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.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class Solution {

 

    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int n =s.nextInt();
        int k = s.nextInt();
        if(k%2==0){
            System.out.println("YES");
            int hotels =k;
            for(int i=0;i<4;i++){
                for(int j=0;j<n;j++){
                    if(i==1 && j>0 && hotels>k/2){
                        System.out.print("#");
                        hotels--;
                    }
                    else if(i==2 && j>0 && hotels>0){
                        System.out.print("#");
                        hotels--;
                    }
                    else{
                        System.out.print(".");
                    }
                }
            
                System.out.println();
            }
        }
        else {
            System.out.println("YES");
            int hotels =k;
            int h1;
            if(k>=n-2){
                h1 = n-2;
            }else{
                h1 = k;
            }
            // System.out.println(h1);
             for(int i=0;i<4;i++){
                for(int j=0;j<n;j++){
                   if(i==1 && j>=(n/2)-(h1/2) && j<=(n/2)+(h1/2)){
                       System.out.print("#");
                       hotels--;
                       continue;
                   }if((i==2 && j>=1 && j<1+(hotels/2) && hotels>0) || (j>=n-1-(hotels/2)  && j<n-1 && i==2 && hotels>0)){
                       System.out.print("#");
                   }else{
                       System.out.print(".");
                   }
                    
                }
                
                     // System.out.println(hotels);
                System.out.println();
            }
        }
    }
}
