C. Binary String Reconstruction
2-sat; brute force; constructive algorithms; greedy
Consider the following process. You have a binary string (a string where each character is either 0 or 1) \(w\) of length \(n\) and an integer \(x\). You build a new binary string \(s\) consisting of \(n\) characters. The \(i\)-th character of \(s\) is chosen as follows: if the character \(w_{i-x}\) exists and is equal to 1, then \(s_i\) is 1 (formally, if \(i > x\) and \(w_{i-x} = \) 1, then \(s_i = \) 1); if the character \(w_{i+x}\) exists and is equal to 1, then \(s_i\) is 1 (formally, if \(i + x \le n\) and \(w_{i+x} = \) 1, then \(s_i = \) 1); if both of the aforementioned conditions are false, then \(s_i\) is 0. You are given the integer \(x\) and the resulting string \(s\). Reconstruct the original string \(w\).
The first line contains one integer \(t\) (\(1 \le t \le 1000\)) — the number of test cases.Each test case consists of two lines. The first line contains the resulting string \(s\) (\(2 \le |s| \le 10^5\), each character of \(s\) is either 0 or 1). The second line contains one integer \(x\) (\(1 \le x \le |s| - 1\)).The total length of all strings \(s\) in the input does not exceed \(10^5\).
For each test case, print the answer on a separate line as follows: if no string \(w\) can produce the string \(s\) at the end of the process, print \(-1\); otherwise, print the binary string \(w\) consisting of \(|s|\) characters. If there are multiple answers, print any of them.