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.io.*;

public class Main
{
    public static void main(String[] args) throws IOException //use buffered reader?
    {
        Scanner inp = new Scanner(System.in);
        int t = inp.nextInt();
        for (int tc = 0; tc < t; tc++)
        {
            String s = inp.next();
            int x = inp.nextInt();
            char[] w = new char[s.length()];
            Arrays.fill(w,'1');
            for(int i = 0; i < s.length(); i++)
            {
                if(s.charAt(i)=='0')
                {
                    if(i-x >= 0)
                        w[i-x] = '0';
                    if(i+x < s.length())
                        w[i+x] = '0';
                }
            }

            boolean good = true;
            for(int i = 0; i < s.length(); i++)
            {
                if(i-x < 0 && i+x >= s.length())
                {
                    if (s.charAt(i) == '1')
                        good = false;
                }
                else if(i-x < 0 && i+x < s.length())
                {
                    if((s.charAt(i)=='1' && w[i+x]=='0') || (s.charAt(i)=='0' && w[i+x]=='1'))
                        good = false;
                }
                else if(i+x >= s.length() && i-x >= 0)
                {
                    if ((s.charAt(i) == '1' && w[i - x] == '0') || (s.charAt(i) == '0' && w[i - x] == '1'))
                        good = false;
                }
                else if(!(w[i-x]=='0' && w[i+x]=='0' && s.charAt(i)=='0') && !((w[i-x]=='1' || w[i+x]=='1') && s.charAt(i)=='1'))
                        good = false;
            }
            if(!good)
                System.out.println(-1);
            else
            {
                String res = "";
                for(int i = 0; i < s.length(); i++)
                    res += w[i];

                System.out.println(res);
            }

        }

    }
}
