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;
long long q, n, x, w[100005];
char s[100005];
signed main() {
  cin >> q;
  while (q--) {
    scanf("%s%lld", s + 1, &x);
    n = strlen(s + 1);
    for (long long i = 1; i <= n; w[i] = -1, i++)
      ;
    for (long long i = 1; i <= n; i++)
      if (s[i] == '0') {
        if (i - x >= 1) w[i - x] = 0;
        if (i + x <= n) w[i + x] = 0;
      }
    bool flag = true;
    for (long long i = 1; i <= n; i++)
      if (s[i] == '1') {
        bool f = false;
        if (i - x >= 1 && (w[i - x] == 1 || w[i - x] == -1))
          w[i - x] = 1, f = true;
        else if (i + x <= n && (w[i + x] == 1 || w[i + x] == -1))
          w[i + x] = 1, f = true;
        if (!f) {
          flag = false;
          break;
        }
      }
    if (!flag) {
      puts("-1");
      continue;
    }
    for (long long i = 1; i <= n; i++)
      if (w[i] == -1)
        cout << 1;
      else
        cout << w[i];
    puts("");
  }
  return 0;
}
