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.io.*;

public class Coding {

    public static void main(String[] args) {
        BufferedReader bi = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter writer = new BufferedWriter(new OutputStreamWriter(System.out));
        try {
            int t = Integer.parseInt(bi.readLine());
            while (t > 0) {
               String input = bi.readLine();
               int x = Integer.parseInt(bi.readLine());
               int[] ans = new int[input.length()];
               for(int i=0;i<input.length();++i) {
                   int left = i-x;
                   int right = i+x;
                   ans[i] = 1;
                   if (left>=0 && input.charAt(left)=='0') {
                       ans[i] = 0;
                   }
                   if (right<input.length() && input.charAt(right)=='0') {
                       ans[i] = 0;
                   }
               }
               boolean poss = true;
               for(int i=0;i<input.length();++i) {
                   if (input.charAt(i)=='0') {
                       continue;
                   }
                   boolean exists = false;
                   int left = i-x;
                   if (left>=0 && ans[left]==1) {
                       exists = true;
                   }
                   int right = i+x;
                   if (right<input.length() && ans[right]==1) {
                       exists = true;
                   }
                   if (!exists) {
                       poss = false;
                       break;
                   }
               }
               if (poss) {
                   for(int i=0;i<input.length();++i) {
                       writer.append(String.valueOf(ans[i]));
                   }
               } else {
                   writer.append("-1");
               }
               writer.append('\n');
               t--;
            }
            writer.flush();
        } catch (Exception e) {
            e.printStackTrace();
        }
    }
}
