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.Scanner;

public class code3_25_08_2020 {

	public static void main(String[] args) {
		Scanner s=new Scanner(System.in);
		int t=s.nextInt();
		for(int q=0;q<t;q++)
		{
			String str=s.next();
			int x=s.nextInt();
			int n=str.length();
			char output[]=new char[n];
			for(int i=0;i<n;i++)
				output[i]='1';
			boolean bo=true;
			for(int i=0;i<n;i++)
			{
				if(str.charAt(i)=='0')
				{
					if(i-x>=0)
						output[i-x]='0';
					if(i+x<n)
						output[i+x]='0';
				}
			}
			for(int i=0;i<n;i++)
			{
				if(str.charAt(i)=='1')
				{
					boolean f1=true,f2=true;
					if(i-x>=0)
					{
						if(output[i-x]!='0')
							f1=false;
					}
					if(i+x<n)
					{
						if(output[i+x]!='0')
							f2=false;
					}
					if(f1&&f2)
					{
						bo=false;
						break;
					}
				}
			}
			if(!bo)
			{
				System.out.println("-1");
			}
			else
			{
				System.out.println(String.valueOf(output));
			}

		}

	}

}