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.*;
public class A{
	public static void main(String[] args) {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		int k = scan.nextInt();
		char arr[][] = new char[4][n];
		for(char a[] : arr)
			Arrays.fill(a,'.');
		if (k == 2*(n-2))
		{
			for(int i = 1;i<=2;i++)
				for(int j = 1;j<n-1;j++)
					arr[i][j] = '#';
		}
		else
		{
			boolean odd = false;
			if (k%2!=0)
			{
				k--;
				odd = true;
			}
			int f,e;
			for(int i = 1;i <= 2;i++)
			{
				if (k == 0)
					break;
				for(int j = 1;j<n-1;j++)
				{
					f = j;
					e = n-j-1;
					if (f == e && !odd)
						break;
					else if (f == e && odd)
					{
						arr[i][f] = arr[i][e] = '#';
						break;
					}
					arr[i][f] = arr[i][e] = '#';
					k-=2;
					if (k == 0)
						break;
				}
			}
			if (odd)
				arr[1][(n)/2] = '#'; 
		}
		System.out.println("YES");
		for(int i = 0;i < 4;i++)
		{
			for(int j = 0;j < n;j++)
				System.out.print(arr[i][j]);
			System.out.println();
		}

	}
}