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.*;
import java.io.*;
public class Solution{
   
   
   
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        
        
        
            
            System.out.println("YES");
            char[][] rep = new char[4][n];
            
            for(int i=0;i<4;i++) Arrays.fill(rep[i],'.');
            
            if(k%2==0){
                for(int i=1;i<n-1;i++){
                    if(k==0) break;
                    rep[1][i] = '#';
                    rep[2][i] = '#';
                    k -= 2;
                    
                }
                
            }else{
                
                k--;
                rep[2][n/2] = '#';
                int c = 1;
                int kk = k;
                for(int i=n/2 + 1;i<n-1 && i<=n/2 + kk/2;i++){
                    rep[c][i] = '#';
                    if(c==1) c = 2;
                    else c = 1;
                    k--;
                }
                c = 1;
                for(int i=n/2-1;i>0;i--){
                    if(k==0) break;
                    rep[c][i] = '#';
                    if(c==1) c = 2;
                    else c = 1;
                    k--;
                }
                
                
                if(k>0){
                    rep[c][1] = '#';
                    rep[c][n-2] = '#';
                    k -= 2;
                    for(int i=2;i<n-2;i++){
                        if(k==0) break;
                        if(rep[1][i]=='.') rep[1][i] = '#';
                        if(rep[2][i]=='.') rep[2][i] = '#';
                        k--;
                    }
                }
                
            }
            
            
            for(int i=0;i<4;i++){
                for(int j=0;j<n;j++){
                    System.out.print(rep[i][j]);
                }
                System.out.println("");
            }
        
    }
    
}