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.math.BigInteger;
import java.util.*;
public class Main {   
    
     
    public static void main(String args[])  {
        Scanner sc =new Scanner(System.in);
        int a=sc.nextInt();
        int b=sc.nextInt();
        System.out.println("YES");
        int x[][]=new int[4][a];
        if(b%2==0){
        	for(int n=1;n<a-1;n++){
	        	if(b==0)break;
	        	else{
	        		b-=2;
	        		x[1][n]=1;
	        		x[2][n]=1;
	        	}
	        }
        }
        else{
        	x[2][a/2]=1;
        	b--;
        	for(int n=1;n<=2;n++){
        		if(b==0)break;
        		for(int m=a/2-1;m>=1;m--){
        			if(b==0)break;
        			b-=2;
        			x[n][m]=1;
        			x[n][a-m-1]=1;
        		}
        	}
        }
        
        for(int n=0;n<4;n++){
        	for(int m=0;m<a;m++){
        		if(x[n][m]==0)System.out.print(".");
        		else System.out.print("#");
        	}
        	System.out.println();
        }
        
       
    }
     
     
}
