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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class B2 {

	public static void main(String[] args) {
		FastScanner fs=new FastScanner();
		int width=fs.nextInt()-2;
		int toPlace=fs.nextInt();
		
		boolean[][] board=new boolean[width][2];
		if (toPlace>=width) {
			toPlace-=width;
			for (int i=0; i<width; i++) {
				board[i][0]=true;
			}
		}
		for (int i=0; i<toPlace/2; i++) {
			board[i][1]=true;
			board[width-i-1][1]=true;
		}
		if (toPlace%2==1) {
			board[width/2][1]=true;
		}
		/*else if (toPlace%2==0) {
			for (int i=0; i<toPlace/2; i++)
				board[i][1]=board[i][0]=true;
		}*/
		System.out.println("YES");
		for (int i=0; i<width+2; i++) {
			System.out.print('.');
		}
		System.out.println();
		System.out.print('.');
		for (int i=0; i<width; i++)
			System.out.print(board[i][0]?'#':'.');
		System.out.println('.');
		System.out.print('.');
		for (int i=0; i<width; i++)
			System.out.print(board[i][1]?'#':'.');
		System.out.println('.');
		for (int i=0; i<width+2; i++) {
			System.out.print('.');
		}
//		System.out.println();
	}

	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		public String next() {
			while (!st.hasMoreElements())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					// TODO Auto-generated catch block
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		public int nextInt() {
			return Integer.parseInt(next());
		}
		
		public int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++)
				a[i]=nextInt();
			return a;
		}
	}
	
}
