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;
const int mod = (int)1000000000 + 7;
const int MOD = (int)998244353;
const int INF = (int)1e18;
bool cmp(const pair<int, int>& a, const pair<int, int>& b) {
  return a.second - a.first < b.second - b.first;
}
long long bit_ct1(long long x) {
  long long ct = 0;
  while (x > 0) {
    x = x & (x - 1);
    ct++;
  }
  return ct;
}
long long cc[27] = {0};
void solve() {
  string s;
  long long p;
  cin >> s >> p;
  long long ln = s.length();
  vector<char> w(ln), ans(ln);
  for (long long i = 0; i < ln; i++) {
    w[i] = '1';
  }
  for (long long i = 0; i < ln; i++) {
    if (s[i] == '0') {
      if (i - p >= 0) w[i - p] = '0';
      if (i + p < ln) w[i + p] = '0';
    }
  }
  for (long long i = 0; i < ln; i++) {
    if (i + p < ln && w[i + p] == '1') {
      ans[i] = '1';
    } else if (i - p >= 0 && w[i - p] == '1') {
      ans[i] = '1';
    } else {
      ans[i] = '0';
    }
  }
  for (long long i = 0; i < ln; i++) {
    if (s[i] != ans[i]) {
      cout << -1 << '\n';
      return;
    }
  }
  for (long long i = 0; i < ln; i++) {
    cout << w[i];
  }
  cout << '\n';
  return;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
  clock_t timest = clock();
  cerr << "[Executes in " << (double)(clock() - timest) / CLOCKS_PER_SEC << "s]"
       << '\n';
}
