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
.....
.###.
.....
.....
//Codeforces Round #480 (Div. 2)
import java.io.*;
import java.util.*;

public class TaskB {

    public static void main (String[] args) throws IOException {
        FastScanner fs = new FastScanner(System.in);
        PrintWriter pw = new PrintWriter(new BufferedOutputStream(System.out));
        
        int n = fs.nextInt();
        int k = fs.nextInt();
        
        pw.println("YES");

        
        for (int i = 0; i < n; i++) {
            pw.print(".");
        }            
        pw.println();

        if ((k & 1) == 0) {
            pw.print(".");
            int q = k >> 1;
            for (int i = 0; i < q; i++) {
                pw.print("#");
            }
            for (int i = q; i < n-1; i++) {
                pw.print(".");
            }
            pw.println();
            pw.print(".");
            for (int i = 0; i < q; i++) {
                pw.print("#");
            }
            for (int i = q; i < n-1; i++) {
                pw.print(".");
            }
            pw.println();
        } else {
            if (k <= n-2) {
                pw.print(".");
                for (int i = 0; i < (n-2-k)/2; i++) {
                    pw.print(".");
                }    
                for (int i = 0; i < k; i++) {
                    pw.print("#");
                }
                for (int i = 0; i < (n-2-k)/2; i++) {
                    pw.print(".");
                }
                pw.println(".");
                for (int i = 0; i < n; i++) {
                    pw.print(".");
                }            
                pw.println();
            } else {
                pw.print(".");
                for (int i = 0; i < n-2; i++) {
                    pw.print("#");
                }            
                pw.println(".");                
                k -= n-2;
                if (k == 1) {
                    pw.print(".");
                    for (int i = 0; i < (n-2-k)/2; i++) {
                        pw.print(".");
                    }    
                    for (int i = 0; i < k; i++) {
                        pw.print("#");
                    }
                    for (int i = 0; i < (n-2-k)/2; i++) {
                        pw.print(".");
                    }
                    pw.println(".");
                } else {
                    pw.print(".");
                    for (int i = 0; i < k-1; i++) {
                        pw.print("#");
                    }
                    for (int i = 0; i < n-k-2; i++) {
                        pw.print(".");
                    }
                    pw.println("#.");
                }
            }
        }

        for (int i = 0; i < n; i++) {
            pw.print(".");
        }            
        pw.println();        
        

        pw.close();
    }

    static class FastScanner {
        BufferedReader reader;
        StringTokenizer tokenizer;
        FastScanner(InputStream i) {
            reader = new BufferedReader(new InputStreamReader(i));
            tokenizer = new StringTokenizer("");
        }
        String next() throws IOException {
            while(!tokenizer.hasMoreTokens()) tokenizer = new StringTokenizer(reader.readLine());
            return tokenizer.nextToken();
        }
        int nextInt() throws IOException {
            return Integer.parseInt(next());
        }
        long nextLong() throws IOException {
            return Long.parseLong(next());
        }
    }
}