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;
import java.awt.image.BandedSampleModel;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.lang.reflect.Array;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;
public class C {


    public static void main(String args[])
    {
        Scanner sc=new Scanner(System.in);
        int cases = sc.nextInt();
        for(int i=0;i<cases;i++)
        {
            String s=sc.next();
            int n=s.length();
            int x = sc.nextInt();
            int arr[][] = new int[n][2];
            for(int j=0;j<n;j++)
            {
                arr[j][0]=2;
                arr[j][1]=2;
            }
            for(int j=x;j<s.length();j++)
            {
                arr[j-x][0]=s.charAt(j)-'0';
            }
            for(int j=x;j<s.length();j++)
            {
                arr[j][1]=s.charAt(j-x)-'0';
            }
            boolean check=true;
            StringBuilder ans=new StringBuilder();
            for(int j=0;j<n;j++)
            {
                //if(arr[j][0]==2||arr[j][1]==2||(arr[j][0]==arr[j][1]))
                {

                    if(arr[j][0]==2&&arr[j][1]==2)
                    {
                        ans.append(0);
                    }
                    else if(arr[j][0]==2)
                    {
                        ans.append(arr[j][1]);
                    }
                    else if(arr[j][1]==2)
                    {
                        ans.append(arr[j][0]);
                    }
                    else if(arr[j][0]!=arr[j][1])
                    {
                        ans.append(0);
                    }
                    else
                    {
                        ans.append(arr[j][0]);
                    }
                }
//                else
//                {
//                    check=false;
//                    break;
//                }

            }
//            for(int j=0;j<n;j++)
//            {
//                if(j>=x&&(((s.charAt(j-x)+"").equals(ans.charAt(j)+"")==false)&&(ans.charAt(j)+"").equals("1")))
//                {
//                    check=false;
//                    break;
//                }
//
//                if(j<n-x&&(((s.charAt(j+x)+"").equals(ans.charAt(j)+"")==false)&&(ans.charAt(j)+"").equals("1")))
//                {
//                    check=false;
//                    break;
//                }
//                if(j<x&&j>=n-x&&((ans.charAt(j+x)+"").equals("1")))
//                {
//                    check=false;
//                    break;
//                }
//            }
            StringBuilder checker=new StringBuilder();
            int arrf[]=new int[n];
            for(int j=0;j<n;j++)
            {
                arrf[j]=2;
            }
            for(int j=0;j<n;j++)
            {
                if(j>=x&&("1").equals(ans.charAt(j)+""))
                {
                    arrf[j-x]=1;
                }

                 if(j<n-x&&("1").equals(ans.charAt(j)+""))
                {
                    arrf[j+x]=1;
                }

            }
            for(int j=0;j<n;j++)
            {
                if(arrf[j]==2)
                {
                    arrf[j]=0;
                }
                checker.append(arrf[j]);
            }


            if(checker.toString().equals(s))
            {
                System.out.println(ans);
            }
            else
            {
                System.out.println(-1);
            }
        }

    }
}
