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.Arrays;
import java.util.Scanner;

public class BinaryStringReconstruction {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		while (t-- > 0) {
			String s = sc.next();
			int x = sc.nextInt();
			solve(s, x);
		}
	}

	private static void solve(String S, int x) {
		// TODO Auto-generated method stub
		char s[] = S.toCharArray();
		int n = S.length();
		char ans[] = new char[n];
		Arrays.fill(ans, '1');
		for (int i = 0; i < n; i++) {
			if (s[i] == '0') {
				if (isValid(i - x, n)) ans[i - x] = '0';
				if (isValid(i + x, n)) ans[i + x] = '0';
			}
		}
		boolean res = true;
		for (int i = 0; i < n; i++) { 
			if (s[i] == '1') 
				res &= ((isValid(i - x, n) && ans[i - x] == '1') 
					|| (isValid(i + x, n) && ans[i + x] == '1'));
		}
		if (res) System.out.println(ans);
		else System.out.println(-1);
	}

	private static boolean isValid(int x, int n) {
		return x >= 0 && x < n;
	}
}
