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 Main
{
	static int n,k;
	public static void main(String[] args)
	{
		Scanner sc = new Scanner(System.in);
		n=sc.nextInt();
		k=sc.nextInt();
		char[][] grid = new char[4][n];
		for(int i=0;i<4;i++)
			Arrays.fill(grid[i], '.');
		if(k%2==0) 
		{
			int j = 1;
			while(k>0)
			{
				k-=2;
				grid[1][j]=grid[2][j] = '#';
				j++;
			}
		}
		else
		{
			int mid = n/2;
			grid[1][mid] = '#';
			k--;
			for(int d=1;d<n/2 && k>0;k-=2,d++)
				grid[1][mid+d] = grid[1][mid-d] = '#';
			for(int d=1;d<n/2 && k>0;k-=2,d++)
				grid[2][mid+d] = grid[2][mid-d] = '#';
		}
		System.out.println("YES");
		for(int i=0;i<4;i++)
		{
			for(int j=0;j<n;j++)
				System.out.print(grid[i][j]);
			System.out.println();
		}
	}
}
 