/contest/2259/problem/B \"Codeforces Round 1119 (Div. 3)\")\n\n**Hint 1**\n\nWhen comparing two numbers that are initially not equal, the only way they can become equal after some number of operations is if at least one of them has an operation performed on it when it is $$$ \\\\lt 2$$$.\n\n**Hint 2**\n\nIf two elements are equal at some point, they'll be equal no matter how many more operations are performed. Therefore, it suffices to look at the end behavior of each element.\n\n**Solution**\n\nTutorial is loading...\n\n**Code**\n\n```\n#include <bits/stdc++.h>\nusing namespace std;\n \nint main() {\n    int t;\n    cin >> t;\n    \n    while (t--) {\n        int n;\n        cin >> n;\n        \n        vector<int> vec(n); for (auto &x: vec) cin >> x;\n        \n        int mod_4[] {0, 0, 0, 0};\n        for (auto &x: vec) mod_4[x%4]++;\n        cout << max({mod_4[0], mod_4[2], mod_4[1] + mod_4[3]}) << \"\\n\";\n    }\n}\n\n```\n\n**Difficulty**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too hard\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") A bit on the harder side\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good difficulty\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Easy\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too easy\n\n**Quality**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Amazing\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") So-so\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Bad\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Awful\n\n[2259C - 101](https://codeforces.com/contest/2259/problem/C \"Codeforces Round 1119 (Div. 3)\")\n\n**Hint 1**\n\nIf a $$$-1$$$ is in between two $$$1$$$s, it would only hurt the answer to make it a $$$1$$$.\n\n**Hint 2**\n\nIf a $$$-1$$$ is not in between two $$$1$$$ s, the $$$-1$$$ would only be included in a subarray satisfying the conditions if it was an endpoint.\n\n**Solution**\n\nTutorial is loading...\n\n**Code**\n\n```\n#include <bits/stdc++.h>\nusing namespace std;\n \nint main() {\n    int t;\n    cin >> t;\n    \n    while (t--) {\n        int n;\n        cin >> n;\n        \n        vector<int> vec(n); for (auto &x: vec) cin >> x;\n        \n        for (int i = 0; i < n; i++) {\n            if (vec[i] == -1) vec[i] = 1;\n            if (vec[i] == 1) break;\n        }\n        \n        for (int i = n-1; i >= 0; i--) {\n            if (vec[i] == -1) vec[i] = 1;\n            if (vec[i] == 1) break;\n        }\n        \n        \n        for (auto &x: vec) cout << max(x, 0) << \" \";\n        cout << \"\\n\";\n    }\n}\n\n```\n\n**Difficulty**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too hard\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") A bit on the harder side\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good difficulty\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Easy\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too easy\n\n**Quality**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Amazing\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") So-so\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Bad\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Awful\n\n[2259D - MEX Multiset](https://codeforces.com/contest/2259/problem/D \"Codeforces Round 1119 (Div. 3)\")\n\n**Hint 1**\n\nIf there is only one $$$0$$$ in the array, then exactly one set will have a mex greater than zero\n\n**Hint 2**\n\n$$$MEX(A) = MEX(B), MEX(C) = 0$$$ satisfies the constraints.\n\n**Solution**\n\nTutorial is loading...\n\n**Code**\n\n```\n#include <bits/stdc++.h>\nusing namespace std;\n \nint main() {\n    int t;\n    cin >> t;\n \n    while (t--) {\n        int n;\n        cin >> n;\n \n        vector<int> vec(n); for (auto &x: vec) cin >> x;\n        if (count(vec.begin(), vec.end(), 0) == 1) {\n            cout << \"NO\\n\";\n            continue;\n        }\n        cout << \"YES\\n\";\n        bool seen_zero = false;\n        for (int i = 0; i < n; i++) {\n            if (vec[i] != 0) cout << 'A';\n            else if (seen_zero) cout << 'B';\n            else {\n                seen_zero = true;\n                cout << 'C';\n            }\n        }\n        cout << \"\\n\";\n    }\n}\n\n```\n\n**Difficulty**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too hard\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") A bit on the harder side\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good difficulty\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Easy\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too easy\n\n**Quality**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Amazing\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") So-so\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Bad\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Awful\n\n[2259E - Treasure Map Destruction (Constructive Version)](https://codeforces.com/contest/2259/problem/E \"Codeforces Round 1119 (Div. 3)\")\n\n**Hint 1**\n\nIf an element $$$x$$$ at index $$$i$$$ is not equal to $$$-1$$$, there must be a treasure at either island $$$i + x$$$ or $$$i - x$$$\n\n**Hint 2**\n\nIf an element $$$x$$$ at index $$$i$$$ is not equal to $$$-1$$$, there must no treasures in the exclusive range of indices ($$$i + x$$$, $$$i - x$$$)\n\n**Solution**\n\nTutorial is loading...