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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.OutputStream;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;
import java.io.BufferedOutputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Kattio in = new Kattio(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        public void solve(int testNumber, Kattio in, PrintWriter out) {
            int n = in.nextInt();
            int k = in.nextInt();


            out.println("YES");
            char[][] ans = new char[4][n];
            if (k % 2 == 0) {
                for (int j = 0; j < n; ++j) {
                    for (int i = 0; i < 4; ++i) {
                        if (k > 0 && i > 0 && j > 0 && i < 3 && j < n - 1) {
                            ans[i][j] = '#';
                            --k;
                        } else {
                            ans[i][j] = '.';
                        }
                    }
                }
            } else if (k % (n - 2) == 0) {
                for (int i = 0; i < 4; ++i) {
                    for (int j = 0; j < n; ++j) {
                        if (i > 0 && i < 3 && j > 0 && j < n - 1 && k > 0) {
                            ans[i][j] = '#';
                            --k;
                        } else
                            ans[i][j] = '.';
                    }
                }
            } else {
                for (int i = 0; i < 4; ++i) {
                    if (i == 0 || i == 4) {
                        for (int j = 0; j < n; ++j)
                            ans[i][j] = '.';
                    } else {
                        if (k > 0 && k % 2 == 1) {
                            ans[i][n / 2] = '#';
                            --k;
                        } else ans[i][n / 2] = '.';
                        for (int j = (n / 2) + 1, t = (n / 2) - 1; j < n - 1 && t > 0; ++j, --t) {
                            if (k > 0) {
                                ans[i][j] = ans[i][t] = '#';
                                k -= 2;
                            } else {
                                ans[i][j] = ans[i][t] = '.';
                            }
                        }

                        ans[i][0] = ans[i][n - 1] = '.';
                    }
                }
            }


            for (int i = 0; i < 4; ++i) {
                for (int j = 0; j < n; ++j)
                    out.print(ans[i][j]);
                out.println();
            }
        }

    }

    static class Kattio extends PrintWriter {
        private BufferedReader r;
        private String line;
        private StringTokenizer st;
        private String token;

        public Kattio(InputStream i) {
            super(new BufferedOutputStream(System.out));
            r = new BufferedReader(new InputStreamReader(i));
        }

        public Kattio(InputStream i, OutputStream o) {
            super(new BufferedOutputStream(o));
            r = new BufferedReader(new InputStreamReader(i));
        }

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

        private String peekToken() {
            if (token == null)
                try {
                    while (st == null || !st.hasMoreTokens()) {
                        line = r.readLine();
                        if (line == null) return null;
                        st = new StringTokenizer(line);
                    }
                    token = st.nextToken();
                } catch (IOException e) {
                }
            return token;
        }

        private String nextToken() {
            String ans = peekToken();
            token = null;
            return ans;
        }

    }
}

