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.io.*;
import java.util.*;

public class Codeforces480Div2B {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] sp = br.readLine().split(" ");
		int n = Integer.parseInt(sp[0]);
		int k = Integer.parseInt(sp[1]);
		
		System.out.println("YES");
		char[][] table = new char[4][n];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < 4; j++) {
				table[j][i] = '.';
			}
		}
		
		if (k%2 == 0) {
			for (int i = 1; i <= k/2; i++) {
				for (int j = 1; j <= 2; j++) {
					table[j][i] = '#';
				}
			}
		}
		else if (k <= (n-2)) {
			for (int i = (n-k)/2; i <= (n+k-2)/2; i++) {
				table[1][i] = '#';
			}
		}
		else {
			for (int i = 1; i < n-1; i++) {
				for (int j = 1; j <= 2; j++) {
					table[j][i] = '#';
				}
			}
			k = 2*(n-2)-k;
			for (int i = (n-k)/2; i <= (n+k-2)/2; i++) {
				table[1][i] = '.';
			}
		}
		
		//print
		for (int j = 0; j < 4; j++) {
			for (int i = 0; i < n; i++) {
				System.out.print(table[j][i]);
			}
			System.out.println();
		}
	}

}
