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.util.regex.*;
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 int find(String str,char c){
        int k=0,count=0;
        while(k<str.length()){
            if(str.charAt(k)==c){
                count++;
            }
            if(count>0){
                break;
            }
            k++;
        }
        return count;
    }*/
	public static void main (String[] args) throws java.lang.Exception
	{
	    Scanner sc= new Scanner(System.in);
	    int n=sc.nextInt();//String a; char c; int l,k,count;
	    while(n-->0){
	        String s= sc.next();
	        int x= sc.nextInt();
	        int arr[]= new int[s.length()];
	        Arrays.fill(arr,1);
	        
	        for(int i=0;i<s.length();i++){
	            if(s.charAt(i)=='0'){
	                if(i+x<s.length()){
	                    arr[i+x]=0;
	                }
	                if(i-x>=0){
	                    arr[i-x]=0;
	                }
	            }
	        }
	        int p=0;
	        for(int i=0;i<s.length();i++){
	            if(s.charAt(i)=='1'){
	                if(i+x<s.length()&&arr[i+x]==1){
	                    //arr[i+x]=0;
	                }
	                else if(i-x>=0&&arr[i-x]==1){
	                    //arr[i-x]=0;
	                }
	                else{
	                    System.out.println("-1");
	                    p=1;
	                    break;
	                }
	            }
	        }
	        
	        if(p==0){
	            //System.out.println("ok");
	            for(int i=0;i<s.length();i++)
	            {
	                //int i=3;
	                System.out.print(arr[i]);
	            }
	            System.out.println();
	        }
	    }
	   
	    }
	    	// your code goes here
	}

