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 in = new Scanner(System.in);
        int n = in.nextInt();
        int k = in.nextInt();
        if (k%2==0){
            System.out.println("YES");
            for (int j=0;j<n;j++){
                System.out.print('.');
            }
            System.out.println();
            int t = k/2;
            for (int j=0;j<n;j++){
                if (j>0&&j<=t){
                    System.out.print('#');
                }else {
                    System.out.print('.');
                }
            }
            System.out.println();
            for (int j=0;j<n;j++){
                if (j>0&&j<=t){
                    System.out.print('#');
                }else {
                    System.out.print('.');
                }
            }
            System.out.println();
            for (int j=0;j<n;j++){
                System.out.print('.');
            }



        }else if (k<=n-2){//放中间
            System.out.println("YES");

            int t = (n-k)/2;

            for (int j=0;j<n;j++){
                System.out.print('.');
            }
            System.out.println();

            for (int j=1;j<=n;j++){
                if (j>=t+1&&j<=n-t){
                    System.out.print('#');
                }else {
                    System.out.print('.');
                }
            }
            System.out.println();

            for (int j=0;j<n;j++){
                System.out.print('.');
            }
            System.out.println();


            for (int j=0;j<n;j++){
                System.out.print('.');
            }

        }else if (k>=n){//封死一条 封死两边

            System.out.println("YES");

            for (int j=0;j<n;j++){
                System.out.print('.');
            }
            System.out.println();

            for (int j=0;j<n;j++){
                if (j==0||j==n-1) {
                    System.out.print('.');
                }else {
                    System.out.print('#');
                }
            }
            System.out.println();
            int t = k-n;
            int temp = 0;
            for (int j=1;j<=n;j++){
                if (j==2||j==n-1){
                    System.out.print('#');
                }else if (j==1||j==n){
                    System.out.print('.');
                }else if (temp<t){
                    temp++;
                    System.out.print('#');
                }else {
                    System.out.print('.');
                }
            }
            System.out.println();
            for (int j=0;j<n;j++){
                System.out.print('.');
            }


        }else if (k==n-1){
            System.out.println("YES");
            for (int j=0;j<n;j++){
                System.out.print('.');
            }
            System.out.println();

            for (int j=0;j<n;j++){
                if (j==0||j==n-1){
                    System.out.print('.');
                }else {
                    System.out.print('#');
                }
            }
            System.out.println();

            for (int i=1;i<=n;i++){
                if (i==(n+1)/2){
                    System.out.print('#');
                }else {
                    System.out.print('.');
                }
            }
            System.out.println();
            for (int j=0;j<n;j++){
                System.out.print('.');
            }

        }
    }
}
