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.Scanner;

public class Round480B {

    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        boolean[][] hotels = new boolean[4][n] ;

        if(k >= 4){
            int width = (k+1)/2;
            hotels[1][1] = true;
            hotels[2][1] = true;
            hotels[1][width] = true;
            hotels[2][width] = true;
            int left = k-4;
            for(int i = 2; i < width; i++){
                hotels[1][i] = true;
            }
            left -= width-2;
            for(int i = 0; i< left; i++){
                hotels[2][2+i] = true;
            }

        } else if(k%2==0){
            for(int i = 1; i < (k/2)+1; i++){
                hotels[1][i] = true;
                hotels[2][i] = true;
            }

        } else{
            if(k<=(n-2)) {
                int mid = n/2;
                hotels[1][mid] = true;
                for (int i = 1; i < (k / 2) + 1; i++) {
                    hotels[1][mid-i] = true;
                    hotels[1][mid+i] = true;
                }
            }
        }
        System.out.println("YES");
        StringBuilder sb = new StringBuilder();
        for(int i = 0; i < 4; i++){
            for (int j = 0; j < n; j++){
                sb.append(hotels[i][j]? '#':'.');
            }
            sb.append('\n');
        }
        System.out.print(sb.toString());
    }
}
