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.*;
import java.io.*;

public class C_Binary_String_Reconstruction{
    public static void main(String[] args) {
        FastScanner s= new FastScanner();
        StringBuilder res = new StringBuilder();
        int t=s.nextInt();
        int p=0;
        while(p<t){
        String str=s.nextToken();
        int x=s.nextInt();
        int n=str.length();
        char ans[]= new char[n];
        for(int i=0;i<n;i++){
            ans[i]='1';
        }
        for(int i=0;i<n;i++){
            char ch=str.charAt(i);
            if(ch=='0'){
                if((i-x)>=0){
                    ans[i-x]='0';
                }
                if((i+x)<n){
                    ans[i+x]='0';
                }
            }
        }
        int check=0;
        for(int i=0;i<n;i++){
            char ch=str.charAt(i);
            if(ch=='1'){
               
                if((i-x)>=0 && ans[i-x]=='1'){
                   continue;
                }
                else if((i+x)<n && ans[i+x]=='1'){
                   continue;
                }
                else{
                    check=1;
                    break;
                }
            }

        }
        if(check==1){
            res.append("-1\n");
            p++;
            continue;
        }
        else{
            for(int i=0;i<n;i++){
                res.append(ans[i]);
            }
            res.append("\n");
        }
        p++;
    }
    System.out.println(res);
    }
    static class FastScanner {
		BufferedReader br;
		StringTokenizer st;
 
		public FastScanner(String s) {
			try {
				br = new BufferedReader(new FileReader(s));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
		}
 
		public FastScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
 
		String nextToken() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					// TODO Auto-generated catch block
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
 
		int nextInt() {
			return Integer.parseInt(nextToken());
		}
 
		long nextLong() {
			return Long.parseLong(nextToken());
		}
 
		double nextDouble() {
			return Double.parseDouble(nextToken());
		}
	}




}