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;
string check(const string &s, long long int x) {
  string z;
  for (long long int i = 0; i < s.length(); i++) {
    bool flag1 = false, flag2 = false;
    if (i - x >= 0 && s[i - x] == '1') {
      flag1 = true;
    }
    if (i + x <= s.length() - 1 && s[i + x] == '1') {
      flag2 = true;
    }
    if (flag1 || flag2) {
      z += '1';
    } else {
      z += '0';
    }
  }
  return z;
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long int t;
  cin >> t;
  while (t--) {
    string s;
    long long int x;
    cin >> s >> x;
    char arr[s.length()];
    for (long long int i = 0; i < s.length(); i++) {
      arr[i] = '@';
    }
    bool flag = false;
    for (long long int i = 0; i < s.length(); i++) {
      if (s[i] == '0') {
        if (i + x < s.length()) {
          if (arr[i + x] == '@' || arr[i + x] == '0') {
            arr[i + x] = '0';
          } else {
            flag = true;
            break;
          }
        }
        if (i - x >= 0) {
          if (arr[i - x] == '@' || arr[i - x] == '0') {
            arr[i - x] = '0';
          } else {
            flag = true;
            break;
          }
        }
      }
    }
    for (long long int i = s.length() - 1; i >= 0; i--) {
      if (s[i] == '0') {
        if (i + x < s.length()) {
          if (arr[i + x] == '@' || arr[i + x] == '0') {
            arr[i + x] = '0';
          } else {
            flag = true;
            break;
          }
        }
        if (i - x >= 0) {
          if (arr[i - x] == '@' || arr[i - x] == '0') {
            arr[i - x] = '0';
          } else {
            flag = true;
            break;
          }
        }
      }
    }
    if (flag) {
      cout << -1;
      continue;
    }
    for (long long int i = 0; i < s.length(); i++) {
      if (arr[i] == '@') {
        arr[i] = '1';
      }
    }
    string z;
    for (long long int i = 0; i < s.length(); i++) {
      z += arr[i];
    }
    if (check(z, x) == s) {
      cout << z << '\n';
    } else {
      cout << -1 << '\n';
    }
  }
  return 0;
}
