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 h = in.nextInt();
		System.out.println("YES");
		for(int i = 0; i < n; i++) {
			System.out.print(".");
		}
		System.out.println();

		boolean world[][] = new boolean[2][n];
		for(int i = 1; i < n/2; i++) {
			if(h >= 2) {
				h-= 2;
				world[0][i] = true;
				world[0][n - 1 - i] = true;
			}
		}
		for(int i = 1; i < n/2; i++) {
			if(h >= 2) {
				h-= 2;
				world[1][i] = true;
				world[1][n - 1 - i] = true;
			}
		}
		if(h == 2) {
			world[0][n/2 ]=true;
			world[1][n/2] = true;
		}
		if(h == 1) {
			world[0][n/2 ] = true;
		}
		for(int i = 0; i < n; i++) {
			if(world[0][i]) {
				System.out.print('#');
			} else {
				System.out.print('.');
			}
		}System.out.println();
		for(int i = 0; i < n; i++) {
			if(world[1][i]) {
				System.out.print('#');
			} else {
				System.out.print('.');
			}
		}System.out.println();
		for(int j = 0; j < n; j++) {
			System.out.print(".");
		}
	}
}
