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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;
public class test{
	 public static void main(String[] args) throws IOException{
		 //Scanner in = new Scanner(System.in);
		 BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
         StringTokenizer st = new StringTokenizer(br.readLine());
         int n = Integer.parseInt(st.nextToken());
         int k = Integer.parseInt(st.nextToken());
         
         int [][] arr = new int[5][n+2];
         for(int i = 1;i<=4;i++){
        	 for(int j = 1;j<=n;j++){
        		 arr[i][j] = '.';
        	 }
         }
         System.out.println("YES");
         if(k%2 == 0){
        	 for(int i = 1;i<=(k/2);i++){
        		 arr[2][i+1] = '#';
        		 arr[3][i+1] = '#';
        	 }
        	 for(int i = 1;i<=4;i++){
        		 for(int j = 1;j<=n;j++){
        			 System.out.print((char)arr[i][j]);
        		 }
        		 System.out.println();
        	 }
         }
         else{
        	 arr[2][(n+1)/2] = '#';
        	 k--;
        	 for(int i = 2;i<=n/2 && k>0; i++){
        		 arr[2][i] = '#';
        		 arr[2][n-i+1] = '#';
        		 k = k-2;
        	 }
        	 for(int i = 2;i<=n/2 && k>0; i++){
        		 arr[3][i] = '#';
        		 arr[3][n-i+1] = '#';
        		 k = k-2;
        	 }
        	 for(int i = 1;i<=4;i++){
        		 for(int j = 1;j<=n;j++){
        			 System.out.print((char)arr[i][j]);
        		 }
        		 System.out.println();
        	 }
         }
         
	 }
 }