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.Closeable;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.ListIterator;
import java.util.Map.Entry;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
 
public class B {
	
	public static void main(String[] args) throws IOException {
		try (Scanner sc = new Scanner(System.in)) {
			final int n = sc.nextInt();
			int k = sc.nextInt();
			
			boolean[][] map = new boolean[4][n];
			if(k % 2 == 0) {
				for(int j = 1; j < n - 1 && k > 0; j++) {
					map[1][j] = map[2][j] = true;
					k -= 2;
				}
			}else if(k % 2 != 0){
				if(k >= 1) { map[1][n / 2] = true; k--; }
				for(int j = 1; j < (n / 2) && k > 0; j++) {
					map[1][n / 2 - j] = true; k--;
					map[1][n / 2 + j] = true; k--;
				}
				
				if(k >= 2) {
					if(n - 2 == 1) {
						map[2][1] = map[2][n - 2] = true; k -= 1; 
					}else {
						map[2][1] = map[2][n - 2] = true; k -= 2; 
					}
					
					for(int j = 2; j < n - 2 && k > 0; j++) {
						map[2][j] = true; k--;
					}
				}
			}
			
			if(k == 0) {
				System.out.println("YES");
				for(int i = 0; i < 4; i++) {
					for(int j = 0; j < n; j++) {
						System.out.print(map[i][j] ? "#" : ".");
					}
					System.out.println();
				}
			}else {
				System.out.println("NO");
			}
		}
	}
	
	public static class Scanner implements Closeable {
		private BufferedReader br;
		private StringTokenizer tok;
 
		public Scanner(InputStream is) throws IOException {
			br = new BufferedReader(new InputStreamReader(is));
		}
 
		private void getLine() throws IOException {
			while (!hasNext()) {
				tok = new StringTokenizer(br.readLine());
			}
		}
 
		private boolean hasNext() {
			return tok != null && tok.hasMoreTokens();
		}
 
		public String next() throws IOException {
			getLine();
			return tok.nextToken();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
 
		public int[] nextIntArray(int n) throws IOException {
			final int[] ret = new int[n];
			for (int i = 0; i < n; i++) {
				ret[i] = this.nextInt();
			}
			return ret;
		}
 
		public long[] nextLongArray(int n) throws IOException {
			final long[] ret = new long[n];
			for (int i = 0; i < n; i++) {
				ret[i] = this.nextLong();
			}
			return ret;
		}
 
		public void close() throws IOException {
			br.close();
		}
	}
}