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
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner s=new Scanner(System.in);
		int t=s.nextInt();
		while(t-->0)
		{
		    s.nextLine();
		    String str=s.nextLine();
		    int x=s.nextInt();
		    int n=str.length();
		    StringBuilder sb=new StringBuilder();
		    int arr[]=new int[n];
		    Arrays.fill(arr,1);
		    for(int i=0;i<str.length();i++)
		    {
		        if(str.charAt(i)=='0')
		        {
		            if(i-x>=0)
		            arr[i-x]=0;
		            if(i+x<str.length())
		            arr[i+x]=0;
		        }
		    }
	        int ans=0;
	        for(int i=0;i<str.length();i++)
		    {
		        if(str.charAt(i)=='1')
		        {
		            int f=0;
		            int g=0;
		            if(i-x>=0&&arr[i-x]==1)
		            f=1;
		            if(i+x<str.length()&&arr[i+x]==1)
		            g=1;
		            if(f==0&&g==0)
		            {
		                ans=-1;
		                break;
		            }
		        }
		    }
		    if(ans==-1)
		    {System.out.println(-1);continue;}
		    for(int i=0;i<str.length();i++)
		    {
		        sb.append(arr[i]);
		    }
		    System.out.println(sb.toString());
		}
	}
}
