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() {
  int t;
  int x;
  int n;
  string s;
  cin >> t;
  while (t--) {
    cin >> s;
    cin >> x;
    n = s.length();
    vector<char> ans(n, '1');
    vector<int> depended(n, -1);
    int flag;
    for (int i = 0; i < n; i++) {
      if (s[i] == '1') {
        flag = 1;
        if (i >= x) {
          if ((depended[i - x] == -1 || depended[i - x] == 1)) {
            flag = 0;
            depended[i - x] = 1;
          } else {
            flag = 1;
          }
        } else if (flag == 1) {
          if (i + x < n) {
            if ((depended[i + x] == -1 || depended[i + x] == 1)) {
              flag = 0;
              depended[i + x] = 1;
            }
          }
        }
      } else if (s[i] == '0') {
        int flag1 = 0, flag2 = 0;
        if (i - x >= 0) {
          if (depended[i - x] == -1 || depended[i - x] == 0) {
            depended[i - x] = 0;
            flag1 = 0;
            ans[i - x] = '0';
          }
        }
        if (i + x < n) {
          if (depended[i + x] == -1 || depended[i + x] == 0) {
            depended[i + x] = 0;
            flag2 = 0;
            ans[i + x] = '0';
          }
        }
      }
    }
    string temp;
    for (int i = 0; i < n; i++) {
      int flag = 1;
      if (i + x < n) {
        if (ans[i + x] == '1') {
          temp = temp + '1';
          flag = 0;
        }
      }
      if (flag == 1) {
        if (i - x >= 0) {
          if (ans[i - x] == '1') {
            temp = temp + '1';
            flag = 0;
          }
        }
      }
      if (flag == 1) {
        temp = temp + '0';
      }
    }
    if (temp == s) {
      for (int i = 0; i < n; i++) {
        cout << ans[i];
      }
      cout << endl;
    } else {
      cout << -1 << endl;
    }
  }
}
