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