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 ≤ 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.

Input

The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases.

Each test case consists of two lines. The first line contains the resulting string s (2 ≤ |s| ≤ 10^5, each character of s is either 0 or 1). The second line contains one integer x (1 ≤ x ≤ |s| - 1).

The total length of all strings s in the input does not exceed 10^5.

Output

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. 

Example

Input


3
101110
2
01
1
110
1


Output


111011
10
-1
#include <bits/stdc++.h>
using namespace std;
int main() {
  long t;
  scanf("%ld", &t);
  while (t--) {
    int x, i, n;
    string w, s;
    cin >> s >> x;
    n = s.length();
    w = string(n, '1');
    for (i = 0; i < n; i++) {
      if (s[i] == '0') {
        if (i - x >= 0) w[i - x] = '0';
        if (i + x < n) w[i + x] = '0';
      }
    }
    for (i = 0; i < n; i++) {
      if ((i - x >= 0 && w[i - x] == '1') || (i + x < n && w[i + x] == '1')) {
        if (s[i] != '1') break;
      } else if (s[i] != '0')
        break;
    }
    if (i < n)
      cout << -1;
    else
      cout << w;
    cout << endl;
  }
  return 0;
}
