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.*;

// Main

public class Main 
{    
  public static void main (String[] argv) 
  {
	  new Main();
  } 
  
  boolean test = false;
  public Main(){
	  FastReader in = new FastReader(new BufferedReader(new InputStreamReader(System.in)));
	  //FastReader in = new FastReader(new BufferedReader(new FileReader("Main.in")));
      int n = in.nextInt();
      int k = in.nextInt();
      System.out.println("YES");
      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 ncol = k / 2;
          for (int i = 1; i <= 2; i++) {
              for (int j = 1; j < 1 + ncol; j++)
                  grid[i][j] = '#';              
          }          
      }else {
          --k;
          grid[1][n/2] = '#';
          int hf = n / 2 - 1;
          if (k <= 2 * hf) {
              int ncol = k / 2;
              for (int j = 1; j < 1 + ncol; j++) {
                  grid[1][j] = '#';
                  grid[1][n-1-j] = '#';
              }
          }else {
              int ncol = hf;
              for (int j = 1; j < 1 + ncol; j++) {
                  grid[1][j] = '#';
                  grid[1][n-1-j] = '#';
              }
              
          k -= 2 * hf;
          ncol = k / 2;
              for (int j = 1; j < 1 + ncol; j++) {
                  grid[2][j] = '#';
                  grid[2][n-1-j] = '#';
              }
          }
      }
      
      for (int i = 0; i < 4; i++) {
          for (int j = 0; j < n; j++) System.out.print(grid[i][j]);
          System.out.println();
      }
  }
  
  
  static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader(BufferedReader in)
        {            
            br = in;
        }
 
        String next()
        {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    String line = br.readLine();
                    if (line == null || line.length() == 0) return "";
                    st = new StringTokenizer(line);
                }
                catch (IOException  e)
                {
                    return "";
                    //e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt()
        {
            return Integer.parseInt(next());
        }
 
        long nextLong()
        {
            return Long.parseLong(next());
        }
 
        double nextDouble()
        {
            return Double.parseDouble(next());
        }
 
        String nextLine()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                return "";
                //e.printStackTrace();
            }
            return str;
        }
    }
}