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.math.BigDecimal;
import java.math.BigInteger;
import java.math.MathContext;
import java.math.RoundingMode;
import java.util.*;

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

            System.out.print(".");
            int cols = k / 2;
            for(int i = 0; i < cols; i++) {
                System.out.print("#");
            }
            for(int i = cols+1; i < n;i++) {
                System.out.print(".");
            }
            System.out.println();

            System.out.print(".");
            for(int i = 0; i < cols; i++) {
                System.out.print("#");
            }
            for(int i = cols+1; i < n;i++) {
                System.out.print(".");
            }
            System.out.println();

            for(int i = 0; i < n; i++) {
                System.out.print(".");
            }
            System.out.println();
        }  /*else if(k <= n-2) {
            System.out.println("YES");
            for(int i = 0; i < n; i++) {
                System.out.print(".");
            }
            System.out.println();

            int temp = (n-k)/2;
            for(int i = 0; i < temp; i++) {
                System.out.print(".");
            }
            for(int i = 0; i < k; i++) {
                System.out.print("#");
            }
            for(int i = 0; i < temp; i++) {
                System.out.print(".");
            }
            System.out.println();

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

            for(int i = 0; i < n; i++) {
                System.out.print(".");
            }
            System.out.println();
        } */else {
            System.out.println("YES");
            for(int i = 0; i < n; i++) {
                System.out.print(".");
            }
            System.out.println();


            if(k <= n-2) {
                int temp = (n-k)/2;
                for(int i = 0; i < temp; i++) {
                    System.out.print(".");
                }
                for(int i = 0; i < k; i++) {
                    System.out.print("#");
                }
                for(int i = 0; i < temp; i++) {
                    System.out.print(".");
                }
                System.out.println();

                for(int i = 0; i < n; i++) {
                    System.out.print(".");
                }
                System.out.println();
            } else {
                System.out.print(".");
                for(int i = 0; i < n-2; i++) {
                    System.out.print("#");
                }
                System.out.print(".");
                System.out.println();

                k -= n-2;
                System.out.print(".");
                int temp = k/2;
                for(int i = 0; i < temp; i++) {
                    System.out.print("#");
                }
                for(int i = 0; i < n-2-k; i++) {
                    System.out.print(".");
                }
                for(int i = 0; i < temp; i++) {
                    System.out.print("#");
                }
                System.out.print(".");
                System.out.println();
            }


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

}