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.*;	
public class Solution {

	public static int mod=1000000007;


	public static void main(String[] args) {
			Scanner sc=new Scanner(System.in);
			int t=sc.nextInt();
			
			while(t-->0) {
			String str=sc.next();
			int x=sc.nextInt();
			
			char c[]=new char[str.length()];
			Arrays.fill(c, '2');
			boolean flag=false;
			for(int i=0;i<str.length();i++) {
				char curr=str.charAt(i);
				if(curr=='0')
				{
					if(i+x<str.length()) {
					c[i+x]='0';	
					}
					if(i>=x)
					{
						c[i-x]='0';
					}
					
				}
			
				
			}
			
			for(int i=0;i<str.length();i++) {
				char curr=str.charAt(i);
				boolean flag1=false;
				boolean flag2=false;
				if(curr=='0')
					continue;
				if(curr=='1') {
					if(i+x<str.length()) {
						
							if(c[i+x]!='0') {
								c[i+x]='1';
								flag1=true;
							}
					}
					if(i>=x) {
						if(c[i-x]!='0') {
							c[i-x]='1';
							flag2=true;
						}
					}
				}
				if(flag1 || flag2)
					continue;
				else
				{
					flag=true;
					break;
				}
				
			}
			
			if(flag)
			{
				System.out.println(-1);
				continue;
			}
			
			
			for(char ch:c)
				if(ch=='2')
					System.out.print(1);
				else
					System.out.print(ch);
			System.out.println();
			
			}
			
			
	}
	
}
		




		
		
	

	
	
	
	
	
	
		
	
	
	
	
		
	
	

		
		

	
	
	
	

			
	
		
	
	
		
	
	
	
	
	


