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 B {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int k = sc.nextInt();
		char[][] grid = new char[4][n];
		
		if(k%2==0){
			System.out.println("YES");
			for(int i=0;i<n;i++){
				for(int j=0;j<4;j++){
					if(i==0 || i==n-1 || j==0 || j==3)
						grid[j][i] = '.';
					else{
						if(k>0){
							grid[j][i] = '#';
							k--;
						}
						else
							grid[j][i] = '.';
					}
						
				}
			}
			for(int i=0;i<4;i++){
				for(int j=0;j<n;j++){
					System.out.print(grid[i][j]);
				}
				System.out.println();
			}
		}
		else{
		
				System.out.println("YES");
				int kk = k;
				int il=0;
				int jl=0;
			for(int i=0;i<4;i++){
				for(int j=0;j<n;j++){
					if(i==0 || i==3 || j==0 || j==(n-1))
						grid[i][j] = '.';
					else{
						if(k>0 && j>=(n-k)/2 && i==1){
							grid[i][j] = '#';
							k--;
							if(k==0){
								il=i;
								jl=j;
							}
						}
						else if(k>0 && i==2){
							grid[i][j] = '#';
							k--;
							if(k==0){
								il=i;
								jl=j;
							}
						}
						else
							grid[i][j] = '.';
					}
						
				}
			}
			if(il==2){
				grid[il][jl] = '.';
				grid[il][n-2] = '#';
			}
			for(int i=0;i<4;i++){
				for(int j=0;j<n;j++){
					System.out.print(grid[i][j]);
				}
				System.out.println();
			}
			
		}
	}

}
