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.FilterInputStream;
import java.io.BufferedInputStream;
import java.io.InputStream;

/**
 * @author Jenish
 */
public class Main {
    public static void main(String[] ARGS) {
        new Thread(null, new Runnable() {
            public void run() {
                new Main().solve();
            }
        }, "1", 1 << 26).start();
    }

    void solve() {
        InputStream IS = System.in;
        OutputStream OS = System.out;
        ScanReader in = new ScanReader(IS);
        PrintWriter out = new PrintWriter(OS);
        BMarlin bmarlin = new BMarlin();
        bmarlin.solve(1, in, out);
        out.close();
    }

    static class BMarlin {
        public void solve(int testNumber, ScanReader in, PrintWriter out) {
            int n = in.scanInt();
            int k = in.scanInt();
            char arr[][] = new char[4][n];

            for (int i = 0; i < 4; i++) {
                for (int j = 0; j < n; j++) {
                    arr[i][j] = '.';
                }
            }
            if (k % 2 == 0) {

                int row = 1;
                int x1 = 1;
                int y1 = n - 1 - 1;
                while (k > 0) {
                    if (row > 2) {
                        break;
                    }
                    if (x1 < y1) {
                        arr[row][x1] = '#';
                        arr[row][y1] = '#';
                        x1++;
                        y1--;
                        k--;
                        k--;
                    } else {
                        x1 = 1;
                        y1 = n - 1 - 1;
                        row++;
                    }
                }
                if (k == 0) {
                    out.println("YES");
                    for (int i = 0; i < 4; i++) {
                        for (int j = 0; j < n; j++) {
                            out.print(arr[i][j]);
                        }
                        out.println();
                    }
                } else {
                    if (k == 2) {
                        arr[1][n / 2] = '#';
                        arr[2][n / 2] = '#';
                        out.println("YES");
                        for (int i = 0; i < 4; i++) {
                            for (int j = 0; j < n; j++) {
                                out.print(arr[i][j]);
                            }
                            out.println();
                        }
                    } else {
                        out.println("NO");
                        return;
                    }
                }
            } else {
                arr[1][n / 2] = '#';
                k--;

                int row = 1;
                int x1 = 1;
                int y1 = n - 1 - 1;
                while (k > 0) {
                    if (row > 2) {
                        break;
                    }
                    if (x1 < y1) {
                        arr[row][x1] = '#';
                        arr[row][y1] = '#';
                        x1++;
                        y1--;
                        k--;
                        k--;
                    } else {
                        x1 = 1;
                        y1 = n - 1 - 1;
                        row++;
                    }
                }
                if (k == 0) {
                    out.println("YES");
                    for (int i = 0; i < 4; i++) {
                        for (int j = 0; j < n; j++) {
                            out.print(arr[i][j]);
                        }
                        out.println();
                    }
                } else {
                    if (k == 1) {
                        arr[2][n / 2] = '#';
                        out.println("YES");
                        for (int i = 0; i < 4; i++) {
                            for (int j = 0; j < n; j++) {
                                out.print(arr[i][j]);
                            }
                            out.println();
                        }
                    } else {
                        out.println("NO");
                        return;
                    }
                }

            }
        }

    }

    static class ScanReader {
        private byte[] buf = new byte[4 * 1024];
        private int index;
        private BufferedInputStream in;
        private int Total_Char;

        public ScanReader(InputStream inputStream) {
            in = new BufferedInputStream(inputStream);
        }

        private int scan() {
            if (index >= Total_Char) {
                index = 0;
                try {
                    Total_Char = in.read(buf);
                } catch (Exception e) {
                    e.printStackTrace();
                }
                if (Total_Char <= 0) return -1;
            }
            return buf[index++];
        }

        public int scanInt() {
            int integer = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    integer *= 10;
                    integer += n - '0';
                    n = scan();
                }
            }
            return neg * integer;
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
            else return false;
        }

    }
}

