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.Scanner;
/*
3 4 2
1 3 3 3
0 3 3 2
3 0 1 1
*/
public class Main {


    public static void main(String[] args) {
        Scanner s=new Scanner(System.in);
        int rows=4;
        int columns=s.nextInt();
        int k=s.nextInt();
        int available=rows*columns-(2*(rows+columns)-4);
        if(k>available){
            System.out.println("NO");
        }else if(k==available){
            System.out.println("YES");
            StringBuilder str=new StringBuilder("");
            for(int i=0;i<columns;i++){
                str.append(".");
            }
            System.out.println(str);
            for(int j=1;j<3;j++){
                StringBuilder ansStr=new StringBuilder("");
                for(int i=0;i<columns;i++) {

                    if(i==0||i==columns-1){
                        ansStr.append(".");
                    }else {
                        ansStr.append("#");
                    }
                }
                System.out.println(ansStr);
            }
            System.out.println(str);
        }
        else if(k==available-1){

            System.out.println("YES");
            StringBuilder str=new StringBuilder("");
            for(int i=0;i<columns;i++){
                str.append(".");
            }
            System.out.println(str);
            for(int j=1;j<2;j++){
                StringBuilder ansStr=new StringBuilder("");
                for(int i=0;i<columns;i++) {
                    if(i==0||i==columns-1){
                        ansStr.append(".");
                    }else {
                        ansStr.append("#");
                    }
                }
                System.out.println(ansStr);
            }
            int middle=((columns+1)/2) -1;
            for(int j=1;j<2;j++){
                StringBuilder ansStr=new StringBuilder("");
                for(int i=0;i<columns;i++) {

                    if(i==0||i==columns-1){
                        ansStr.append(".");
                    }else if(i==middle){
                        ansStr.append(".");
                    }else {
                        ansStr.append("#");
                    }
                }
                System.out.println(ansStr);
            }
            System.out.println(str);
        }else {
            System.out.println("YES");
            StringBuilder str=new StringBuilder("");
            for(int i=0;i<columns;i++){
                str.append(".");
            }
            int half=k/2;
            int extra=k-half*2;
            int middle=((columns+1)/2) -1;
            System.out.println(str);
            for(int j=1;j<3;j++){
                StringBuilder ansStr=new StringBuilder("");
                int i=0;
                for(;i<middle;i++){
                    if(i==0){
                        ansStr.append(".");
                    }else if(half>0){
                        ansStr.append("#");
                        half--;
                    }else {
                        ansStr.append(".");
                    }
                }
                StringBuilder temp=new StringBuilder(ansStr);
                ansStr.reverse();
                if(extra>0){
                    temp.append("#");
                    extra--;
                }else {
                    temp.append(".");
                }
                temp.append(ansStr);
                System.out.println(temp);
            }
            System.out.println(str);
        }

    }
}

