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.util.Scanner;
import java.io.*;
import java.io.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.Scanner; 
import java.util.StringTokenizer;

import javax.lang.model.util.ElementScanner6; 

public class C1400
{
    static class FastReader
    { 
        BufferedReader br; 
        StringTokenizer st; 

        public FastReader() 
        { 
            br = new BufferedReader(new
                    InputStreamReader(System.in)); 
        } 

        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 

        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 

        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 

        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 

        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
    
    static int[] readarrint(int n)
    {
        int arr[]=new int[n];
        FastReader in=new FastReader();
        for(int i=0;i<n;i++)
        {
            arr[i]=in.nextInt();
        }
        return arr;
    }

    
    static long[] readarrlong(int n)
    {
        long arr[]=new long[n];
        FastReader in=new FastReader();
        for(int i=0;i<n;i++)
        {
            arr[i]=in.nextLong();
        } 
        return arr;
    }

    
    public static void main(String args[])
    {  
        FastReader in=new FastReader();
        int t=1;

        t=in.nextInt();
        while(t-->0)
        {
            String S=in.nextLine();
            int n=S.length();
            int x=in.nextInt();
       
            char[] ch=new char[n];
            Arrays.fill(ch, '1');
            boolean flag=true;
           
        
            for(int i=0;i<n;i++)
            {
                if(S.charAt(i)=='0')
                {
                    if(i-x>=0)
                    {
                        ch[i-x]='0';
                    }
                    if(i+x<n)
                    {
                        ch[i+x]='0';
                    }
                }
                
            }   
        
            for(int i=0;i<n;i++)
            {
                boolean subflag=true;
                if(S.charAt(i)=='1')
                {
                    subflag=false;
     
                    if((i-x)>=0)
                    {

                      
                        if(ch[i-x]=='1')
                            subflag=true;
                    }
                    if((i+x)<n)
                    {
                      
                        if(ch[i+x]=='1')
                            subflag=true;
                        
                    }
                }
     
                if(subflag==false)  
                {
                    flag=false;
                    break;
                }
            }
            if(flag)
            System.out.println(ch);
            else
            System.out.println(-1);
             
            
           
        }
    }
}