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.lang.*;
import java.io.*;
import java.util.*;
import java.math.*;
import java.net.*;

import static java.lang.Math.*;

public class Solution implements Runnable {
    
    void solve() throws Exception {
        int n = sc.nextInt();
        int k = sc.nextInt();
        out.println("YES");
        char[][] c = new char[4][n];
        for (int i = 0; i < 4; i++) {
            Arrays.fill(c[i], '.');
        }
        for (int l = 1, r = n - 2; l <= r && k > 0; l++, r--) {
            if (k > 1 && l != r) {
                c[1][l] = '#';
                c[1][r] = '#';
                k -= 2;
            } else if (l == r) {
                c[1][l] = '#';
                --k;
            }
        }
        for (int l = 1, r = n - 2; l <= r && k > 0; l++, r--) {
            if (k > 1 && l != r) {
                c[2][l] = '#';
                c[2][r] = '#';
                k -= 2;
            } else if (l == r) {
                c[2][l] = '#';
                --k;
            }
        }
        for (int i = 0; i < 4; i++) {
            out.println(new String(c[i]));
        }
    }

    BufferedReader in;
    PrintWriter out;
    FastScanner sc;

    final String INPUT_FILE = "";
    final String OUTPUT_FILE = "";

    static Throwable throwable;

    public static void main(String[] args) throws Throwable {
        Thread thread = new Thread(null, new Solution(), "", (1 << 26));
        thread.start();
        thread.join();
        thread.run();
        if (Solution.throwable != null)
            throw Solution.throwable;
    }

    public void run() {
        try {
            if (INPUT_FILE.equals("")) {
                in = new BufferedReader(new InputStreamReader(System.in));
            } else {
                in = new BufferedReader(new FileReader(INPUT_FILE));
            }
            if (OUTPUT_FILE.equals("")) {
                out = new PrintWriter(System.out);
            } else {
                out = new PrintWriter(OUTPUT_FILE);
            }
            sc = new FastScanner(in);
            solve();
        } catch (Exception e) {
            throwable = e;
        } finally {
            out.close();
        }
    }

}

class FastScanner {
	
    BufferedReader reader;
    StringTokenizer strTok;

    FastScanner(BufferedReader reader) {
        this.reader = reader;
    }

    public String nextToken() throws Exception {
        while (strTok == null || !strTok.hasMoreTokens()) {
            strTok = new StringTokenizer(reader.readLine());
        }
        return strTok.nextToken();
    }

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

    public double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }

    public long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }
}