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 cp;

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

public class CF {
	
    static FastReader sc = new FastReader();
    
    public static void main(String[] args) {
        int t = sc.nextInt();
        while (t-- > 0) {
            solve();
        }
    	//solve();
    }


    static void solve() {
    	String str = sc.next();
    	int x = sc.nextInt();
    	char ch[] = str.toCharArray();
    	char c[] = new char[ch.length];
    	for(int i=0 ; i<ch.length ; i++) {
    		c[i] = '1';
    	}
    	for(int i=0 ; i<ch.length ; i++) {
    		if(ch[i] == '0') {
    			if(i-x >=0) {
    				c[i-x] = '0';
    			}
    			if(i+x < ch.length) {
    				c[i+x] = '0';
    			}
    		}
    	}
    	boolean flag = false;
    	for(int i=0 ; i<ch.length ; i++) {
    		if(ch[i] == '1') {
    			if(i-x >=0 && c[i-x]=='1' || i+x < ch.length && c[i+x]=='1') {
    				continue;
    			}
    			else {
    				flag = true;
    				break;
    			}
    		}
    	}
    	if(flag == true) {
    		System.out.println(-1);
    	}
    	else {
    		System.out.println(String.valueOf(c));
    	}
    }
    //fast input reader
    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}
