We call a bitstring$$$^{\text{∗}}$$$ perfect if it has the same number of $$$\mathtt{101}$$$ and $$$\mathtt{010}$$$ subsequences$$$^{\text{†}}$$$. Construct a perfect bitstring of length $$$n$$$ where the number of $$$\mathtt{1}$$$ characters it contains is exactly $$$k$$$.
It can be proven that the construction is always possible. If there are multiple solutions, output any of them.
$$$^{\text{∗}}$$$A bitstring is a string consisting only of the characters $$$\mathtt{0}$$$ and $$$\mathtt{1}$$$.
$$$^{\text{†}}$$$A sequence $$$a$$$ is a subsequence of a string $$$b$$$ if $$$a$$$ can be obtained from $$$b$$$ by the deletion of several (possibly zero or all) characters.
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 500$$$). The description of the test cases follows.
The first line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 100$$$, $$$0 \le k \le n$$$) — the size of the bitstring and the number of $$$\mathtt{1}$$$ characters in the bitstring.
For each test case, output the constructed bitstring. If there are multiple solutions, output any of them.
54 25 35 56 21 1
1010 10110 11111 100010 1
In the first test case, the number of $$$\mathtt{101}$$$ and $$$\mathtt{010}$$$ subsequences is the same, both being $$$1$$$, and the sequence contains exactly two $$$\mathtt{1}$$$ characters.
In the second test case, the number of $$$\mathtt{101}$$$ and $$$\mathtt{010}$$$ subsequences is the same, both being $$$2$$$, and the sequence contains exactly three $$$\mathtt{1}$$$ characters.
In the third test case, the number of $$$\mathtt{101}$$$ and $$$\mathtt{010}$$$ subsequences is the same, both being $$$0$$$, and the sequence contains exactly five $$$\mathtt{1}$$$ characters.
| Codeforces Round 1030 (Div. 2) |
|---|
| Finished |
