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.*;
import java.util.*;
import java.io.IOException;
import java.io.InputStream;

import static java.lang.Math.ceil;
import static java.lang.Math.max;
import static java.lang.Math.toDegrees;

public class Main {
    public static void main(String[] args) {

        File file = new File("in.txt");
        File fileOut = new File("out.txt");
        InputStream inputStream = null;
        OutputStream outputStream = null;
        // try {inputStream= new FileInputStream(file);} catch (FileNotFoundException ex){return;};
//        try {outputStream= new FileOutputStream(fileOut);} catch (FileNotFoundException ex){return;};
        inputStream = System.in;
        outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();

        solver.solve(1, in, out);
        out.close();
    }


}

class Task {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int n = in.nextInt();
        int k = in.nextInt();

        if(k > 2 * (n-2)){
            out.println("NO");
            return;
        }
        out.println("YES");
        char[][] map = new char[4][n];
        for(int i=0; i<4; i++){
            Arrays.fill(map[i], '.');
        }

        int perLine = (n-2)/2;
        int firstLine = Math.min(k/2, perLine);
        k -= firstLine * 2;
        fillLine(map[1], firstLine);
        int secondLine = Math.min(k/2, perLine);
        k -= secondLine * 2;
        fillLine(map[2], secondLine);
        if(k>0){
            map[1][perLine+1] = '#';
            k--;
        }
        if(k>0){
            map[2][perLine+1] = '#';
            k--;
        }
        for(int i=0; i<4; i++){
            StringBuilder sb = new StringBuilder();
            for(int j=0; j<n; j++){
                sb.append(map[i][j]);
            }
            out.println(sb.toString());
        }








    }


    public void fillLine(char[] map, int count){
        for(int i=1; i<1+count; i++){
            map[i] = '#';
            map[map.length-1-i] = '#';
        }
    }





}



class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public String nextLine(){
        try {
            return reader.readLine();
        } catch (IOException e){
            throw new RuntimeException(e);
        }
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }
    public long nextLong() { return Long.parseLong(next()); }

}



class Pair<F, S> {
    public final F first;
    public final S second;




    public Pair(F first, S second) {
        this.first = first;
        this.second = second;
    }

    @Override
    public boolean equals(Object o) {
        if (!(o instanceof Pair)) {
            return false;
        }
        Pair<?, ?> p = (Pair<?, ?>) o;
        return Objects.equals(p.first, first) && Objects.equals(p.second, second);
    }

    @Override
    public int hashCode() {
        return (first == null ? 0 : first.hashCode()) ^ (second == null ? 0 : second.hashCode());
    }

    @Override
    public String toString() {
        return "(" + first + ", " + second + ')';
    }
}

class IntPair extends Pair<Integer, Integer>{
    public IntPair(Integer first, Integer second){
        super(first, second);
    }
}

class LPair extends Pair<Long, Long>{
    public LPair(Long first, Long second){
        super(first, second);
    }
}