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.IOException;
import java.io.BufferedReader;
import java.util.regex.Pattern;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author amalev
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(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, FastScanner in, PrintWriter out) {
            int n = in.nextInt();
            int k = in.nextInt();
            int[][] a = new int[4][n];
            if (k % 2 == 0) {
                for (int i = 1; i <= k / 2; i++) {
                    a[1][i] = 1;
                    a[2][i] = 1;
                }
            } else {
                if (k <= n - 2) {
                    for (int j = n / 2 - k / 2; j <= n / 2 + k / 2; j++) {
                        a[1][j] = 1;
                    }
                } else {
                    for (int j = 1; j <= n - 2; j++) {
                        a[1][j] = 1;
                    }
                    k -= n - 2;
                    for (int j = 1; j <= k / 2; j++) {
                        a[2][j] = 1;
                        a[2][n - j - 1] = 1;
                    }
                }
            }
            out.println("YES");
            for (int i = 0; i < 4; i++) {
                for (int j = 0; j < n; j++) {
                    if (a[i][j] == 0) {
                        out.print(".");
                    } else {
                        out.print("#");
                    }
                    if (j == n - 1) out.println();
                }
            }
        }

    }

    static class FastScanner {
        final BufferedReader input;
        String[] buffer;
        int pos;
        final static Pattern SEPARATOR = Pattern.compile("\\s+");

        public FastScanner(InputStream inputStream) {
            input = new BufferedReader(new InputStreamReader(inputStream));
        }

        private String[] readAndSplit() {
            try {
                return SEPARATOR.split(input.readLine());
            } catch (IOException ex) {
                throw new RuntimeException(ex);
            }
        }

        private String readToBuffer() {
            if (buffer == null || pos >= buffer.length) {
                buffer = readAndSplit();
                pos = 0;
            }
            return buffer[pos++];
        }

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

    }
}

