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
.....
.###.
.....
.....
// Marcelino Galarza
// May 8th, 2018

import java.util.*;

public class b
{

	public static int R = 4;
	public static int C;
	public static char grid[][];
	public static void main(String args[])
	{
		Scanner in = new Scanner(System.in);
		C = in.nextInt();
		int hotels = in.nextInt();
		grid = new char[R][C];
		for (int i = 0; i < R; i++)
			Arrays.fill(grid[i], '.');
		

		System.out.println("YES");
		for (int i = 1; i < R-1; i++)
		{	
			if (hotels%2==1 && hotels < C-2)
			{
				grid[i][C/2] = '#';
				hotels--;
			}
			for (int j = 1, x = C-2; j <= x && hotels > 0; j++, x--)
			{
				grid[i][x] = '#';
				grid[i][j] = '#';
				if (x == j)
					hotels--;
				else
					hotels-=2;
			}
		}

		for (int i = 0; i < R; i++)
			for (int j = 0; j < C; j++)
				System.out.print(grid[i][j] + (j == C-1 ? "\n" : ""));
		
		in.close();
	}
}
