You are given two integers $$$n$$$ and $$$k$$$.
Construct a binary string$$$^{\\text{∗}}$$$ $$$s$$$ of length $$$n$$$, such that both of the following conditions hold:
Or determine that no such string exists.
$$$^{\\text{∗}}$$$A binary string is a string where each character is either $$$\\mathtt{0}$$$ or $$$\\mathtt{1}$$$.
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \\le t \\le 1000$$$). The description of the test cases follows.
The only line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$2 \\le n \\le 2 \\cdot 10^5$$$, $$$0 \\le k \\le n-1$$$).
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \\cdot 10^5$$$.
For each test case, output a binary string $$$s$$$ of length $$$n$$$ — the string you constructed. Print $$$-1$$$ if such a string does not exist.
If there are multiple answers, you may output any of them.
85 24 36 15 07 34 23 27 4
01110-11010010101001000110011-10111000
In the first test case, one possible answer is $$$s=\\mathtt{01110}$$$. It contains three characters $$$\\mathtt{1}$$$ and two characters $$$\\mathtt{0}$$$, and there are exactly $$$2$$$ adjacent equal pairs in $$$s$$$: $$$(s_2, s_3)$$$ and $$$(s_3, s_4)$$$.
In the second test case, $$$k=n-1$$$. All characters in $$$s$$$ should be equal, so the numbers of characters $$$\\mathtt{0}$$$ and $$$\\mathtt{1}$$$ could not differ by at most $$$1$$$. Thus, the answer is $$$-1$$$.
In the third test case, note that $$$\\mathtt{010110}$$$ is also a possible answer.