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.util.*;
import java.io.*;

public class B
{
   public static void main(String[] args) throws Exception
   {
      PrintWriter out = new PrintWriter(System.out);
      new B(new FastScanner(System.in), out);
      out.close();
   }

   public B(FastScanner in, PrintWriter out)
   {
      int N = in.nextInt();
      int K = in.nextInt();

      char[][] grid = new char[4][N];
      for (int i=0; i<4; i++)
         for (int j=0; j<N; j++)
            grid[i][j] = '.';
     
      if (K % 2 == 0)
      {
         int col = 1;
         for (int k=0; k<K; k+=2)
         {
            grid[1][col] = grid[2][col] = '#';
            col++;
         }
      }
      else if (N <= K)
      {
         for (int x=1; x<=N-2; x++)
            grid[1][x] = '#';
         grid[2][1] = grid[2][N-2] = '#';

         K -= N;
         for (int k=0; k<K; k++)
            grid[2][k+2] = '#';
      }
      else if (K == N-2)
      {
         for (int x=1; x<=N-2; x++)
            grid[1][x] = '#';
      }
      else if (K >= 5)
      {
         K -= 2;
         for (int x=1; x<=K; x++)
         {
            grid[1][x] = '#';
         }
         grid[2][1] = grid[2][K] = '#';
      
      }
      else if (K == 1)
      {
         int m = N/2;
         grid[2][m] = '#';
      }
      else if (K == 3)
      {
         int m = N/2;
         grid[2][m] = '#';
         grid[1][m-1] = '#'; 
         grid[1][m+1] = '#'; 
      }
      else
      {
         out.println("NO");
         return;
      }
      
      out.println("YES");
      for (char[] cur : grid)
         out.println(new String(cur)); 
   }
}

class FastScanner{
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    
    public FastScanner(InputStream stream)
    {
        this.stream = stream;
    }
    
    int read()
    {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars){
            curChar = 0;
            try{
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }
    
    boolean isSpaceChar(int c)
    {
        return c==' '||c=='\n'||c=='\r'||c=='\t'||c==-1;
    }
    
    boolean isEndline(int c)
    {
        return c=='\n'||c=='\r'||c==-1;
    }
    
    int nextInt()
    {
        return Integer.parseInt(next());
    }
    
    long nextLong()
    {
        return Long.parseLong(next());
    }
    
    double nextDouble()
    {
        return Double.parseDouble(next());
    }
    
    String next(){
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do{
            res.appendCodePoint(c);
            c = read();
        }while(!isSpaceChar(c));
        return res.toString();
    }
    
    String nextLine(){
        int c = read();
        while (isEndline(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do{
            res.appendCodePoint(c);
            c = read();
        }while(!isEndline(c));
        return res.toString();
    }
}
