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 T>
inline void MAX(T &x) {
  x = std::numeric_limits<T>::max();
}
template <typename T>
inline void MIN(T &x) {
  x = std::numeric_limits<T>::min();
}
inline int cset(const int x) { return __builtin_popcount(x); }
inline int cset(const long long x) { return __builtin_popcountll(x); }
inline int cset(const unsigned long long x) { return __builtin_popcountll(x); }
using namespace std;
template <class c>
struct rge {
  c b, e;
};
template <class c>
rge<c> range(c i, c j) {
  return rge<c>{i, j};
}
template <class c>
auto dud(c *x) -> decltype(cout << *x, 0);
template <class c>
char dud(...);
struct debug {
  ~debug() { cout << '\n'; }
  template <class c>
  typename enable_if<sizeof dud<c>(0) != 1, debug &>::type operator<<(c i) {
    cout << boolalpha << i;
    return *this;
  }
  template <class c>
  typename enable_if<sizeof dud<c>(0) == 1, debug &>::type operator<<(c i) {
    return *this << range(begin(i), end(i));
  }
  template <class c, class b>
  debug &operator<<(pair<b, c> d) {
    return *this << "(" << d.first << ", " << d.second << ")";
  }
  template <class c>
  debug &operator<<(rge<c> d) {
    *this << "[";
    for (auto it = d.b; it != d.e; ++it) *this << ", " + 2 * (it == d.b) << *it;
    return *this << "]";
  }
};
const long double PI = acos(-1);
const int M = (int)1e9 + 7;
signed main(void) {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int t;
  cin >> t;
  while (t--) {
    string s;
    cin >> s;
    int n = s.size();
    s = '*' + s;
    int x;
    cin >> x;
    vector<int> ans(n + 1, -1);
    for (int i = 1; i <= n; i++) {
      if (s[i] == '0') {
        if (i > x) ans[i - x] = 0;
        if (i + x <= n) ans[i + x] = 0;
      }
    }
    for (int i = 1; i <= n; i++) {
      if (s[i] == '1') {
        if (i > x && ans[i - x] == -1) ans[i - x] = 1;
        if (i + x <= n && ans[i + x] == -1) ans[i + x] = 1;
      }
    }
    for (int i = 1; i <= n; i++)
      if (ans[i] == -1) ans[i] = 0;
    string s1 = "";
    for (int i = 1; i <= n; i++) {
      if (i > x && ans[i - x] == 1)
        s1 += '1';
      else if (i + x <= n && ans[i + x] == 1)
        s1 += '1';
      else
        s1 += '0';
    }
    if (s1 == s.substr(1)) {
      for (int i = 1; i <= n; i++) cout << ans[i];
      cout << '\n';
    } else {
      cout << "-1" << '\n';
    }
  }
}
