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_Task_980 {

    public static void main(String... args) {
        Scanner scanner = new Scanner(System.in);
        int width = scanner.nextInt();
        int hotels = scanner.nextInt();
        int availableSpace = 2 * (width - 2);

        int resultConfig = 0;
        if (hotels <= (width - 2) && hotels % 2 == 1) {
            resultConfig = 1;
        } else if (hotels <= availableSpace && hotels % 2 == 0) {
            resultConfig = 2;
        } else if (hotels <= availableSpace && hotels % 2 == 1) {
            resultConfig = 3;
        }

        //output result
        if (resultConfig > 0) {
            System.out.println("YES");
            printLineOfDots(width, true);
            if (resultConfig == 1) {
                int sideWays = (width - hotels) / 2;
                printLineOfDots(sideWays, false);
                for (int i = 0; i < hotels; i++) {
                    System.out.print('#');
                }
                printLineOfDots(sideWays, true);
                printLineOfDots(width, true);
            } else if (resultConfig == 2) {
                int hotelsPerRow = hotels / 2;
                int rightSideway = width - 1 - hotelsPerRow;
                System.out.print('.');
                for (int i = 0; i < hotelsPerRow; i++) {
                    System.out.print('#');
                }
                printLineOfDots(rightSideway, true);
                System.out.print('.');
                for (int i = 0; i < hotelsPerRow; i++) {
                    System.out.print('#');
                }
                printLineOfDots(rightSideway, true);
            } else {
                int emptySpace = availableSpace - hotels;
                System.out.print('.');
                for (int i = 0; i < width-2; i++) {
                    System.out.print('#');
                }
                System.out.println('.');
                int lowerHotels = hotels - (width - 2);
                int leftHotels = lowerHotels / 2;
                System.out.print('.');
                for (int i = 0; i < leftHotels; i++) {
                    System.out.print('#');
                }
                printLineOfDots(emptySpace, false);
                for (int i = 0; i < leftHotels; i++) {
                    System.out.print('#');
                }
                System.out.println('.');
            }
            printLineOfDots(width, true);
        } else {
            System.out.print("NO");
        }
    }

    private static void printLineOfDots(int count, boolean toNextLine) {
        for (int i = 0; i < count; i++) {
            System.out.print('.');
        }
        if (toNextLine) {
            System.out.print("\n");
        }
    }
}
