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 find(string s, int x) {
  int i;
  string st;
  for (i = 0; i < s.length(); i++) {
    if (i - x >= 0 && s[i - x] == '1')
      st.push_back('1');
    else if (i + x < s.length() && s[i + x] == '1')
      st.push_back('1');
    else
      st.push_back('0');
  }
  return st;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t, i, x, k;
  string str;
  cin >> t;
  while (t--) {
    cin >> str;
    cin >> x;
    string str1;
    for (i = 0; i < str.length(); i++) str1.push_back('1');
    for (i = 0; i < str.length(); i++) {
      if (str[i] == '0') {
        if (i - x >= 0) str1[i - x] = '0';
        if (i + x < str.length()) str1[i + x] = '0';
      }
    }
    for (i = 0; i < str.length(); i++) {
      if (str[i] == '0') {
        if (i - x >= 0 && str1[i - x] == '1') {
          break;
        }
        if (i + x < str1.length() && str1[i + x] == '1') break;
      } else {
        if (i - x >= 0 && str1[i - x] == '1') continue;
        if (i + x < str1.length() && str1[i + x] == '1')
          continue;
        else
          break;
      }
    }
    if (i != str.length())
      cout << -1 << '\n';
    else
      cout << str1 << '\n';
  }
}
