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 static java.util.Arrays.*;
import static java.lang.Math.*;

public class B {
	static Scanner scan = new Scanner(System.in);
	
	
	public static void main(String[] args) {
		int n = scan.nextInt();
		int k = scan.nextInt();
		char[][]B = new char[4][n];
		for(char[]b:B)fill(b,'.');
		
		if(k%2==1){
			B[1][n/2]='#';
			k--;
		}else if(k>1){
			B[1][n/2]=B[2][n/2]='#';
			k-=2;
		}
		for(int i=1;i<n/2;i++){
			for(int j=1;j<3;j++){
				if(k>0){
					B[j][i]=B[j][n-i-1]='#';
					k-=2;
				}
			}
		}
		System.out.println("YES");
		for(char[]b:B)System.out.println(new String(b));
	}
}
