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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t;
  cin >> t;
  while (t--) {
    int x;
    string s;
    cin >> s >> x;
    int n = s.length();
    char w[n + 2];
    for (int i = 0; i < n + 2; i++) {
      w[i] = '@';
    }
    bool canchange[n + 2];
    for (int i = 0; i < n + 2; i++) {
      canchange[i] = true;
    }
    int i;
    for (i = 0; i < n; i++) {
      if (i - x < 0 && i + x >= n) {
        if (s[i] == '1') {
          break;
        }
        continue;
      } else if (i - x < 0) {
        if (!canchange[i + x] && (w[i + x] != '@' && w[i + x] != s[i])) {
          break;
        }
        w[i + x] = s[i];
        canchange[i + x] = false;
      } else if (i + x >= n) {
        if (!canchange[i - x] && (w[i - x] != '@' && w[i - x] != s[i])) {
          break;
        }
        w[i - x] = s[i];
        canchange[i - x] = false;
      } else {
        if (s[i] == '1') {
          if (w[i - x] == '@') {
            w[i - x] = '1';
            canchange[i - x] = false;
          } else if (w[i - x] == '0') {
            if (!canchange[i - x]) {
              if (!canchange[i + x] && w[i + x] == '0') {
                break;
              }
              w[i + x] = '1';
              canchange[i + x] = false;
            } else {
              w[i - x] = '1';
              canchange[i - x] = false;
              w[i + x] = '0';
            }
          } else {
            w[i + x] = '0';
          }
        } else {
          if (w[i - x] != '0') {
            if (!canchange[i - x]) {
              break;
            } else {
              w[i - x] = '0';
              canchange[i - x] = false;
            }
          }
          if (w[i + x] != '0') {
            if (!canchange[i + x]) {
              break;
            } else {
              w[i + x] = '0';
              canchange[i + x] = false;
            }
          }
        }
      }
    }
    if (i < n) {
      cout << -1 << endl;
      continue;
    }
    for (i = 0; i < n; i++) {
      if (w[i] != '@') {
        cout << w[i];
      } else {
        cout << '1';
      }
    }
    cout << endl;
  }
}
