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
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.StringTokenizer;

public class Solution1400C {
  public static void main(String[] args) {
    InputReader in = new InputReader(System.in);
    PrintWriter out = new PrintWriter(System.out);
    Solver1400C solver = new Solver1400C();
    int n = in.nextInt();
    for (int i = 0; i < n; i++) {
      solver.solve(i, in, out);
    }
    out.close();
  }

  static class Solver1400C {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
      String s = in.next();
      int x = in.nextInt();
      char[] res = new char[s.length()];
      Arrays.fill(res, '1');
      for (int i = 0; i < s.length(); i++) {
        char c = s.charAt(i);
        if (c == '0') {
          if (i - x >= 0) {
            res[i-x] = '0';
          }
          if (i + x < s.length()) {
            res[i+x] = '0';
          }
        }
      }

      for (int i = 0; i < s.length(); i++) {
        char c = s.charAt(i);
        boolean hasone = false;
        if (c == '1') {
          if (i - x >= 0 && res[i-x] == '1') {
            hasone = true;
          }
          if (i + x < s.length() && res[i+x] == '1') {
            hasone = true;
          }
          if (!hasone) {
            out.println(-1);
            return;
          }
        }
      }
      out.println(new String(res));
    }
  }

  static class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
      reader = new BufferedReader(new InputStreamReader(stream), 32768);
      tokenizer = null;
    }

    public String next() {
      while (tokenizer == null || !tokenizer.hasMoreTokens()) {
        try {
          tokenizer = new StringTokenizer(reader.readLine());
        } catch (IOException e) {
          throw new RuntimeException(e);
        }
      }
      return tokenizer.nextToken();
    }

    public int nextInt() {
      return Integer.parseInt(next());
    }
  }
}