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.*;
import java.lang.*;

public class marlin
{
   
   public static void main(String args[])
   {
       
       int n=0,k=0;
        Scanner in= new Scanner(System.in);
        n=in.nextInt();
        k=in.nextInt();
        
        char r1[]=new char[n];
        char r2[]=new char[n];
        char r3[]=new char[n];
        char r4[]=new char[n];
        
        for(int i=0; i<n; i++)
        {
            r1[i]='.';r2[i]='.';r3[i]='.';r4[i]='.';
        }
        
        if(k%2==0)
        {
            for(int i=1; i<(k/2)+1; i++)
        {
            r2[i]='#';r3[i]='#';
        }
        System.out.println("YES");
        for(int i=0; i<n; i++)
        {
            System.out.print(r1[i]);
           
        }
        System.out.println();
         for(int i=0; i<n; i++)
        {
            System.out.print(r2[i]);
           
        }
        System.out.println();
        
         for(int i=0; i<n; i++)
        {
            System.out.print(r3[i]);
           
        }
        System.out.println();
        
         for(int i=0; i<n; i++)
        {
            System.out.print(r4[i]);
           
        }
        System.out.println();
            
            
        }
        
        else if((k%2!=0)&&(k<=n-2))
        {
            for(int i=0; i<=(k-1)/2; i++)
        {
            r2[(n-1)/2 +i]='#';
            r2[(n-1)/2 -i]='#';
            
        }
        System.out.println("YES");
        for(int i=0; i<n; i++)
        {
            System.out.print(r1[i]);
           
        }
        System.out.println();
         for(int i=0; i<n; i++)
        {
            System.out.print(r2[i]);
           
        }
        System.out.println();
        
         for(int i=0; i<n; i++)
        {
            System.out.print(r3[i]);
           
        }
        System.out.println();
        
         for(int i=0; i<n; i++)
        {
            System.out.print(r4[i]);
           
        }
        System.out.println();
            
        }
        else if((k%2!=0)&&(k>n-2)&&(k>4))
        {
            
            
            for(int i=1; i<=(k+1)/2; i++)
            r2[i]='#';
            
            for(int i=1; i<=(k+1)/2; i++)
            r3[i]='#';
            
            r2[(k+1)/2 -1]='.';
            
            System.out.println("YES");
        for(int i=0; i<n; i++)
        {
            System.out.print(r1[i]);
           
        }
        System.out.println();
         for(int i=0; i<n; i++)
        {
            System.out.print(r2[i]);
           
        }
        System.out.println();
        
         for(int i=0; i<n; i++)
        {
            System.out.print(r3[i]);
           
        }
        System.out.println();
        
         for(int i=0; i<n; i++)
        {
            System.out.print(r4[i]);
           
        }
        System.out.println();
            
            
        }
        
        
        else
        System.out.println("NO");
       
       
   }
}
