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.Scanner;
public class ed94_2_3 {

	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();
			int a[] = new int[s.length()];
			for(int i=0;i<s.length();i++) {
				a[i] = 1;
			}
			
			String ans="";
			for(int i=0;i<s.length();i++) {
				if(s.charAt(i) == '0') {
					if(i + x < s.length()) {
						a[i+x] = 0;
					}
					if(i - x >= 0) {
						a[i - x] = 0;
					}
				}
			}
			
			for(int i=0;i<s.length();i++) {
				ans += a[i];
			}
			
			int flag = 0;
			for(int i=0;i<s.length();i++) {
				if(i+x < s.length() && ans.charAt(i+x) == '1') {
					if(s.charAt(i) == '0') {
						flag = 1;
						break;
					}
				}
				else if(i-x >= 0 && ans.charAt(i-x) == '1') {
					if(s.charAt(i) == '0') {
						flag = 1;
						break;
					}
				}
				else {
					if(s.charAt(i) == '1') {
						flag = 1;
						break;
					}
				}
			}
			
			if(flag == 0) {
				System.out.println(ans);
			}
			else {
				System.out.println("-1");
			}
		}
		sc.close();
	}

}
