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;
void dbg_out() { cerr << endl; }
template <typename Head, typename... Tail>
void dbg_out(Head H, Tail... T) {
  cout << ' ' << H;
  dbg_out(T...);
}
void run_case() {
  string S;
  int X;
  cin >> S >> X;
  int N = int(S.size());
  string W(N, '1');
  for (int i = 0; i < N; i++)
    if (S[i] == '0') {
      if (i - X >= 0) W[i - X] = '0';
      if (i + X < N) W[i + X] = '0';
    }
  for (int i = 0; i < N; i++) {
    bool one = false;
    one = one || (i - X >= 0 && W[i - X] == '1');
    one = one || (i + X < N && W[i + X] == '1');
    if (S[i] != one + '0') {
      cout << -1 << '\n';
      return;
    }
  }
  cout << W << '\n';
}
int main() {
  int t;
  cin >> t;
  while (t--) {
    run_case();
  }
}
