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.math.*;
public class Main
{
	public static void main(String[] args) {
		Scanner sc=new Scanner(System.in);
	    int n=sc.nextInt();
	    int k=sc.nextInt();
	    char[][] arr=new char[4][n];
	    for(int i=0;i<4;i++)
	    Arrays.fill(arr[i],'.');
	    
		System.out.println("YES");
		
		int i=n/2-1;
		if(k%2==1)
		{
		    arr[1][n/2]='#';
		    k--;
		}
		else if(k>0&&k%2==0)
		{
		    arr[1][n/2]=arr[2][n/2]='#';
		    k-=2;
		}
		int l=1;
		while(k>0)
		{
		  if(i==0)
		  {l=2;i=(n/2)-1;}
		  arr[l][i]=arr[l][i+2*(n/2-i)]='#';
		  i--;
		  k-=2;
		}
		for(i=0;i<4;i++)
		{
		    for(int j=0;j<n;j++)
		    System.out.print(arr[i][j]);
		    System.out.println("");
		}
	}
}