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
.....
.###.
.....
.....
// TODAY I WILL BECOME EXPERT !
import java.util.*;
import java.math.*;
import java.io.*;


public class q_6 {
    static Scanner sc;

    public static void main(String[] args){
        sc = new Scanner(System.in);
        int n = getInt();
        int k = getInt();
        int v = k;
        int x1 = 1;
        int c1 = 1;
        int x2 = 1;
        int c2 = n-2;
        int[][] mat = new int[4][n];
        for(int i=0 ; i<k ;){
            if(v>=2){
                if(c2-c1>=1){
                   mat[x1][c1++]=1;
                   mat[x2][c2--]=1;
                   i+=2;
                   v-=2;
                }
                else {
                    if(x1==1){
                        x1=2;
                        x2=2;
                        c1=1;
                        c2=n-2;
                    }
                    else {
                        if(v==2){
                            if(mat[1][n/2]==0 && mat[2][n/2]==0){
                                mat[1][n/2] = mat[2][n/2] = 1;
                                i+=2;
                                v-=2;
                            }
                            else {
                                System.out.println("NO");
                                return;
                            }
                        }
                        else {
                            System.out.println("NO");
                            return;
                        }
                    }
                }
            }
            else {
                if(mat[1][n/2]==0){
                    mat[1][n/2]=1;
                    v--;
                    i++;
                }
                else {
                    if(mat[2][n/2]==0){
                        mat[2][n/2]=1;
                        v--;
                        i++;
                    }
                    else {
                        System.out.println("NO");
                        return;
                    }
                }
            }
        }
        System.out.println("YES");
        int cc = 0;
        for(int i=0 ; i<4 ; i++){
            for(int j=0 ; j<n ; j++){
                if(mat[i][j]==1){
                    cc++;
                }
                System.out.print((mat[i][j]==0)?('.'):('#'));
            }
            System.out.println();
        }
        
    }





    public static int getInt(){
        return sc.nextInt();
    }

    public static String getString(){
        return sc.next();
    }

    public static String nextLine(){
        return sc.nextLine();
    }

    public static long nextLong(){
        return sc.nextLong();
    }

}
