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.*;

public class A
{
       public static void main(String args[])
       {
              Scanner sc=new Scanner(System.in);
              int n=sc.nextInt();
              int k=sc.nextInt();
              int t=k;
              if(t<=2*(n-2))
              {
                     System.out.println("YES");
              for(int i=0;i<4;i++)
              {
                     for(int j=0;j<n;j++)
                     {
                            if(i==0 || i==3 || j==0 || j==n-1 || k==0)
                                   System.out.print(".");
                            else if(k>=n-2)
                            {
                                   k--;
                                   System.out.print("#");
                            }
                            else
                            {
                                   if(t%2==1 && j==(n/2) && k!=0)
                                   {
                                          k--;
                                          System.out.print("#");
                                   }
                                   else if(j<=t/2 && k!=0)
                                   {
                                          k--;
                                          System.out.print("#");
                                   }
                                   else if(j>=(n-(t/2)-1) && k!=0)
                                   {
                                          k--;
                                          System.out.print("#");
                                   }
                                   else
                                          System.out.print(".");
                            }
                     }
                     t=k;
                     System.out.println();
              }
              }
              else
                     System.out.println("NO");
       }
}
