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.io.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;

public class Marlin {
    public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    PrintWriter out = new PrintWriter(System.out);

    int n = sc.nextInt(), k = sc.nextInt();
        out.println("YES");
    char[][] a = new char[4][n];
        for (char[] aa:a) Arrays.fill(aa,'.');
        for (int c = 0; c < (n - 2) / 2; c++) {
        for (int row = 1; row < 3; row++) {
            if(k>1){
                a[row][c+1]='#';
                a[row][n-2-c]='#';
                k-=2;
            }
        }
    }
    int row=1;
        while(k>0){
        k--;
        a[row++][n/2]='#';
    }

        for (char[] aa : a)
            out.println(new String(aa));

        out.flush();
}
}
