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.Scanner;

public class marlin {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
         int n , k ;
         Scanner in = new Scanner(System.in) ;
         n = in.nextInt() ; k = in.nextInt() ; 
         char [][] arr = new char[4][n] ; 
         for(int i=0;i<4;i++){
        	 for(int j=0;j<n;j++){
        		 arr[i][j] = '.' ; 
        	 }
         }
         System.out.println("YES");
         if(k%2==0){
        	 int dist = 1 ;
        	 while(k>0 && dist<n/2){
        		 arr[1][n-dist-1] = '#' ; 
        		 arr[1][dist] = '#' ; 
        		 k -= 2 ;dist++;
        	 }
        	 dist =1 ;
        	 while(k>0 && dist<n/2){
        		 arr[2][n-dist-1] = '#' ; 
        		 arr[2][dist] = '#' ; 
        		 k -= 2 ;dist++;
        	 }
        	 if(k>0){
        		 arr[1][n/2] = '#' ; arr[2][n/2] ='#' ; 
        	 }
         }
         else{
        	 int dist = 1 ;
        	 while(k>1 && dist<n/2){
        		 arr[1][n-dist-1] = '#' ; 
        		 arr[1][dist] = '#' ; 
        		 k -= 2 ;dist++;
        	 }
        	 dist =1 ;
        	 while(k>1 && dist<n/2){
        		 arr[2][n-dist-1] = '#' ; 
        		 arr[2][dist] = '#' ; 
        		 k -= 2 ;dist++;
        	 }
        	 if(k==1){
        		 arr[1][n/2] = '#' ;
        	 }
        	 
         }
         for(int i=0;i<4;i++){
        	 for(int j=0;j<n;j++){
        		 System.out.print(arr[i][j]);
        	 }
        	 System.out.println();
         }
         
	}

}
