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;
template <typename P, typename Q>
P CeilDiv(P _dividend, Q _divider) {
  return static_cast<P>((_dividend - 1LL + _divider) / _divider);
}
template <typename Tp>
inline void outarr(Tp _begin, Tp _end, const char* _delim = " ") {
  for (Tp current = _begin; current != _end; ++current) {
    std::cout << *current << _delim;
  }
  std::cout << '\n';
}
using ll = long long;
using pii = std::pair<int, int>;
constexpr int INF = 0x3f3f3f3f;
constexpr int MOD = static_cast<const int>(1e9 + 7);
string Gen(const string& s, int x) {
  string res(static_cast<int>((s).size()), '0');
  for (int i = 0; i < (static_cast<int>((s).size())); ++i) {
    if (i - x >= 0 && s[i - x] == '1') {
      res[i] = '1';
    }
    if (i + x < static_cast<int>((s).size()) && s[i + x] == '1') {
      res[i] = '1';
    }
  }
  return res;
}
int main() {
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(nullptr);
  int test_cases;
  cin >> test_cases;
  while (test_cases--) {
    string s;
    int x;
    cin >> s >> x;
    string ans(static_cast<int>((s).size()), '1');
    for (int i = 0; i < (static_cast<int>((s).size())); ++i) {
      if (s[i] == '1') {
        continue;
      }
      if (i - x >= 0) {
        ans[i - x] = '0';
      }
      if (i + x < static_cast<int>((s).size())) {
        ans[i + x] = '0';
      }
    }
    if (s != Gen(ans, x)) {
      cout << -1 << "\n";
    } else {
      cout << ans << "\n";
    }
  }
  return 0;
}
