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.Scanner;
public class B {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt(), k = sc.nextInt();
		int r = 2, c = n - 2;
		boolean[][] mid = new boolean[r][c];
		if(k > r * c){
			System.out.println("NO");
			return;
		}
		for(int i = 0; i < c; ++i){
			if(k < 2) break;
			int cr = i % 2, cc = i / 2;
			mid[cr][cc] = true;
			mid[cr][c - 1 - cc] = true;
			if(cc == c - 1 - cc) k--;
			else k -= 2;
		}
		if(k == 1){
			mid[r - 1][c / 2] = true;
		}
		
		System.out.println("YES");
		for(int i = -1; i < r + 1; ++i){
			for(int j = -1; j < c + 1; ++j){
				if(i >= 0 && i < r && j >= 0 && j < c && mid[i][j]){
					System.out.print('#');
				}
				else{
					System.out.print('.');
				}
			}
			System.out.println();
		}
	}
}