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 Main {

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);
			
		int n = sc.nextInt();
		int m= sc.nextInt();
		
		char [][] p = new char[4][n];
		for (int i =0;i<4;i++)
			Arrays.fill(p[i], '.');
		
		if (m%2==0 && m>0) {
			p[1][n/2]='#';
			p[2][n/2]='#';
			m-=2;
		}else if (m%2!=0) {
			
			p[1][n/2]='#';
			m--;
		}
		//System.out.println(m);
		for (int i=1;i<3;i++) {
			if(m==0)
				break;
			int j=1,k=n-2;
			while(j<k) {
				p[i][j]='#';
				m--;
				j++;
				if (m==0)
					break;
				p[i][k]='#';
				m--;
				k--;
				if (m==0)
					break;
			}
		}
		if(m>0)System.out.println("NO");
		else
		{
			System.out.println("YES");
			for (int i =0;i<4;i++) {
				for (int j =0;j<n;j++) {
					System.out.print(p[i][j]);
				}
				System.out.println();
			}
		}
		
		sc.close();

	}

}
