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.*;

public class taskCedu94 {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int t = in.nextInt();
        while(t-- > 0){
            String s = in.next();
            // System.out.println();
            int x = in.nextInt();
            int f = 0;
            // System.out.println(s);
            HashMap<Integer, Character> map = new HashMap<>();
            for(int i = 0 ; i < s.length() ; i++){
                if(s.charAt(i) == '0'){
                    if(i + x < s.length()){
                        map.put(i + x , '0');
                    }
                    if(i - x >= 0){
                        map.put(i - x , '0');
                    }
                }
            }

            for(int i = 0 ; i < s.length() ; i++){
                if(s.charAt(i) == '1'){
                    if(map.getOrDefault(i + x, '1') == '0' && map.getOrDefault(i - x, '1') == '0'){
                        f = 1;
                    }
                    else{
                        if((i + x <= s.length() - 1) && map.getOrDefault(i + x, '1') == '1')
                            f = 0;
                        else if((i - x >= 0 && map.getOrDefault(i - x, '1') == '1'))
                            f = 0;
                        else f = 1;
                    }
                if(f == 1) break;
                }
            }

            if(f == 1){
                System.out.println(-1);
                continue;
            }

            StringBuilder ans = new StringBuilder();

            for(int i = 0 ; i < s.length(); i++){
                ans.append(map.getOrDefault(i, '1'));
            }
            System.out.println(ans.toString());
        }
        in.close();
    }
    
}