\n\n**Code**\n\n```\n#include <bits/stdc++.h>\nusing namespace std;\n#define ll long long\n \nint main() {\n    int t;\n    cin >> t;\n \n \n    while (t--) {\n        int n;\n        cin >> n;\n \n        vector<int> vec(n); for (auto &x: vec) cin >> x;\n \n        vector<int> diff(n+1);\n        for (int i = 0; i < n; i++) {\n            if (vec[i] > 0) {\n                diff[max(0, i-vec[i]+1)]++; \n                diff[min(n, i+vec[i])]--; \n            }\n        }\n        vector<bool> restricted(n);\n        int curr_count = 0;\n        for (int i = 0; i < n; i++) {\n            curr_count += diff[i];\n            restricted[i] = curr_count > 0;\n        }\n        bool possible = true;\n        for (int i = 0; i < n && possible; i++) {\n            if (vec[i] >= 0) {\n                if (i - vec[i] >= 0 && !restricted[i - vec[i]]) continue;\n                if (i + vec[i] < n && !restricted[i + vec[i]]) continue;\n                possible = false;\n            }\n        }\n \n        if (!possible) cout << -1 << \"\\n\";\n        else {\n            for (auto x: restricted) cout << !x;\n            cout << \"\\n\";\n        } \n    }\n}\n\n```\n\n**Difficulty**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too hard\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") A bit on the harder side\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good difficulty\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Easy\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too easy\n\n**Quality**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Amazing\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") So-so\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Bad\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Awful\n\n[2259F - Binary Bubble Sort Inversions](https://codeforces.com/contest/2259/problem/F \"Codeforces Round 1119 (Div. 3)\")\n\n**Hint 1**\n\nLook at performing some bubbles and reverse bubbles on small arrays. How many elements are moved?\n\n**Hint 2**\n\nA bubble will result is the leftmost 1 being moved all the way to the right. Similarly, a reverse bubble will result in the rightmost 0 being moved all the way to the left.\n\n**Hint 3**\n\nSince prefix zeroes and suffix ones don't matter, if we continuously remove them, then a bubble removes the last element of the array and a reverse bubble removes the first element of the array. Is there a way to remove the first and last elements of an array in constant time?\n\n**Solution**\n\nTutorial is loading...\n\n**Code**\n\n```\n#include <bits/stdc++.h>\nusing namespace std;\n \n#define ll long long\nint main() {\n    int t;\n    cin >> t;\n \n    while (t--) {\n        int n;\n        cin >> n;\n \n        vector<int> vec(n); for (auto &x: vec) cin >> x;\n        string s;\n        cin >> s;\n \n        ll inversions = 0;\n        int cnt_ones = 0;\n        for (int i = 0; i < n; i++) {\n            cnt_ones += vec[i];\n            if (vec[i] == 0) inversions += cnt_ones;\n        }\n        cout << inversions << \" \";\n        \n        deque<int> dq;\n        for (auto &x: vec) dq.push_back(x);\n        int cnt_zeroes = count(vec.begin(), vec.end(), 0);\n        for (int i = 0; i < n; i++) {\n            while (dq.size() > 0 && dq.front() == 0) {\n                dq.pop_front();\n                cnt_zeroes--;\n            }\n            while (dq.size() > 0 && dq.back() == 1) dq.pop_back();\n            if (dq.size() == 0) {\n                cout << 0 << \" \";\n                continue;\n            }\n            if (s[i] == '0') {\n                inversions -= (dq.size() - cnt_zeroes);\n                dq.pop_back();\n                cnt_zeroes--;\n            }\n            else {\n                inversions -= cnt_zeroes;\n                dq.pop_front();\n            }\n            cout << inversions << \" \";\n        }\n        cout << \"\\n\";\n    }\n}\n\n```\n\n**Difficulty**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too