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.*;
import java.util.*;

/**
 * Accomplished using the EduTools plugin by JetBrains https://plugins.jetbrains.com/plugin/10081-edutools
 */

public class Main {
   public static void main(String[] args) throws IOException {
      BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
      BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

      int t = Integer.parseInt(br.readLine());

      while (t-- > 0) {
         String s = br.readLine();
         int x = Integer.parseInt(br.readLine()), n = s.length();
         char[] ans = new char[n];
         boolean possible = true;

         for (int i = 0; i < n; ++i) {
            if (s.charAt(i) == '0') {
               if (i >= x) {
                  if (ans[i - x] == '1') {
                     possible = false;
                     break;
                  } else if (ans[i - x] == '\u0000') {
                     ans[i - x] = '0';
                  }
               }
               if (i + x < n) {
                  ans[i + x] = '0';
               }
            } else {
               if (i >= x && ans[i - x] != '0') {
                  if (ans[i - x] == '\u0000') {
                     ans[i - x] = '1';
                  }
               } else if (i + x < n && ans[i + x] != '0') {
                  if (ans[i + x] == '\u0000') {
                     ans[i + x] = '1';
                  }
               } else {
                  possible = false;
                  break;
               }
            }
         }

         if (possible) {
            for (int i = 0; i < n; ++i) {
               if (ans[i] == '\u0000') {
                  ans[i] = '0';
               }
            }
         }

         bw.write(possible ? new String(ans) : "-1");
         bw.newLine();
      }

      bw.close();
      br.close();
   }
}