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.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc = new Scanner(System.in);
	int n = sc.nextInt();
	int k = sc.nextInt();
	char arr[][] = new char[7][n+4];
	for(int i=0;i<=4;i++){
		Arrays.fill(arr[i],'.');
	}
	if(k==(2*(n-2))){
		for(int i=2;i<=3;i++){
			int p=1;
			while(k>0){
				arr[i][1+p] = '#';
				arr[i][n-p] = '#';
				k-=2;
				p++;
				if(p>=n/2){
					break;
				}
			}
			
		}
		arr[2][n/2+1] = '#';
		arr[3][n/2+1] = '#';
	} else if(k%2==0){
		for(int i=2;i<=3;i++){
			
			int p=1;
			while(k>0){
				arr[i][1+p] = '#';
				arr[i][n-p] = '#';
				k-=2;
				p++;
				if(p>=n/2){
					break;
				}
			}
			
		}	
	} else{
		arr[2][n/2+1] = '#';
		k--;
		for(int i=2;i<=3;i++){
			
			int p=1;
			while(k>0){
				arr[i][1+p] = '#';
				arr[i][n-p] = '#';
				k-=2;
				p++;
				if(p>=n/2){
					break;
				}
			}
			
		}		
	}
	System.out.println("YES");
		for(int i=1;i<=4;i++){
		for(int ii=1;ii<=n;ii++){
			System.out.print(arr[i][ii]);
		} System.out.println();
	}
	}
}