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 acmp{
	static Scanner in = new Scanner(System.in);
		// int size = in.nextInt();
		// int[] array = new int[size];
		// for(int i = 0; i<size; i++){
		// 	array[i] = in.nextInt();
		// }

		// int min = Integer.MAX_VALUE;
  		// int max = Integer.MIN_VALUE;
 	
	public static void main(String[] args) {
		//zhan
		//dos
		//md
		int test = in.nextInt();
		while(test>0){
			solve();
			test--;
		}
	}

	public static void solve(){
		String s = in.next();
		int x = in.nextInt();

		int n = s.length();
		StringBuilder w = new StringBuilder();
		for(int i = 0; i<n; i++){
			w.append("1");
		}
		for(int i = 0; i<n; i++){
			if(s.charAt(i) == '0'){
				if(i-x>=0){
					w.replace(i-x, i-x+1, "0");
				}
				if(i+x<n){
					w.replace(i+x, i+x+1, "0");
				}
			}
		}

		StringBuilder t = new StringBuilder();
		for(int i = 0; i<n; i++){
			t.append("0");
		}
		for(int i = 0; i<n; i++){
			if(i+x < n && w.charAt(i+x) == '1'){
				t.replace(i, i+1, "1");
			}
			if(i-x >= 0 && w.charAt(i-x) == '1'){
				t.replace(i, i+1, "1");
			}
		}
		System.out.println((t.toString().equals(s.toString()) ? w : "-1"));
	}
}