CF2118A Equal Subsequences

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.

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.