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
//package com.example.myPackage;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class BinaryString {
    private static FastScanner fs = new FastScanner();

    public static void main(String[] args) {
        int t = fs.nextInt();
        while(t-->0)
        {
            String s = fs.next();
            int n = s.length();
            int x = fs.nextInt();
          char []res = new char[n];
            Arrays.fill(res,'1');
           for(int i =0;i<n;i++)
           {
               if(s.charAt(i)=='0')
               {
                   if(legal(i-x,n)) res[i-x] ='0';
                   if(legal(i+x,n)) res[i+x] ='0';
               }

           }

           int flag =0;
           for(int i=0;i<n;i++)
           {
               if(s.charAt(i)=='1')
               {
                   if(legal(i-x,n))
                   {
                       if(res[i-x]=='1') continue;

                   }
                   if(legal(i+x,n))
                   {
                       if(res[i+x]=='1') continue;
                   }
                   flag =1;

               }


           }
           if(flag==1) System.out.println(-1);
           else
           {
               String result = new String(res);
               System.out.println(result);
           }




        }

    }
    private static boolean  legal(int a,int n)
    {
        if(a>=0 && a<n) return true;
        return false;
    }


    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

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

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

        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

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




