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 B_Marlin {
    private static Scanner scanner = new Scanner(System.in);

    public static void main(String[] args) {
        int n = scanner.nextInt();
        int k = scanner.nextInt();

        String dot = "";
        for (int i = 0; i < n; i++) {
            dot += ".";
        }

        String hotelAndDot = ".";
        if (k % 2 == 0) {
            // Correct
            System.out.println("YES");
            System.out.println(dot);
            System.out.println(evenK(n, k));
            System.out.println(evenK(n, k));
            System.out.println(dot);
        } else if (k < 2 * (n - 2)) {
            System.out.println("YES");
            System.out.println(dot);
            hotelAndDot = ".";
            if (k <= n - 2) {
                System.out.println(f(n,k));
                System.out.println(dot);
                System.out.println(dot);
            } else {
                String hotel = ".";
                for (int i = 0; i < n-2; i++) {
                    hotel+="#";
                }
                hotel+=".";
                System.out.println(hotel);
                k = k - (n - 2);
                hotelAndDot = ".";
                int remainDot = (n - 2) - k;
                hotel = "";
                for (int i = 0; i < k/2; i++) {
                    hotel += "#";
                }
                String remainDotString = "";
                for (int i = 0; i < remainDot / 2; i++) {
                    remainDotString += ".";
                }
                hotelAndDot += hotel;
                hotelAndDot += remainDotString;
                hotelAndDot+=".";
                hotelAndDot += remainDotString;
                hotelAndDot += hotel;
                hotelAndDot += ".";
                System.out.println(hotelAndDot);
                System.out.println(dot);
            }
        } else {
            System.out.println("NO");
        }
    }

    private static String f(int n, int k) {
        String hotelAndDot = ".";
        int k2 = (k - 1) / 2;
        int remainDot = (n - 2) - k;
        String hotel = "";
        for (int i = 0; i < k2; i++) {
            hotel += "#";
        }
        String remainDotString = "";
        for (int i = 0; i < remainDot / 2; i++) {
            remainDotString += ".";
        }
        hotelAndDot += hotel;
        hotelAndDot += remainDotString;
        hotelAndDot += "#";
        hotelAndDot += remainDotString;
        hotelAndDot += hotel;
        hotelAndDot += ".";
        return hotelAndDot;
    }

    private static String evenK(int n, int k) {
        String hotelAndDot = ".";
        for (int i = 0; i < k / 2; i++) {
            hotelAndDot += "#";
        }
        for (int i = 0; i < (n - 2) - (k / 2); i++) {
            hotelAndDot += ".";
        }
        hotelAndDot += ".";
        return hotelAndDot;
    }

}
