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.util.StringTokenizer;

public class codeforces {
	static final long MOD = 1_000_000_007;
	public static void main(String[] args) {
		
		FS scan = new FS(System.in);
		int N = scan.nextInt(), K = scan.nextInt();
		
		char[][] mat = new char[4][N];
		for(int  i=0;i<4;i++)for(int j=0;j<N;j++)mat[i][j] = '.';
		if(K%2==0) {
			for(int i=0;i<K/2;i++) {
				for(int j=1;j<=2;j++) {
					mat[j][1+i] = '#';
				}
			}
		}else {
			if(K>=N-2) {
				K-=N-2;
				for(int i=1;i<N-1;i++)mat[1][i] = '#';
			}
			for(int i=1;K>1;K-=2,i++) {
				mat[2][N/2-i] = mat[2][N/2+i] = '#';
			}
			if(K==1)mat[2][N/2] = '#';
		}
		
		
		System.out.println("YES");
		for(int i=0;i<4;i++) {
			for(int j=0;j<N;j++) {
				System.out.print(mat[i][j]);
			}
			System.out.println();
		}
	}
	
	private static class FS {
		BufferedReader br;
		StringTokenizer st;
		public FS(InputStream in) {
			br = new BufferedReader(new InputStreamReader(in));
		}
		String next(){
			while(st==null||!st.hasMoreElements()){
				try{st = new StringTokenizer(br.readLine());}
				catch(IOException e){e.printStackTrace();}
			}
			return st.nextToken();
		}
		int nextInt() {return Integer.parseInt(next());}
		long nextLong() {return Long.parseLong(next());}
		double nextDouble() { return Double.parseDouble(next());}
	}
}
