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

public class GFG {
    static void fun(String s,int n){
       char arr []=new char[s.length()];
       Arrays.fill(arr,'1');
       for(int i=0;i<s.length();i++){
           if(s.charAt(i)=='0'){
               if(i-n>=0){arr[i-n]='0';}
               if(i+n<s.length()){arr[i+n]='0';}
           }
       }
       for(int i=0;i<s.length();i++){
           if(s.charAt(i)=='1'){
               if(!((i-n>=0 && arr[i-n]=='1') || (i+n<s.length() && arr[i+n]=='1'))){System.out.println(-1);return;}
           }
       }
       StringBuilder sb=new StringBuilder();
       for(char c:arr){sb.append(c);}
       System.out.println(sb);
    }
    public static void main(String [] args)throws Exception
    {BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
    int t=Integer.parseInt(br.readLine());
    
    while(t-->0){
        String str=br.readLine();
        int n=Integer.parseInt(br.readLine());
        fun(str,n);
        
    }
        
	}
}