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

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
    
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		BufferedReader buf=new BufferedReader(new InputStreamReader(System.in));
		int t=Integer.parseInt(buf.readLine());
		StringBuilder sb=new StringBuilder();
		for(int i=0;i<t;i++)
		{
		    String s=buf.readLine();
		    char ch[]=s.toCharArray();
		   int arr[]=new int[ch.length];
		    for(int j=0;j<ch.length;j++)
		    arr[j]=ch[j]-'0';
		    int x=Integer.parseInt(buf.readLine());
		    int n=ch.length;
		    int w[]=new int[n];
		    Arrays.fill(w,1);
		    for(int j=0;j<w.length;j++)
		    {
		        if(arr[j]==0)
		        {
		            if(j-x>=0)
		            w[j-x]=0;
		            if(j+x<n)
		            w[j+x]=0;
		        }
		    }
		    
		    int j=0,flag=0;
		    while(j<arr.length)
		    {
		        int m=arr[j];
		        if(m==1)
		        {
		            if(j-x>=0)
		            {
		                if(w[j-x]==1)
		                j=j+1;
		                else
		                {
		                    if(j+x<n)
		                    {
		                        if(w[j+x]==1)
		                        j=j+1;
		                        else
		                        {
		                            flag=1;
		                            break;
		                        }
		                    }
		                    else
		                    {
		                        flag=1;
		                            break;
		                    }
		                }
		            }
		            else
		            {
		                if(j+x<n)
		                    {
		                        if(w[j+x]==1)
		                        j=j+1;
		                        else
		                        {
		                            flag=1;
		                            break;
		                        }
		                    }
		                    else
		                    {
		                        flag=1;
		                        break;
		                    }
		            }
		        }
		        else
		        j=j+1;
		    }
		    if(flag==1)
		    sb.append("-1"+"\n");
		    else
		    {
		        for(int z=0;z<w.length;z++)
		        sb.append(w[z]);
		        sb.append("\n");
		    }
		   
		}
		System.out.println(sb);
	}
}
