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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.io.PrintWriter;
public class B980 
{
    static class Scanner
    {
        BufferedReader br;
        StringTokenizer tk=new StringTokenizer("");
        public Scanner(InputStream is) 
        {
            br=new BufferedReader(new InputStreamReader(is));
        }
        public int nextInt() throws IOException
        {
            if(tk.hasMoreTokens())
                return Integer.parseInt(tk.nextToken());
            tk=new StringTokenizer(br.readLine());
            return nextInt();
        }
        public long nextLong() throws IOException
        {
            if(tk.hasMoreTokens())
                return Long.parseLong(tk.nextToken());
            tk=new StringTokenizer(br.readLine());
            return nextLong();
        }
        public String next() throws IOException
        {
            if(tk.hasMoreTokens())
                return (tk.nextToken());
            tk=new StringTokenizer(br.readLine());
            return next();
        }
        public String nextLine() throws IOException
        {
            tk=new StringTokenizer("");
            return br.readLine();
        }
        public double nextDouble() throws IOException
        {
            if(tk.hasMoreTokens())
                return Double.parseDouble(tk.nextToken());
            tk=new StringTokenizer(br.readLine());
            return nextDouble();
        }
        public char nextChar() throws IOException
        {
            if(tk.hasMoreTokens())
                return (tk.nextToken().charAt(0));
            tk=new StringTokenizer(br.readLine());
            return nextChar();
        }
        public int[] nextIntArray(int n) throws IOException
        {
            int a[]=new int[n];
            for(int i=0;i<n;i++)
                a[i]=nextInt();
            return a;
        }
        public long[] nextLongArray(int n) throws IOException
        {
            long a[]=new long[n];
            for(int i=0;i<n;i++)
                a[i]=nextLong();
            return a;
        }
        public int[] nextIntArrayOneBased(int n) throws IOException
        {
            int a[]=new int[n+1];
            for(int i=1;i<=n;i++)
                a[i]=nextInt();
            return a;
        }
        public long[] nextLongArrayOneBased(int n) throws IOException
        {
            long a[]=new long[n+1];
            for(int i=1;i<=n;i++)
                a[i]=nextLong();
            return a;
        }
    
    
    }
    
    public static void main(String args[]) throws IOException
    {
        Scanner in=new Scanner(System.in);
        PrintWriter out=new PrintWriter(System.out);
        int n=in.nextInt();
        int k=in.nextInt();
        if(k%2==0)
        {
            out.println("YES");
            for(int i=0;i<n;i++)
                out.print(".");
            out.println();
            out.print(".");
            for(int i=0;i<k/2;i++)
                out.print("#");
            for(int i=1;i<n-k/2;i++)
                out.print(".");
            out.println();
            out.print(".");
            
            for(int i=0;i<k/2;i++)
                out.print("#");
            for(int i=1;i<n-k/2;i++)
                out.print(".");
            out.println();
            for(int i=0;i<n;i++)
                out.print(".");
            out.println();
        }
        else
        {
            if(k<=n-2)
            {
                out.println("YES");
                for(int i=0;i<n;i++)
                    out.print(".");
                out.println();
                for(int i=0;i<(n-k)/2;i++)
                    out.print(".");
                for(int i=0;i<k;i++)
                    out.print("#");
                for(int i=0;i<(n-k)/2;i++)
                    out.print(".");
                
                out.println();
                for(int i=0;i<n;i++)
                out.print(".");
                out.println();
                for(int i=0;i<n;i++)
                out.print(".");
                out.println();
            }
            else
            {
                out.println("YES");
                for(int i=0;i<n;i++)
                    out.print(".");
                out.println();
                for(int i=0;i<1;i++)
                    out.print(".");
                for(int i=0;i<n-2;i++)
                    out.print("#");
                for(int i=0;i<1;i++)
                    out.print(".");
                
                out.println();
                k-=n;
                k+=2;
                out.print(".");
                for(int i=0;i<k/2;i++)
                    out.print("#");
                for(int i=0;i<n-k-2;i++)
                    out.print(".");
                for(int i=0;i<k/2;i++)
                    out.print("#");
                out.print(".");
                out.println();
                for(int i=0;i<n;i++)
                    out.print(".");
                out.println();
            }
        }
        out.close();
    }

}
