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.util.Arrays;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.Reader;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Nathaniel Lahn
 */
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();

            //handle n = 3 case separate


            char[][] grid = new char[4][n];
            for (int i = 0; i < 4; i++) {
                Arrays.fill(grid[i], '.');
            }
            if (k % 2 == 0) {
                for (int i = 0; i < k; i++) {
                    int c = i / (2);
                    int r = i % (2);
                    grid[r + 1][c + 1] = '#';
                }
            } else {//k is odd
                if (k <= n - 2) {
                    int start = (n - 2 - k) / 2 + 1;
                    for (int i = start; i < start + k; i++) {
                        grid[1][i] = '#';
                    }
                } else {
                    //blockade
                    k -= n - 2;
                    for (int i = 0; i < n - 2; i++) {
                        grid[1][i + 1] = '#';
                    }
                    k -= 2;
                    grid[2][1] = '#';
                    grid[2][n - 2] = '#';
                    int start = 2;
                    for (int i = start; i < start + k; i++) {
                        grid[2][i] = '#';
                    }
                }
            }
            StringBuilder sb = new StringBuilder();
            sb.append("YES\n");
            for (int i = 0; i < grid.length; i++) {
                for (int j = 0; j < grid[i].length; j++) {
                    sb.append(grid[i][j]);
                }
                sb.append('\n');
            }
            out.print(sb);
        }

    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }

        public FastScanner(InputStream in) {
            this(new InputStreamReader(in));
        }

        public String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

    }
}

