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.ArrayList;
import java.util.Arrays;
import java.util.Scanner;





public class C {
	
	static int mod = (int) 1e9 + 7;

	static int ar[];
	static Scanner sc = new Scanner(System.in);
	static StringBuilder out = new StringBuilder();

	static ArrayList<Integer> gr[];
	int n;

	
	static class pair implements Comparable<pair> {

		int f;
		int s;

		public pair(int a, int b) {
			f = a;
			s = b;
		}

		@Override
		public int compareTo(pair o) {
			// TODO Auto-generated method stub
			if (this.s == o.s)
				return o.f - this.f;
			return this.s - o.s;
		}

	}


	public static void main(String[] args) {
		// TODO Auto-generated method stub

		
		int tc=sc.nextInt();
		while(tc-->0){
			
			String s=sc.next();
			int n=sc.nextInt();
			char []ch=new char[s.length()+1];
			
			 boolean flag=true;
			
			 Arrays.fill(ch, '1');
			for(int i=0;i<s.length();i++){
				
				if(s.charAt(i)=='0'){
					int l=i-n;
					int r=i+n;
					if(l>=0){
						ch[l]='0';
					}
					if(r<s.length())ch[r]='0';
				}
			}
			
			for(int i=0;i<s.length();i++){
				
				if(s.charAt(i)=='1'){
					
					int l=(i-n);
					char l1=l>=0?ch[l]:'0';
					int r=i+n;
					char r1=r<s.length()?ch[r]:'0';
					if(l1=='0' && r1=='0'){
						flag=false;break;
					}
					
				
					
					
				}
				
			}
			
			
			if(flag){
				for(int i=0;i<s.length();i++){
					out.append(ch[i]);
				}
			}
			else out.append(-1);
				
			out.append("\n");
			
			
		}
		System.out.println(out);

	}

}