C. Binary String Reconstructiontime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputConsider 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.InputThe 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.OutputFor 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. ExampleInput
3
101110
2
01
1
110
1
Output
111011
10
-1

3
101110
2
01
1
110
1

111011 10 -1 
['2-sat', 'brute force', 'constructive algorithms', 'greedy', '*1500']