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;
int MOD = 1e9 + 7;
long long int power(long long int a, long long int b) {
  long long int res = 1;
  a = a % MOD;
  while (b > 0) {
    if (b & 1) {
      res = (res * a) % MOD;
      b--;
    }
    a = (a * a) % MOD;
    b >>= 1;
  }
  return res;
}
long long int fermat_inv(long long int y) { return power(y, MOD - 2); }
long long int gcd(long long int a, long long int b) {
  return (b == 0) ? a : gcd(b, a % b);
}
long long int min(long long int a, long long int b) { return (a > b) ? b : a; }
long long int max(long long int a, long long int b) { return (a > b) ? a : b; }
bool prime[1000001];
vector<int> primes;
void SieveOfEratosthenes(int n) {
  memset(prime, true, sizeof(prime));
  for (int p = 2; p * p <= n; p++) {
    if (prime[p] == true) {
      for (int i = p * p; i <= n; i += p) prime[i] = false;
    }
  }
  for (int p = 2; p < 1000001; p++)
    if (prime[p]) primes.push_back(p);
}
long long int fact[1001];
void factorial(int n) {
  fact[0] = 1;
  for (int i = 1; i <= n; i++) fact[i] = fact[i - 1] * i, fact[i] %= MOD;
}
long long int ncr(long long int n, long long int r) {
  if (n < r)
    return -1;
  else {
    long long int x = fact[r] * fact[n - r] % MOD;
    return fact[n] * fermat_inv(x) % MOD;
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t = 1;
  cin >> t;
  while (t--) {
    string s;
    int x;
    cin >> s >> x;
    int n = s.size();
    string ans = "";
    for (int i = 0; i < n; i++) ans += '1';
    for (int i = 0; i < n; i++) {
      if (s[i] == '1') continue;
      if (i + x < n) ans[i + x] = '0';
      if (i - x >= 0) ans[i - x] = '0';
    }
    bool b = true;
    for (int i = 0; i < n; i++) {
      if (s[i] == '0') continue;
      bool c = false;
      if (i + x < n && ans[i + x] == '1') c = true;
      if (i - x >= 0 && ans[i - x] == '1') c = true;
      if (!c) b = false;
    }
    if (b)
      cout << ans << '\n';
    else
      cout << "-1\n";
  }
}
