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.*;
import java.io.*;
public class grid_new{
    public static void main(String[] args)throws IOException {
        Scanner in=new Scanner(System.in);
        //int t=in.nextInt();
        //while(t-->0)
        //{
        int n=in.nextInt();
        int k=in.nextInt();
        int i,j;
        int l=k/2,m=(n-2)-k,s=k,a=(k-(n-2))/2;
        System.out.println("YES");
        for(i=0;i<4;i++)
        {
            for(j=0;j<n;j++)
            {
                if(i==0 || i==3)
                System.out.print(".");
                else if(j==0 || j==(n-1))
                System.out.print(".");
                else
                {
                    if(k%2==0)
                    {
                        if(j<=l)
                        System.out.print("#");
                        else
                        System.out.print(".");
                    }
                    else
                    {
                    if(k>=(n-2) && i==1)
                    {
                        System.out.print("#");
                        
                    }
                    else if(k<(n-2) && i==1)
                    {
                        if(j>=(n-k)/2 && s>0)
                        {
                            System.out.print("#");
                            s--;
                        }
                        else
                        System.out.print(".");
                    }
                    else if(k>(n-2) && i==2)
                    {
                        if((n-1-j)<=a || j<=a)
                        System.out.print("#");
                        else
                        System.out.print(".");
                    }
                    else
                    System.out.print(".");
                }
                }
            }
            System.out.println();
        }
   //}
    }
}