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
/******************************************************************************

                            Online Java Compiler.
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Write your code in this editor and press "Run" button to execute it.

*******************************************************************************/
import java.util.*;
public class Main
{
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int t=sc.nextInt();
		while(t-->0)
		{
		   sc.nextLine();
		   String s=sc.nextLine();
		   int x=sc.nextInt();
		   int n=s.length();
		   char w[]=new char[n];
		   for(int i=0;i<n;i++)
		   w[i]='1';
		   boolean flag=true;
		   for(int i=0;i<n;i++)
		   {
		       if(s.charAt(i)=='0')
		       {
		           if(i-x>=0)
		           w[i-x]='0';
		           if(i+x<n)
		           w[i+x]='0';
		       }
		   }
		   char ss[]=new char[n];
		   for(int i=0;i<n;i++)
		   {
		       if(i-x>=0 && w[i-x]=='1')
		       ss[i]='1';
		       else if(i+x<n && w[i+x]=='1')
		       ss[i]='1';
		       else
		       ss[i]='0';
		   }
		   for(int i=0;i<n;i++)
	       {
	           if(ss[i]!=s.charAt(i))
	           {
	               flag=false;
	               System.out.println("-1");
	               break;
	           }
	           
		   }
		   if(flag)
		   for(int i=0;i<n;i++)
		   System.out.print(w[i]);
		   System.out.println();
		}
	}
}
