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
.....
.###.
.....
.....
//Meet Arora 2016055

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.InputStream;
import java.util.*;


public class b{
	public static void main(String[] args) throws IOException {
		Reader.init(System.in);
		int n = Reader.nextInt();
		int k = Reader.nextInt();

		int row = 4;
		int col = n;

		char[][] matrix = new char[4][n];
		if(k%2==0) {
			for (int i=0; i<col; i++) {
				for (int j=0; j<row; j++) {
					if ((j==1 || j==2) && (i!=0 && i!=n-1)) {
						if (k>0) {
							matrix[j][i]='#';
							k--;
						}
						else {
							matrix[j][i]='.';
						}
					}
					else {
						matrix[j][i]='.';
					}
				}
			}
			System.out.println("YES");
		}
		else {
			for (int i=0; i<row; i++) {
				for (int j=0; j<col; j++) {
					matrix[i][j]='.';
				}
			}

			int mid = n/2;
			matrix[1][mid]='#';
			k--;
			int i, j;
			for ( i=mid-1,  j=mid+1; i>0 && j<n-1; i--, j++) {
				if (k>0) {
					matrix[1][i]='#';
					matrix[1][j]='#';
					k-=2;
				}
			}
			for ( i=n-2, j=1; i>mid && j<mid; i--, j++) {
				if (k>0) {
					matrix[2][i]='#';
					matrix[2][j]='#';
					k-=2;
				}
			}
			if (k==1) {
				matrix[2][mid]='#';
			}
			System.out.println("YES");
		}

		for (int i=0; i<row; i++) {
			for (int j=0; j<col; j++) {
				System.out.print(matrix[i][j]);
			}
			System.out.println();
		}
	}
}

class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /**
     * call this method to initialize reader for InputStream
     */
    static void init(InputStream input) {
        reader = new BufferedReader(
                new InputStreamReader(input));
        tokenizer = new StringTokenizer("");
    }

    /**
     * get next word
     */
    static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                    reader.readLine());
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

	static long nextLong() throws IOException {
		return Long.parseLong(next());
	}

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
}
