The city of Fishtopia can be imagined as a grid of 4 rows and an odd number of columns. It has two main villages; the first is located at the top-left cell (1,1), people who stay there love fishing at the Tuna pond at the bottom-right cell (4, n). The second village is located at (4, 1) and its people love the Salmon pond at (1, n).

The mayor of Fishtopia wants to place k hotels in the city, each one occupying one cell. To allow people to enter the city from anywhere, hotels should not be placed on the border cells.

A person can move from one cell to another if those cells are not occupied by hotels and share a side.

Can you help the mayor place the hotels in a way such that there are equal number of shortest paths from each village to its preferred pond?

Input

The first line of input contain two integers, n and k (3 ≤ n ≤ 99, 0 ≤ k ≤ 2×(n-2)), n is odd, the width of the city, and the number of hotels to be placed, respectively.

Output

Print "YES", if it is possible to place all the hotels in a way that satisfies the problem statement, otherwise print "NO".

If it is possible, print an extra 4 lines that describe the city, each line should have n characters, each of which is "#" if that cell has a hotel on it, or "." if not.

Examples

Input

7 2


Output

YES
.......
.#.....
.#.....
.......


Input

5 3


Output

YES
.....
.###.
.....
.....
import java.util.*;

public class JavaApplication82 {

    
    public static void main(String[] args) {
        Scanner Sc=new Scanner(System.in);
        
        int n=Sc.nextInt();
        int k=Sc.nextInt();
        
        if(k>2*(n-2))
        {
            System.out.println("NO");
        }
        
        System.out.println("YES");
        
        char mat[][]=new char[4][n];
        Arrays.fill(mat[0],'.');
        Arrays.fill(mat[1],'.');
        Arrays.fill(mat[2],'.');
        Arrays.fill(mat[3],'.');
        
        int e=(k/2);
      
        int i=1;
        int j=n-2;
        int p=1;
        
        while(e--!=0)
        {
            if(i==j)
            {
                if(p==2)
                {
                    break;
                }
               
                p=2;  
                i=1;
                j=n-2;
                
                if(i==j)
                {
                    break;
                }
            }
            
            
            mat[p][i]='#';
            mat[p][j]='#';
            i++;
            j--;
            k=k-2;
        }
        
        p=1;
        
        while(k--!=0)
        {
            mat[p][n/2]='#';
            p=2;
        }
        
        for(int a=0;a<4;a++)
        {
            for(int b=0;b<n;b++)
            {
                System.out.print(mat[a][b]);
            }
            System.out.println();
        }
        
        
        
    }
    
}