hard\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") A bit on the harder side\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good difficulty\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Easy\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too easy\n\n**Quality**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Amazing\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") So-so\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Bad\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Awful\n\n[2259G - Index Removal](https://codeforces.com/contest/2259/problem/G \"Codeforces Round 1119 (Div. 3)\") \n\n**Hint 1**\n\nIgnoring indexes 1 and $$$n$$$, if we remove index $$$i$$$, if we perform an operation on index $$$j$$$, all elements between $$$\\[i, j\\]$$$ will also have an operation performed on them.\n\n**Hint 2**\n\nIf we remove index $$$i$$$, and we have to reduce the element at index $$$i+1$$$, $$$i+2$$$, etc, what will we subtract it to?\n\n**Solution**\n\nTutorial is loading...\n\n**Code**\n\n```\n#include <bits/stdc++.h>\nusing namespace std;\n \n#define ll long long\nint main() {\n    int t;\n    cin >> t;\n \n    while (t--) {\n        ll n, k;\n        cin >> n >> k;\n \n        vector<ll> vec(n); for (auto &x: vec) cin >> x;\n        vector<ll> vec_2(n); for (int i = 0; i < n; i++) vec_2[i] = vec[i] - i * k;\n \n        vector<ll> prefix(n); prefix[0] = vec[0];\n        for (int i = 1; i < n; i++) prefix[i] = prefix[i-1] + vec[i];\n \n        vector<ll> ans(n);\n        for (int i = 1; i < n-1; i++) {\n            int lo = i+1;\n            int hi = n-1;\n            while (lo <= hi) {\n                int mid = lo + (hi - lo) / 2;\n                if (vec_2[mid] <= (vec[i-1] - i*k)) hi = mid - 1;\n                else lo = mid + 1;\n            }\n            \n            ll num_needed = (lo - i - 1);\n            ans[i] = (prefix[num_needed + i] - prefix[i]) - (k * (num_needed * (num_needed + 1))/2) - vec[i-1] * num_needed;\n        }\n        for (auto &x: ans) cout << x << \" \";\n        cout << \"\\n\";\n    }\n}\n\n```\n\n**Difficulty**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too hard\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") A bit on the harder side\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good difficulty\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Easy\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too easy\n\n**Quality**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Amazing\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") So-so\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Bad\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Awful\n\n[2259H - Treasure Map Destruction (Counting Version)](https://codeforces.com/contest/2259/problem/H \"Codeforces Round 1119 (Div. 3)\")\n\nRead the solution to problem E first\n\n**Hint 1**\n\nLet's consider all locations that we have not restricted: we can separate them into 3 categories: the position is forced to be a treasure, the position has no undestroyed that depend on it, and all other positions. \n\n**Hint 2**\n\nThe islands that are considered \"non-restricted\" form a chain of locations, with each non-restricted chain having a treasure between them. What must be true of the locations in this chain such that no condition is violated?\n\n**Hint 3**\n\nFor every pair of adjacent locations, there must be at least one treasure at one of those locations.\n\n**Solution**\n\nTutorial is loading...\n\n**Code**\n\n```\n#include <bits/stdc++.h>\nusing namespace std;\n#define ll long long\n \nconst ll MOD = 1000000007;\nconst int MAX_N = 200055;\nint main() {\n    int t;\n    cin >> t;\n \n \n    vector<ll> fibo(MAX_N);\n    fibo[1] = 1;\n    fibo[2] = 1;\n    for (int i = 3; i < MAX_N; i++) {\n        fibo[i] = (fibo[i-1] + fibo[i-2]) % MOD;\n    }\n \n    while (t--) {\n        int n;\n        cin >> n;\n \n        vector<int> vec(n); for (auto &x: vec) cin >> x;\n \n        vector<int> diff(n+1);\n        for (int i = 0; i < n; i++) {\n            if (vec[i] > 0) {\n                diff[max(0, i-vec[i]+1)]++; \n                diff[min(n, i+vec[i])]--; \n            }\n        }\n        \n        vector<bool> restricted(n);\n        vector<bool> forced(n);\n        vector<int> non_required;\n        int curr_count = 0;\n        for (int i = 0; i < n; i++) {\n            curr_count += diff[i];\n            restricted[i] = curr_count > 0;\n        }\n \n        bool possible = true;\n        for (int i = 0; i < n; i++) {\n            if (vec[i] != -1) {\n                int cnt = 0;\n                cnt += (i - vec[i] >= 0 && !restricted[i - vec[i]]); \n                cnt += (i + vec[i] < n && !restricted[i + vec[i]]);\n                if (cnt == 0) { possible = false;}\n                if (cnt == 1 || vec[i] == 0) {\n                    if (i + vec[i] < n) forced[i + vec[i]] = true;\n                    if (i - vec[i] >= 0) forced[i - vec[i]] = true;\n                }\n            }\n        }\n        for (int i = 0; i < n; i++) {\n            if (!restricted[i] && !forced[i]) non_required.push_back(i);\n        }\n        if (!possible) {\n            cout << 0 << \"\\n\";\n            continue;\n        }\n \n        ll total = 1;\n        int chain_len = 1;\n        for (int i = 0; i < non_required.size(); i++) {\n            bool cond1 = i == non_required.size() - 1 || vec[(non_required[i] + non_required[i+1])/2] == (non_required[i+1] - non_required[i])/2;\n            bool cond2 = i == non_required.size() - 1 || (non_required[i+1] - non_required[i]) % 2 == 0;\n            //if (i != 1) cout << (non_required[i+1] - non_required[i]) << \"\\n\";\n            if (i == non_required.size() - 1 || !cond1 || !cond2) {\n                //cout << chain_len << \"\\n\";\n                total *= fibo[chain_len+2];\n                total %= MOD;\n                chain_len = 1;\n            }\n            else chain_len++;\n        }\n        if (count(vec.begin(), vec.end(), -1) == n) {\n            total = (total + MOD - 1) % MOD;\n        }\n        cout << total << \"\\n\";\n    }\n}\n\n```\n\n**Difficulty**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too hard\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") A bit on the harder side\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good difficulty\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Easy\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too easy\n\n**Quality**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Amazing\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") So-so\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Bad\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Awful\n\n![](//codeforces.com/codeforces.org/s/21069/images/icons/paperclip-16x16.png) Tutorial of [Codeforces Round 1119 (Div. 3)](https://codeforces.com/contest/2259) \n\n* [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/voteup-gray.png \"Vote: I like it\")](#)\n* +202\n* [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/votedown-gray.png \"Vote: I do not like it\")](#)\n\n* [![Author](//codeforces.com/codeforces.org/s/21069/images/blog/user_16x16.png \"Author\")](https://codeforces.com/profile/nik%5Fexists) [nik\\_exists ](https://codeforces.com/profile/nik%5Fexists)\n* ![Publication date](//codeforces.com/codeforces.org/s/21069/images/blog/date_16x16.png \"Publication date\") 12 days ago\n* [![Comments](//codeforces.com/codeforces.org/s/21069/images/blog/comments_16x16.png \"Comments\")](https://codeforces.com/blog/entry/156457#comments) [118 ](https://codeforces.com/blog/entry/156457#comments)\n\n  \n![Comments](//codeforces.com/codeforces.org/s/21069/images/icons/comments-48x48.png \"Comments\") Comments (118) \n\n[Write comment?](#) \n\n| » [nik\\_exists](https://codeforces.com/profile/nik%5Fexists \"Expert nik_exists\") | 12 days ago, [show (+1)](#) # |\n| -------------------------------------------------------------------------------- | ----------------------------- |\n\n| » [ ![](https://codeforces.com/userpic.codeforces.org/no-avatar.jpg) ](https://codeforces.com/profile/nik%5Fexists) [nik\\_exists](https://codeforces.com/profile/nik%5Fexists \"Expert nik_exists\") | 12 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1390585 \"Link to comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) +8 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) _Auto comment: topic has been updated by [nik\\_exists](https://codeforces.com/profile/nik%5Fexists \"Expert nikexists\") ([previous revision](https://codeforces.com/topic/157099/en2), [new revision](https://codeforces.com/topic/157099/en3), [compare](https://codeforces.com/topic/157099/diff/en2/en3))._ [→](#) [Reply](#) |\n| -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n\n* | » » [wbw121124](https://codeforces.com/profile/wbw121124 \"Specialist wbw121124\") | 11 days ago, [show (+1)](#) # |\n| -------------------------------------------------------------------------------- | ----------------------------- |\n\n| » » [ ![](https://codeforces.com/userpic.codeforces.org/3260004/avatar/bfc5f8da6bb8c097.jpg) ](https://codeforces.com/profile/wbw121124) [wbw121124](https://codeforces.com/profile/wbw121124 \"Specialist wbw121124\") | 