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.*;

public class Marlin {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader inp = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver();
        solver.solve(inp, out);
        out.close();
    }

    static class Solver {
        private void solve(InputReader inp, PrintWriter out) {
            int n = inp.nextInt();
            int k = inp.nextInt();
            boolean[][] res = new boolean[4][n];
            if (k % 2 == 0) {
                int i = 1;
                while (k > 0 && i < n - 1) {
                    res[1][i] = true;
                    res[2][i] = true;
                    k-=2;
                    i++;
                }
            } else {
                res[1][n/2] = true;
                k--;
                int i = 1;
                while (k > 0 && i <= n / 2 + 1) {
                    if (k >= 4) {
                        res[2][n/2 + i] = true;
                        res[2][n/2 - i] = true;
                        k -= 2;
                    }
                    if (k >= 2) {
                        res[1][n/2 + i] = true;
                        res[1][n/2 - i] = true;
                        k -= 2;
                    }
                    i++;
                }
            }

            out.println("YES");
            for (int i = 0; i < 4; i++) {
                for (int j = 0; j < n; j++) {
                    if (res[i][j]) out.print("#");
                    else out.print(".");
                }
                out.print("\n");
            }
        }
    }

    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }
    }
}
