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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class ProblemB {
	static Scanner in = new Scanner(System.in);
	static PrintWriter out = new PrintWriter(System.out);

	public static void main(String[] args) throws IOException {
		int n = in.nextInt(), k = in.nextInt();
		boolean hotel[][] = new boolean[4][n];
		int row = 1;
		if (n == 3) {
			System.out.println("YES");
			for (int i = 0; i < 4; i++) {
				for (int j = 0; j < 3; j++) {
					if (i > 0 && j == 1) {
						if (k > 0) {
							k--;
							System.out.print("#");
						} else
							System.out.print(".");
					} else
						System.out.print(".");
				}
				System.out.println();
			}
			return;
		}
		while (k > 1 && row < 3) {
			for (int i = 1; i < n / 2 && k > 1; i++) {
				hotel[row][i] = hotel[row][n - i - 1] = true;
				k -= 2;
			}
			row++;//
		}
		row = 1;
		while (k-- > 0)
			hotel[row++][n / 2] = true;

		out.println("YES");
		for (int i = 0; i < 4; i++) {
			for (int j = 0; j < n; j++) {
				out.print(!hotel[i][j] ? "." : "#");
			}
			out.println();
		}
		out.flush();
	}

	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		public Scanner(InputStream s) {
			// TODO Auto-generated constructor stub
			br = new BufferedReader(new InputStreamReader(s));
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public String next() throws IOException {
			if (st == null || !st.hasMoreElements())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws NumberFormatException, IOException {
			return Integer.parseInt(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}
	}
}