11 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1390753 \"Link to comment\") [^](#comment-1390585 \"Parent comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) +3 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) where are codesit only have cpp [→](#) [Reply](#) |\n| --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n\n  * | » » » [knkttp](https://codeforces.com/profile/knkttp \"Specialist knkttp\") | 11 days ago, [show](#) # |\n| ------------------------------------------------------------------------- | ------------------------ |\n\n| » » » [ ![](https://codeforces.com/userpic.codeforces.org/5193194/avatar/1319107b0a053e8e.jpg) ](https://codeforces.com/profile/knkttp) [knkttp](https://codeforces.com/profile/knkttp \"Specialist knkttp\") | 11 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1390760 \"Link to comment\") [^](#comment-1390753 \"Parent comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) 0 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) Wait until the hack end [→](#) [Reply](#) |\n| ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n  * | » » » [nik\\_exists](https://codeforces.com/profile/nik%5Fexists \"Expert nik_exists\") | 10 days ago, [show (+1)](#) # |\n| ------------------------------------------------------------------------------------ | ----------------------------- |\n\n| » » » [ ![](https://codeforces.com/userpic.codeforces.org/no-avatar.jpg) ](https://codeforces.com/profile/nik%5Fexists) [nik\\_exists](https://codeforces.com/profile/nik%5Fexists \"Expert nik_exists\") | 10 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1390952 \"Link to comment\") [^](#comment-1390753 \"Parent comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) 0 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) Code has been added! [→](#) [Reply](#) |\n| ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n\n    * | » » » » [wbw121124](https://codeforces.com/profile/wbw121124 \"Specialist wbw121124\") | 10 days ago, [show](#) # |\n| ------------------------------------------------------------------------------------ | ------------------------ |\n\n| » » » » [ ![](https://codeforces.com/userpic.codeforces.org/3260004/avatar/bfc5f8da6bb8c097.jpg) ](https://codeforces.com/profile/wbw121124) [wbw121124](https://codeforces.com/profile/wbw121124 \"Specialist wbw121124\") | 10 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1391001 \"Link to comment\") [^](#comment-1390952 \"Parent comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) 0 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) OK [→](#) [Reply](#) |\n| ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n\n| » [furqansuleymanli](https://codeforces.com/profile/furqansuleymanli \"Newbie furqansuleymanli\") | 12 days ago, [show (+1)](#) # |\n| ----------------------------------------------------------------------------------------------- | ----------------------------- |\n\n| » [ ![](https://codeforces.com/userpic.codeforces.org/5563911/avatar/f4984ba07dcb9e51.jpg) ](https://codeforces.com/profile/furqansuleymanli) [furqansuleymanli](https://codeforces.com/profile/furqansuleymanli \"Newbie furqansuleymanli\") | 12 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1390593 \"Link to comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) +2 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) good contest! [→](#) [Reply](#) |\n| ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n\n* | » » [nik\\_exists](https://codeforces.com/profile/nik%5Fexists \"Expert nik_exists\") | 12 days ago, [show](#) # |\n| ---------------------------------------------------------------------------------- | ------------------------ |\n\n| » » [ ![](https://codeforces.com/userpic.codeforces.org/no-avatar.jpg) ](https://codeforces.com/profile/nik%5Fexists) [nik\\_exists](https://codeforces.com/profile/nik%5Fexists \"Expert nik_exists\") | 12 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1390642 \"Link to comment\") [^](#comment-1390593 \"Parent comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) +7 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) tysm! [→](#) [Reply](#) |\n| ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |\n* | » » [dhiruuu\\_singh26](https://codeforces.com/profile/dhiruuu%5Fsingh26 \"Newbie dhiruuu_singh26\") | 11 days ago, [show](#) # |\n| ------------------------------------------------------------------------------------------------- | ------------------------ |\n\n| » » [ ![](https://codeforces.com/userpic.codeforces.org/4933574/avatar/bca47b478c630dee.jpg) ](https://codeforces.com/profile/dhiruuu%5Fsingh26) [dhiruuu\\_singh26](https://codeforces.com/profile/dhiruuu%5Fsingh26 \"Newbie dhiruuu_singh26\") | 11 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1390883 \"Link to comment\") [^](#comment-1390593 \"Parent comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) 0 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) TIGER! TIGER!........ [→](#) [Reply](#) |\n| ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n* | » » [While.1](https://codeforces.com/profile/While.1 \"Newbie While.1\") | 10 days ago, [show](#) # |\n| ---------------------------------------------------------------------- | ------------------------ |\n\n| » » [ ![](https://codeforces.com/userpic.codeforces.org/5072827/avatar/578ea0266e326443.jpg) ](https://codeforces.com/profile/While.1) [While.1](https://codeforces.com/profile/While.1 \"Newbie While.1\") | 10 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1390954 \"Link to comment\") [^](#comment-1390593 \"Parent comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) 0 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) felt that problem F was more trickier than problem G! [→](#) [Reply](#) |\n| --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n\n| » [why127pan](https://codeforces.com/profile/why127pan \"Newbie why127pan\") | 12 days ago, [show (+1)](#) # |\n| -------------------------------------------------------------------------- | ----------------------------- |\n\n| » [ ![](https://codeforces.com/userpic.codeforces.org/5327650/avatar/5df2e47dfbff541b.jpg) ](https://codeforces.com/profile/why127pan) [why127pan](https://codeforces.com/profile/why127pan \"Newbie why127pan\") | 12 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1390594 \"Link to comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) 0 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) nice round thanks ! [→](#) [Reply](#) |\n| --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n\n* | » » [nik\\_exists](https://codeforces.com/profile/nik%5Fexists \"Expert nik_exists\") | 12 days ago, [show](#) # |\n| ---------------------------------------------------------------------------------- | ------------------------ |\n\n| » » [ ![](https://codeforces.com/userpic.codeforces.org/no-avatar.jpg) ](https://codeforces.com/profile/nik%5Fexists) [nik\\_exists](https://codeforces.com/profile/nik%5Fexists \"Expert nik_exists\") | 12 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1390645 \"Link to comment\") [^](#comment-1390594 \"Parent comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) +6 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) tysm! [→](#) [Reply](#) |\n| ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |\n\n| » [megahertz13](https://codeforces.com/profile/megahertz13 \"Pupil megahertz13\") | 12 days ago, [show (+1)](#) # |\n| ------------------------------------------------------------------------------- | ----------------------------- |\n\n| » [ ![](https://codeforces.com/userpic.codeforces.org/2827759/avatar/2d153e90dd0538bd.jpg) ](https://codeforces.com/profile/megahertz13) [megahertz13](https://codeforces.com/profile/megahertz13 \"Pupil megahertz13\") | 12 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1390596 \"Link to comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) 0 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) good problems, C was kind of annoying to implement [→](#) [Reply](#) |\n\n...201282 bytes truncated...\n\nThe tool call succeeded but the output was truncated. Full output saved to: /Users/zayd/.local/share/opencode/tool-output/tool_0adf2e3c60016NgdBmO89z6SFs\nUse the Task tool to have explore agent process this file with Grep and Read (with offset/limit). Do NOT read the full file yourself - delegate to save context.",
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            {
              "order": 1,
              "content": "The farms are already fixed: split the string into consecutive, non-overlapping blocks of length $k$. You don't get to move the farm boundaries."
            },
            {
              "order": 2,
              "content": "Think about just one farm. Building more than one school there cannot help another farm, so one well-placed school is enough."
            },
            {
              "order": 3,
              "content": "If a farm contains even one `0`, where should you put its school? How many schools on Nhoj's land does that farm require?"
            },
            {
              "order": 4,
              "content": "A farm forces you to use Nhoj's land only when all $k$ of its characters are `1`. Even then, you only need one school, so its contribution is $1$, not $k$."
