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


public class test{
  public static void main(String args[]){ 
    Scanner sc = new Scanner(System.in);
	int tc = sc.nextInt();
	while(tc-- > 0){
		String s= sc.next();
		int x= sc.nextInt();
		int n = s.length();
		char ans[]=new char[n];
		Arrays.fill(ans, '1');		
       
		for(int i=0;i<n;i++){
			if(s.charAt(i)=='0'){
				if(i-x>=0)ans[i-x]='0';
				if(i+x<n)ans[i+x]='0';
			}
		}
		boolean flag=false;
		for(int i=0;i<n;i++){
			if(s.charAt(i)=='1'){
				if(i-x>=0 && ans[i-x]=='1' || i+x<n && ans[i+x]=='1')continue;
				flag=true;
			}
		}
		if(flag)System.out.println(-1);
		else System.out.println(ans);      
	}
	sc.close();
  }  
}
