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 vivek{    
    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(); 
        } 

        char nextChar()
        {
            return next().charAt(0);
        }

        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; 
        } 

        int[] nextArray(int rows)
        {
            int arr[] = new int[rows];            
            for (int i = 0; i < rows; i++)
            arr[i] = nextInt();
            return arr;
        }

        long[] nextLongArray(int rows)
        {
            long arr[] = new long[rows];            
            for (int i = 0; i < rows; i++)
            arr[i] = nextLong();
            return arr;
        }

        char[] nextCharArray(int rows)
        {
            char arr[] = new char[rows];
            for (int i = 0; i < rows; i++)
            arr[i] = next().charAt(0);
            return arr;
        }

        int[][] nextMatrix(int rows, int columns)
        {
            int mat[][] = new int[rows][columns];
            for (int i = 0; i < rows; i++)
            {
                for (int j = 0; j < columns; j++)
                {
                    mat[i][j] = nextInt();
                }
            }
            return mat;
        }
    }
    static boolean legal(int x, int n){
        return x>=0 && x<n;
    }
    public static void main(String args[]){
        FastReader sc=new FastReader();
        PrintWriter p=new PrintWriter(System.out);
        int t=sc.nextInt();
        while(t-->0){
            char s[]=sc.next().toCharArray();
            int x=sc.nextInt();
            int n=s.length;
            char ans[]= new char[n];
            Arrays.fill(ans,'1');
            for(int i=0;i<n;i++){
                if(s[i]=='0'){
                    if(legal(i-x,n)) ans[i-x]='0';
                    if(legal(i+x,n)) ans[i+x]='0';
                }
            }
            boolean check=false;
            for(int i=0;i<n;i++){
                if(s[i]=='1'){
                    if(legal(i-x,n) && ans[i-x]=='1') continue;
                    if(legal(i+x,n) && ans[i+x]=='1') continue;
                    check=true;
                }
            }
            if(check)
                p.println("-1");
            else{
                p.println(ans);
            }
        }
        p.flush();
    }
}