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 Solution
{
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int t, i, x, flag, n, left, right;
		t=sc.nextInt();
		while(t-->0)
		{
			flag=0;
			String w=sc.next();
			x=sc.nextInt();
			n=w.length();
			char[] s = new char[n];
			Arrays.fill(s, '?');
			for(i=0; i<n; i++)
			{
				if(w.charAt(i)=='0')
				{
					if(i-x>=0)
						s[i-x]='0';
					if(i+x<n)
						s[i+x]='0';
				}
			}
			for(i=0; i<n; i++)
			{
				if(w.charAt(i)=='1')
				{
					if(i-x>=0 && (s[i-x]=='?' || s[i-x]=='1'))
						s[i-x]='1';
					else if(i+x<n && s[i+x]=='?')
						s[i+x]='1';
					else
					{
						flag=-1;
						break;
					}
				}
			}
			for(i=0; i<n; i++)
				if(s[i]=='?')
					s[i]='1';
			
			if(flag==-1)
				System.out.println("-1");
			else
				System.out.println(new String(s));
		}
	}
}