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 Marlin {
    public static void main (String[] args){
        Scanner sc = new Scanner(System.in);
        int cols = sc.nextInt();
        int numVil = sc.nextInt();

        System.out.println("YES");
        for(int i = 0; i < cols; i++){
            System.out.print(".");
        }

        System.out.println();

        if(numVil % 2 == 0) {
            for (int n = 0; n < 2; n++) {
                System.out.print(".");
                for (int c = 0; c < cols - 2; c++) {
                    if (c < numVil / 2) {
                        System.out.print("#");
                    } else {
                        System.out.print(".");
                    }
                }
                System.out.print(".");
                System.out.println();
            }
        }
        else {
           int odd = (numVil / 2) + 1;
           int even = numVil / 2;

           if((even % 2) != 0){
               int temp = even;
               even = odd;
               odd = temp;
           }

           int sideVil = even / 2;
           int padding = (cols - 2 - odd) / 2;
           int padding2 = ((cols - 2)/2) - sideVil;

           System.out.print(".");
            for(int i = 0; i < padding; i++) {
                System.out.print(".");
            }
            for(int i = 0; i < odd; i++) {
                System.out.print("#");
            }
            for(int i = 0; i < padding; i++) {
                System.out.print(".");
            }
            System.out.print(".");

            System.out.println();

            System.out.print(".");
            for(int i = 0; i < padding2; i++) {
                System.out.print(".");
            }
            for(int i = 0; i < sideVil; i++) {
                System.out.print("#");
            }
            System.out.print(".");

            for(int i = 0; i < sideVil; i++) {
                System.out.print("#");
            }

            for(int i = 0; i < padding2; i++) {
                System.out.print(".");
            }
            System.out.print(".");
            System.out.println();

        }

        for(int i = 0; i < cols; i++){
            System.out.print(".");
        }
    }
}
