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
	{
		// your code goes here
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		int t=Integer.parseInt(br.readLine());
		while(t-->0){
		  //  String ss[]=br.readLine().split(" ");
		  //  int p=Integer.parseInt(ss[0]);
		  //  int f=Integer.parseInt(ss[1]);
		  //  String s[]=br.readLine().split(" ");
		  //  int cs=Integer.parseInt(s[0]);
		  //  int cw=Integer.parseInt(s[1]);
		  //  String sa[]=br.readLine().split(" ");
		  //  int s=Integer.parseInt(sa[0]);
		  //  int w=Integer.parseInt(sa[1]);
		  //  int a[]=new int[n];
		    int ans=0;
		    String s=br.readLine();
		    StringBuilder sb=new StringBuilder();
		    StringBuilder sbb=new StringBuilder();
		    int n=s.length();
		    for(int i=0;i<n;++i){
		        sb.append('1');
		    }
		    int x=Integer.parseInt(br.readLine());
		    for(int i=0;i<n;++i){
		        if(s.charAt(i)=='0'){
		            if(i>=x)
		            sb.setCharAt(i-x,'0');
		            if(i+x<n)
		            sb.setCharAt(i+x,'0');
		        }
		    }
		    for(int i=0;i<s.length();++i){
		        if(i>=x  && sb.charAt(i-x)=='1'){
		            sbb.append('1');
		        }
		        else if(i+x <n && sb.charAt(i+x)=='1'){
		            sbb.append('1');
		        }
		        else{
		            sbb.append('0');
		        }
		    }
		    if(sbb.toString().equals(s))
		    System.out.println(sb);
		    else
		    System.out.println(-1);
		}
	}
}
