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.Scanner;

public class B {

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int k = in.nextInt();
		System.out.println("YES");

		if((k % (n - 2)) == 0) {
			print(n, '.');
			System.out.println();
			int r = k / (n - 2);
			for(int i = 0; i < r; i++) {
				System.out.print('.');
				print(n - 2, '#');
				System.out.println('.');
			}
			for(int i = 0; i < 4 - r - 1; i++) {
				print(n, '.');
				System.out.println();
			}
		} else if(k % 2 == 0) {
			print(n, '.');
			System.out.println();
			int r = k / 2;
			for(int i = 0; i < 2; i++) {
				System.out.print('.');
				print(r, '#');
				print(n - r - 2, '.');
				System.out.println('.');
			}
			print(n, '.');
			System.out.println();
		} else if(k <= n - 2 && k % 2 == 1) {
			print(n, '.');
			System.out.println();
			print((n - k) / 2, '.');
			print(k, '#');
			print((n - k) / 2, '.');
			System.out.println();
			print(n, '.');
			System.out.println();
			print(n, '.');
			System.out.println();
		} else {
			print(n, '.');
			System.out.println();
			print(1, '.');
			print(n - 2, '#');
			System.out.println('.');
			k -= n - 2;
			print((n - k) / 2, '.');
			print(k - 1, '#');
			print(1, '.');
			print(1, '#');
			print((n - k) / 2, '.');
			System.out.println();
			print(n, '.');
			System.out.println();
		}
		in.close();
	}

	static void print(int n, char c) {
		for(int i = 0; i < n; i++) {
			System.out.print(c);
		}
	}
}