            },
            {
              "order": 5,
              "content": "Count the blocks that contain no `0`. Iterate over starting indices $0,k,2k,\\ldots,n-k$, inspect the next $k$ characters, and add $1$ if they are all `1`. The blocks are independent, so these contributions simply add up."
            }
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          "editorial": "The answer is **the number of farms whose fields are all owned by Nhoj**. One available `0` saves an entire farm from paying him. Tough day for the landlord.\n\n### Why each farm is independent\n\nEvery field belongs to exactly one farm, and every farm needs its own school. A school in one farm cannot satisfy the requirement for another.\n\nIt is enough to build exactly one school per farm: extra schools cannot improve coverage elsewhere or reduce the number built on Nhoj's land.\n\nFor a single block of $k$ fields:\n\n- **It contains a `0`:** build on that field. This farm contributes $0$ to the answer.\n- **It contains only `1`s:** every possible location belongs to Nhoj. We must build on his land at least once, and one school is enough. This farm contributes $1$.\n\nSo we count all-`1` farm blocks, not individual `1`s or arbitrary runs of `1`s. Farm boundaries matter.\n\n### Algorithm\n\nFor each test case:\n\n1. Set `answer = 0`.\n2. Visit block starts `start = 0, k, 2*k, ...` while `start < n`.\n3. Set `allOne = true`, then inspect indices from `start` through `start + k - 1`. If any character is `'0'`, set `allOne = false`.\n4. If `allOne` is still true, increment `answer`.\n5. Print `answer`.\n\nBecause $n$ is divisible by $k$, every block has exactly $k$ characters; there is no leftover block to handle. Reset the flag for every farm, and compare characters with `'0'`, not the integer `0`.\n\nFor example, with $n=8$, $k=2$, and `s = 10011100`, the farms are:\n\n```text\n10 | 01 | 11 | 00\n```\n\nOnly `11` forces a school onto Nhoj's land, so the answer is $1$.\n\n### Correctness proof\n\nLet $A$ be the number of all-`1` farm blocks.\n\n**Lower bound:** Each of these $A$ farms needs a school, and every field in it belongs to Nhoj. Since the farms are disjoint, every valid arrangement must contain at least $A$ schools on his land.\n\n**Achievability:** In each all-`1` farm, build exactly one school on any field. In every other farm, build exactly one school on a field marked `0`. This satisfies every farm and builds exactly $A$ schools on Nhoj's land.\n\nThe minimum is therefore exactly $A$, which the algorithm outputs.\n\n### Complexity\n\nThere are $n/k$ blocks, and we inspect $k$ characters in each, so the time is $O(n)$ per test case. The nested loops do not make this quadratic: each character is inspected once.\n\nThe algorithm uses $O(1)$ auxiliary space, or $O(n)$ total space including the input string.\n\n### Edge cases\n\n- If $k=1$, each field is a farm, so the answer is the number of `1`s.\n- If $k=n$, there is one farm: the answer is $1$ only if the entire string is `1`s.\n- An all-zero string gives $0$; an all-one string gives $n/k$.",
          "solution": "#include <bits/stdc++.h>\nusing namespace std;\n\nusing ll = long long;\n\nvoid setIO() {\n    ios::sync_with_stdio(false);\n    cin.tie(nullptr);\n}\n\nint main() {\n    setIO();\n\n    int t;\n    cin >> t;\n    while (t--) {\n        int n, k;\n        string s;\n        cin >> n >> k >> s;\n\n        int answer = 0;\n        for (int start = 0; start < n; start += k) {\n            bool allOne = true;\n            for (int j = start; j < start + k; ++j) {\n                if (s[j] == '0') allOne = false;\n            }\n            if (allOne) ++answer;\n        }\n\n        cout << answer << '\\n';\n    }\n}\n"
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          "text": "**Verifying mental samples**",
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              "hints": [
                {
                  "order": 1,
                  "content": "The farms are already fixed: split the string into consecutive, non-overlapping blocks of length $k$. You don't get to move the farm boundaries."
                },
                {
                  "order": 2,
                  "content": "Think about just one farm. Building more than one school there cannot help another farm, so one well-placed school is enough."
