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.util.*;

public class Main{

    public static void main(String[] args){
	Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
	int k = sc.nextInt();
	System.out.println("YES");

	char[][] city = new char[4][n];
	for(int i=0; i<4; i++)
	    for(int j=0; j<n; j++)
		city[i][j] = '.';
	if ( k % 2 == 0 ){
	    for(int i=1; i<k/2+1; i++){
		city[1][i] = '#';
		city[2][i] = '#';
	    }
	} else{
	    if ( k == 3 ){
		city[1][1] = '#';
		city[2][1] = '#';
		city[1][(n-2)/2+2] = '#';
	    } else if ( k == 1 ){
		city[1][n/2] = '#';
	    } else{
		int i = 1;
		while ( i < k/2){
		    city[1][i] = '#';
		    city[2][i] = '#';
		    i++;
		}
		city[1][i]='#';
		city[1][i+1]='#';
		city[2][i+1]='#';
	    }
	}

	
	for(int i=0; i<4; i++)
	    System.out.println(city[i]);
	
    }
}
