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 Solution{
    public static int[] nextArray(FastReader sc1, int n){
        int[] arr = new int[n];
        for(int i=0; i<n; i++){
            arr[i] = sc1.nextInt();
        }
        return arr;
    }
    public static void main(String[] args){
        FastReader sc1 = new FastReader();
        StringBuilder sb = new StringBuilder();
        
        int tc = Integer.parseInt(sc1.nextLine());
        int ch = 1;

        while(ch<=tc){
            String str = sc1.nextLine();
            int x = Integer.parseInt(sc1.nextLine());
            
            int[] w = new int[str.length()];

            for(int i=0; i<str.length(); i++){
                w[i] = -1;
            }

            for(int i=0; i<str.length(); i++){
                if(str.charAt(i) == '0'){
                    int left = i-x;
                    int right = i+x;
                    if(left >= 0){
                        w[left] = 0;
                    }
                    if(right < str.length()){
                        w[right] = 0;
                    }
                }
            }

            boolean posi = true;

            for(int i=0; i<str.length(); i++){
                if(str.charAt(i) == '1'){
                    int left = i-x;
                    int right = i+x;

                    int lval = 0;
                    int rval = 0;

                    if(left >= 0 && w[left] != 0){
                        lval = w[left];
                    }
                    if(right < str.length() && w[right] != 0){
                        rval = w[right];
                    }

                    if(lval == 0 && rval == 0){
                        posi = false;
                    }
                }
            }

            if(posi){
                for(int i=0; i<str.length(); i++){
                    if(w[i] == -1){
                        w[i] = 1;
                    }
                    sb.append(w[i]);
                }
            }
            else{
                sb.append("-1");
            }
            sb.append("\n");
            ch++;
        }

        System.out.print(sb.toString());
    }

    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; 
        } 
    }
}