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 Main {

    public static void main(String[] args) {

        Scanner sc= new Scanner(System.in);
        int f=0,j=0;
        f=sc.nextInt();
        Boolean p=false ;
        int x=0,y=0;
        j=sc.nextInt();
        if(j>(f-2)*2){
            System.out.println("NO");
        }else {
            System.out.println("YES");
            if (j % 2 == 0) {
                for (int i = 0; i < 4; i++) {
                    x = j / 2;
                    for (int k = 0; k < f; k++) {
                        if (i != 0 && i != 3 && i != 0 && k != f - 1 && x != 0 && k != 0) {
                            System.out.print("#");
                            x--;
                        } else
                            System.out.print(".");
                    }
                    System.out.println();


                }

            } else
                for (int i = 0; i < 4; i++) {
                    if (i == 1 && j > f - 2) {
                        x = f - 2;
                        j -= f - 2;
                    } else if (j <= f - 2 && i != 0) {
                        x = j;
                        j = 0;
                    }
                    y = x / 2;

                    for (int k = 0; k < f; k++) {
                        if (i != 3 && k != f - 1 && x != 0 && k != 0 && i != 0 && (y - k >= 0 || f - k - 1 <= y)) {
                            System.out.print("#");
                            x--;
                        } else {
                            if (k == f / 2 && i != 0 && i != 3 && k != f - 1 && k != 0 && i != 2) {
                                System.out.print("#");
                                x--;
                            } else {
                                System.out.print(".");
                            }
                        }

                    }


                    System.out.println("");

                }
        }

    }
}