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

public class B {
    public static void main(String args[])
    {
        FastReader Reader=new FastReader(System.in);
        int N=Reader.nextInt();
        int K=Reader.nextInt();
        if(K%2==0)
        {
            System.out.println("YES");
            for(int i=0;i<N;i++)
            {
                System.out.print('.');
            }
            System.out.println();
            System.out.print('.');
            for(int i=1;i<=K/2;i++)
            {
                System.out.print('#');
            }
            for(int i=K/2+1;i<N;i++)
            {
                System.out.print('.');
            }
            System.out.println();
            System.out.print('.');
            for(int i=1;i<=K/2;i++)
            {
                System.out.print('#');
            }
            for(int i=K/2+1;i<N;i++)
            {
                System.out.print('.');
            }
            System.out.println();
            for(int i=0;i<N;i++)
            {
                System.out.print('.');
            }
            System.out.println();
        }
        else if(K<=N-2)
        {
            System.out.println("YES");
            for(int i=0;i<N;i++)
            {
                System.out.print('.');
            }
            System.out.println();
            for(int i=0;i<(N-K)/2;i++)
            {
                System.out.print('.');
            }
            for(int i=0;i<K;i++)
            {
                System.out.print('#');
            }
            for(int i=0;i<(N-K)/2;i++)
            {
                System.out.print('.');
            }
            System.out.println();
            for(int i=0;i<N;i++)
            {
                System.out.print('.');
            }
            System.out.println();
            for(int i=0;i<N;i++)
            {
                System.out.print('.');
            }
            System.out.println();
        }
        else
        {
            System.out.println("YES");
            for(int i=0;i<N;i++)
            {
                System.out.print('.');
            }
            System.out.println();
            System.out.print('.');
            for(int i=0;i<N-2;i++)
            {
                System.out.print('#');
            }
            System.out.print('.');
            System.out.println();
            K=K-N+2;
            System.out.print('.');
            for(int i=0;i<K/2;i++)
            {
                System.out.print('#');
            }
            for(int i=0;i<N-2-K;i++)
            {
                System.out.print('.');
            }
            for(int i=0;i<K/2;i++)
            {
                System.out.print('#');
            }
            System.out.print('.');
            System.out.println();
            for(int i=0;i<N;i++)
            {
                System.out.print('.');
            }
            System.out.println();

        }
    }
}
class FastReader {
    private InputStream stream;
    private byte[] buf = new byte[8192];
    private int curChar;
    private int pnumChars;
    private FastReader.SpaceCharFilter filter;

    public FastReader(InputStream stream) {
        this.stream = stream;
    }

    public int read() {
        if (pnumChars == -1) {
            throw new InputMismatchException();
        }
        if (curChar >= pnumChars) {
            curChar = 0;
            try {
                pnumChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (pnumChars <= 0) {
                return -1;
            }
        }
        return buf[curChar++];
    }

    public String next() {
        return nextString();
    }

    public int nextInt() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c == ',') {
                c = read();
            }
            if (c < '0' || c > '9') {
                throw new InputMismatchException();
            }
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public long nextLong() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public String nextString() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }

    public String nextLine() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isEndOfLine(c));
        return res.toString();
    }


    public boolean isEndOfLine(int c) {
        return c == '\n' || c == '\r' || c == -1;
    }

    public boolean isSpaceChar(int c) {
        if (filter != null) {
            return filter.isSpaceChar(c);
        }
        return isWhitespace(c);
    }

    public static boolean isWhitespace(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);

    }

}