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;
const int maxn = 1e6 + 1000;
int str[maxn];
string w;
int x;
int main() {
  int T;
  cin >> T;
  while (T--) {
    cin >> w;
    cin >> x;
    int len = w.length();
    for (int i = 0; i < len; i++) {
      str[i] = -1;
    }
    for (int i = 0; i < len; i++) {
      if (w[i] == '0') {
        if (i + x < len) {
          str[i + x] = 0;
        }
        if (i - x >= 0) {
          str[i - x] = 0;
        }
      }
    }
    int flag = 1;
    for (int i = 0; i < len; i++) {
      if (w[i] == '1') {
        if (i + x < len && i - x >= 0) {
          if (str[i + x] == 0 && str[i - x] == 0) {
            flag = 0;
            break;
          }
          if (str[i + x] != 0) {
            str[i + x] = 1;
          }
          if (str[i - x] != 0) {
            str[i - x] = 1;
          }
        } else if (i + x >= len && i - x >= 0) {
          if (str[i - x] == 0) {
            flag = 0;
            break;
          }
          if (str[i - x] != 0) {
            str[i - x] = 1;
          }
        } else if (i + x < len && i - x < 0) {
          if (str[i + x] == 0) {
            flag = 0;
            break;
          }
          if (str[i + x] != 0) {
            str[i + x] = 1;
          }
        } else if (i + x >= len && i - x < 0) {
          flag = 0;
        }
      }
    }
    for (int i = 0; i < len; i++) {
      if (str[i] == -1) {
        str[i] = 0;
      }
    }
    if (flag) {
      for (int i = 0; i < len; i++) {
        cout << str[i];
      }
      printf("\n");
    } else {
      printf("-1\n");
    }
  }
  return 0;
}
