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

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.*;

public class Main
{
   static class FastReader
   {
      BufferedReader br;
      StringTokenizer st;

      public FastReader()
      {
         br = new BufferedReader(new
                 InputStreamReader(System.in));
      }

      String next()
      {
         while (st == null || !st.hasMoreElements())
         {
            try
            {
               st = new StringTokenizer(br.readLine());
            }
            catch (IOException  e)
            {
               e.printStackTrace();
            }
         }
         return st.nextToken();
      }

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

      long nextLong()
      {
         return Long.parseLong(next());
      }

      double nextDouble()
      {
         return Double.parseDouble(next());
      }

      String nextLine()
      {
         String str = "";
         try
         {
            str = br.readLine();
         }
         catch (IOException e)
         {
            e.printStackTrace();
         }
         return str;
      }

      int[] readArray(int n, int size){
         int[] a = new int[size];
         for(int i = 0; i < n; i++) {
            a[i] = this.nextInt();
         }

         return a;
      }

      long[] readLongArray(int n, int size){
         long[] a = new long[size];
         for(int i = 0; i < n; i++) {
            a[i] = this.nextLong();
         }
         return a;
      }
   }



   public static void main(String[] args) {
      FastReader s=new FastReader();
      int t = s.nextInt();

      for(int z = 0; z < t; z++) {
         char[] bs = s.next().toCharArray();
         int x = s.nextInt();

         int n = bs.length;
         char[] ans = new char[n];
         Arrays.fill(ans, '1');
         for (int i=0; i<n; i++) {
            if (bs[i]=='0') {
               if(i - x >= 0) ans[i - x] = '0';
               if(i + x < n) ans[i + x] = '0';
            }
         }
         boolean possible = true;
         for (int i=0; i < n && possible; i++) {
            if (bs[i]=='1') {
               if (i - x >= 0 && ans[i-x]=='1') continue;
               if (i + x < n && ans[i+x]=='1') continue;
               possible = false;
            }
         }
         if(!possible) System.out.println(-1);
         else System.out.println(new String(ans));
      }
   }
   static boolean legal(int x, int n) {
      return x>=0 && x<n;
   }

}