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
//package ec92;

import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;

public class C {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc=new Scanner(System.in);
		PrintWriter out=new PrintWriter(System.out);
		
		
		int t=sc.nextInt();
		while(t-->0) {
			String s=sc.next();
			int n=s.length();
			int x=sc.nextInt();
			int a[]=new int[n];
			for(int i=0;i<n;i++) {
				a[i]=s.charAt(i)-'0';
			}
			ans=new int[n];
			Arrays.fill(ans, 1);
			for(int i=0;i<n;i++) {
				if(a[i]==0) {
					if(i-x>=0) {
						ans[i-x]=0;
					}
					if(i+x<n) {
						ans[i+x]=0;
					}
				}
			}
			int flag=0;
			for(int i=0;i<n;i++) {
				if(a[i]==1) {
					int f=0;
					if(x+i<n && ans[i+x]==1) {
						f=1;
					}
					if(i-x>=0 && ans[i-x]==1) {
						f=1;
					}
					if(f==0) {
						flag=1;
						break;
					}
				}
			}
			if(flag==1) {
				System.out.println(-1);
			}
			else {
				for(int i=0;i<n;i++) {
					System.out.print(ans[i]);
				}
				System.out.println();
			}
		}
		sc.close();
		out.close();
	}
	
	static int ans[];
	
}
