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 Test{
    
    public static void main(String[] args){
        Scanner input = new Scanner(System.in);
        int shir = input.nextInt();
        int hotels = input.nextInt();
        
        if (hotels % 2 == 0 && hotels <= (shir - 2) * 2){
            System.out.println("YES");
            paintLine(shir);
            paintEvenLine(shir, hotels / 2);
            paintEvenLine(shir, hotels / 2);
            paintLine(shir);
        } else if (hotels % 2 != 0 && hotels <= (shir - 2)){
    //    } else if (hotels % 2 != 0 && hotels <= (shir - 2)){
            System.out.println("YES");
            paintLine(shir);
            paintSymLine(shir, hotels);
            paintLine(shir);
            paintLine(shir);
        } else if (hotels % 2 != 0 && hotels > (shir - 2) && hotels <= (shir - 2) * 2){
            System.out.println("YES");
            paintLine(shir);
            paintEvenLine(shir, shir - 2);
            int new_hotels = hotels - (shir - 2);
            paintInvertedLine(shir, new_hotels);
            //System.out.println(new_hotels);
            paintLine(shir);
        } else {
            System.out.println("NO");
        }
        
        
        
        
    }
    
    static void paintLine(int n){
        for (int i = 0; i < n - 1; i++){
            System.out.print(".");
        }
        System.out.println(".");
    }
    
    static void paintEvenLine(int n, int even){
        System.out.print(".");
        for (int i = 0; i < even; i++){
            System.out.print("#");
        }
        for (int i = 0; i < n - even - 2; i++){
            System.out.print(".");
        }
        System.out.println(".");
    }
    
    
        static void paintInvertedLine(int n, int hotels){
        System.out.print(".#");
        for (int i = 0; i < n - (hotels - 1) - 3; i++){
            System.out.print(".");
        }
        for (int i = 0; i < hotels - 1; i++){
            System.out.print("#");
        }
        System.out.println(".");
    }
    static void paintSymLine(int n,int hotels){
        System.out.print(".");
        for (int i = 0; i < ((n - hotels) / 2) - 1; i++){
            System.out.print(".");
        }
        for (int i = 0; i < hotels; i++){
            System.out.print("#");
        }
        for (int i = 0; i < ((n - hotels) / 2) - 1; i++){
            System.out.print(".");
        }
        System.out.println(".");
    }
}