                },
                {
                  "order": 3,
                  "content": "If a farm contains even one `0`, where should you put its school? How many schools on Nhoj's land does that farm require?"
                },
                {
                  "order": 4,
                  "content": "A farm forces you to use Nhoj's land only when all $k$ of its characters are `1`. Even then, you only need one school, so its contribution is $1$, not $k$."
                },
                {
                  "order": 5,
                  "content": "Count the blocks that contain no `0`. Iterate over starting indices $0,k,2k,\\ldots,n-k$, inspect the next $k$ characters, and add $1$ if they are all `1`. The blocks are independent, so these contributions simply add up."
                }
              ],
              "editorial": "The answer is **the number of farms whose fields are all owned by Nhoj**. One available `0` saves an entire farm from paying him. Tough day for the landlord.\n\n### Why each farm is independent\n\nEvery field belongs to exactly one farm, and every farm needs its own school. A school in one farm cannot satisfy the requirement for another.\n\nIt is enough to build exactly one school per farm: extra schools cannot improve coverage elsewhere or reduce the number built on Nhoj's land.\n\nFor a single block of $k$ fields:\n\n- **It contains a `0`:** build on that field. This farm contributes $0$ to the answer.\n- **It contains only `1`s:** every possible location belongs to Nhoj. We must build on his land at least once, and one school is enough. This farm contributes $1$.\n\nSo we count all-`1` farm blocks, not individual `1`s or arbitrary runs of `1`s. Farm boundaries matter.\n\n### Algorithm\n\nFor each test case:\n\n1. Set `answer = 0`.\n2. Visit block starts `start = 0, k, 2*k, ...` while `start < n`.\n3. Set `allOne = true`, then inspect indices from `start` through `start + k - 1`. If any character is `'0'`, set `allOne = false`.\n4. If `allOne` is still true, increment `answer`.\n5. Print `answer`.\n\nBecause $n$ is divisible by $k$, every block has exactly $k$ characters; there is no leftover block to handle. Reset the flag for every farm, and compare characters with `'0'`, not the integer `0`.\n\nFor example, with $n=8$, $k=2$, and `s = 10011100`, the farms are:\n\n```text\n10 | 01 | 11 | 00\n```\n\nOnly `11` forces a school onto Nhoj's land, so the answer is $1$.\n\n### Correctness proof\n\nLet $A$ be the number of all-`1` farm blocks.\n\n**Lower bound:** Each of these $A$ farms needs a school, and every field in it belongs to Nhoj. Since the farms are disjoint, every valid arrangement must contain at least $A$ schools on his land.\n\n**Achievability:** In each all-`1` farm, build exactly one school on any field. In every other farm, build exactly one school on a field marked `0`. This satisfies every farm and builds exactly $A$ schools on Nhoj's land.\n\nThe minimum is therefore exactly $A$, which the algorithm outputs.\n\n### Complexity\n\nThere are $n/k$ blocks, and we inspect $k$ characters in each, so the time is $O(n)$ per test case. The nested loops do not make this quadratic: each character is inspected once.\n\nThe algorithm uses $O(1)$ auxiliary space, or $O(n)$ total space including the input string.\n\n### Edge cases\n\n- If $k=1$, each field is a farm, so the answer is the number of `1`s.\n- If $k=n$, there is one farm: the answer is $1$ only if the entire string is `1`s.\n- An all-zero string gives $0$; an all-one string gives $n/k$.",
              "solution": "#include <bits/stdc++.h>\nusing namespace std;\n\nusing ll = long long;\n\nvoid setIO() {\n    ios::sync_with_stdio(false);\n    cin.tie(nullptr);\n}\n\nint main() {\n    setIO();\n\n    int t;\n    cin >> t;\n    while (t--) {\n        int n, k;\n        string s;\n        cin >> n >> k >> s;\n\n        int answer = 0;\n        for (int start = 0; start < n; start += k) {\n            bool allOne = true;\n            for (int j = start; j < start + k; ++j) {\n                if (s[j] == '0') allOne = false;\n            }\n            if (allOne) ++answer;\n        }\n\n        cout << answer << '\\n';\n    }\n}\n"
            },
            "output": "Structured output captured successfully.",
            "metadata": {
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            "title": "Structured Output",
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