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 EdC {

	public static void main(String[] args) throws Exception{
		int num = 998244353;

		// TODO Auto-generated method stub
 		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
 		PrintWriter out = new PrintWriter(System.out);
 		int t = Integer.parseInt(bf.readLine());
 		for(int i = 0;i<t;i++){
//	 		String input1 = bf.readLine().trim();
//	 		String input2 = bf.readLine().trim();
	 		String input = bf.readLine().trim();
	 		int x = Integer.parseInt(bf.readLine());
	 		int[] array = new int[input.length()];
	 		Arrays.fill(array, -1);
	 		for(int j = 0;j<input.length();j++){
	 			if (input.charAt(j) == '0'){
	 				if (j-x >=0)
	 					array[j-x] = 0;
	 				if (j+x < input.length())
	 					array[j+x] = 0;
	 			}
	 		}
	 		for(int j = 0;j<input.length();j++){
	 			if (array[j] == -1)
	 				array[j] = 1;
	 		}
	 		boolean ans = true;
	 		for(int j = 0;j<input.length();j++){
	 			if ((j+x < input.length() && array[j+x] == 1) || (j-x >=0 && array[j-x] == 1)){
	 				if (input.charAt(j) != '1')
	 					ans = false;
	 			}
	 			else{
	 				if (input.charAt(j) != '0')
	 					ans = false;
	 			}
	 		}
	 		if (ans){
	 			for(int j : array){
	 				out.print(j);
	 			}
	 			out.println();
	 		}
	 		else
	 			out.println(-1);
 		}
 		
 		
 		out.println();
	 		
 		out.close();
 		
 		
 		
 	}
}
 	
 
//StringJoiner sj = new StringJoiner(" "); 
//sj.add(strings)
//sj.toString() gives string of those stuff w spaces or whatever that sequence is

 		
 		
 		
 		
	


