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 k=sc.nextInt();
		int x=(n-2)*2;
		int test=0;
		int i;
		int t=(n-2)/2;
		char a[][]=new char[2][n-2];
		for(i=0;i<n-2;i++) {
			a[0][i]='.';
			a[1][i]='.';
		}
		if(k<=x) {
			if(k%2==0) {
			for(i=0;i<k/2;i++) {
				a[0][i]='#';
				a[1][i]='#';
			}
			test=1;
			}
			else if(k<=(n-2)) {
				for(i=0;i<=(k/2);i++) {
					a[0][t+i]='#';
					a[0][t-i]='#';
				}
				test=1;
			}
			else {
				test=1;
				for(i=0;i<(n-2);i++) {
					a[0][i]='#';
				}
				for(i=0;i<((k-n+2)/2);i++) {
					a[1][i]='#';
					a[1][n-3-i]='#';
				}
			}
		}
		if(test==0) {
			System.out.println("NO");
		}
		else if(test==1){
			System.out.println("YES");
			for(i=0;i<n;i++) {
				System.out.print(".");
			}
			System.out.println();
			System.out.print(".");
			for(i=0;i<(n-2);i++) {
				System.out.print(a[0][i]);
			}
			System.out.println(".");
			System.out.print(".");
			for(i=0;i<(n-2);i++) {
				System.out.print(a[1][i]);
			}
			System.out.println(".");
			for(i=0;i<n;i++) {
				System.out.print(".");
			}
		}
	}
}