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.*;
import java.io.*;
public class B{
	public static void main(String[] args) throws IOException
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(System.out);
		String[] s = br.readLine().trim().split(" ");
		int n = Integer.parseInt(s[0]);
		int k = Integer.parseInt(s[1]);
		System.out.println("Yes");
		if(k%2 == 0)
		{
			for(int i = 0; i < n; i++)System.out.print(".");
			System.out.println();
			System.out.print(".");
			for(int i = 0; i < k/2; i++) System.out.print("#");
			for(int i = 0; i < n - 1 - (k/2); i++) System.out.print(".");
			System.out.println();
			System.out.print(".");
			for(int i = 0; i < k/2; i++) System.out.print("#");
			for(int i = 0; i < n - 1 - (k/2); i++) System.out.print(".");
			System.out.println();
			for(int i = 0; i < n; i++)System.out.print(".");
			System.out.println();
		}
		else
		{
			for(int i = 0; i < n; i++)System.out.print(".");
			System.out.println();
			System.out.print(".");
			if(k >= n-2) for(int i = 0; i < n-2; i++)System.out.print("#");
			else
			{
				for(int i = 0; i < n/2 - k/2 - 1; i++) System.out.print(".");
				for(int i = 0; i < k; i++)System.out.print("#");
				for(int i = 0; i < n/2 - k/2 - 1; i++) System.out.print(".");
			}
			System.out.print(".");
			System.out.println();
			
			System.out.print(".");
			if(k >= n-2)
			{
				k = k  - (n-2);
				for(int i = 0; i < k/2; i++) System.out.print("#");
				for(int i = 0; i < n - k - 2; i++) System.out.print(".");
				for(int i = 0; i < k/2; i++) System.out.print("#");
			}
			else for(int i = 0; i < n-2; i++)System.out.print(".");
			System.out.print(".");
			System.out.println();
			
			for(int i = 0; i < n; i++)System.out.print(".");
			System.out.println();
		}
		
	}
}