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.io.*;
import java.util.*;

public class X {

	
	public static void main(String[] args) {
		FastScanner in=new FastScanner();
		PrintWriter out=new PrintWriter(System.out);
		int t=in.nextInt();
		while(t-->0)
		solve(in,out);
		out.close();
	}

   
    static void solve(FastScanner in,PrintWriter out){
     char s[]=in.next().toCharArray();
     int n=s.length;
     char t[]=new char[n];
     Arrays.fill(t,'1');
     int x=in.nextInt();
     for(int i=0;i<n;i++){
         if(s[i]=='0'){
             if(i-x>=0) t[i-x]='0';
             if(i+x<n) t[i+x]='0';
         }
     }
     int flag=0;
     for(int i=0;i<n;i++){
         if(s[i]=='1'){
             if((i-x>=0&&t[i-x]=='1')||(i+x<n&&t[i+x]=='1')) continue; else flag=1;
         }
     }
     if(flag==1) out.println(-1);
     else {
         for(int i=0;i<n;i++) out.print(t[i]); out.println();
     }
    }    
	


	static void sort(int[] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
	
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}

	
}
