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
.....
.###.
.....
.....
//package contest980;

import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);
		int n = input.nextInt();
		int k = input.nextInt();
		int[][] a = new int[4][n];
		for (int i = 0; i < 4; i ++) {
			for (int j = 0; j < n; j ++) {
				a[i][j] = 0;
			}
		}
		for (int i = 1; i <= 2; i ++) {
			for (int j = 1; j < n / 2; j ++) {
				if (k <= 2) {
					break;
				}
				a[i][j] = 1;
				a[i][n-j-1] = 1;
				k = k - 2;
			}
		}
		if (k > 0) {
			a[1][n/2] = 1;
			k = k - 1;
		}
		if (k > 0) {
			a[2][n/2] = 1;
			k = k - 1;
		}
		System.out.println("YES");
		for (int i = 0; i < 4; i ++) {
			for (int j = 0; j < n; j ++) {
				System.out.printf("%c", a[i][j] == 0 ? '.' : '#');
			}
			System.out.println();
		}
		input.close();
	}
	
}
