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>
const long long int mod = 1e9 + 7;
using namespace std;
long long int power(long long int x, long long int y, long long int p) {
  long long int res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
long long int imod(long long int a, long long int m) {
  return power(a, m - 2, m);
}
void myfun() {
  long long int n, x, ans = 1, i, cn;
  string s;
  cin >> s;
  cin >> x;
  n = s.length();
  long long int arr[n];
  for (i = 0; i < n; i++) arr[i] = 1;
  for (i = 0; i < n; i++) {
    if (s[i] == '0') {
      if (i - x >= 0) arr[i - x] = 0;
      if (i + x < n) arr[i + x] = 0;
    }
  }
  for (i = 0; i < n; i++) {
    cn = 0;
    if (s[i] == '1') {
      if (((i - x) >= 0) && ((i + x) < n)) {
        if (arr[i - x] != 1 && arr[i + x] != 1) ans = 0;
      } else if ((i - x) >= 0) {
        if (arr[i - x] == 0) ans = false;
      } else if ((i + x) < n) {
        if (arr[i + x] == 0) ans = false;
      } else
        ans = false;
    }
  }
  if (ans) {
    for (i = 0; i < n; i++) cout << arr[i];
    cout << "\n";
  } else
    cout << "-1\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  ;
  long long int t = 1;
  cin >> t;
  while (t--) myfun();
  return 0;
}
