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.*;

/**
  * Built using my Brain
  * Actual solution is at the bottom
  *
  * @author Lenard Hoffstader
*/

public class cfjava
{
  public static void main(String[] args)
  {
    OutputStream outputStream = System.out;
    FastReader in = new FastReader();
    PrintWriter out = new PrintWriter(outputStream);
    PROBLEM solver = new PROBLEM();
    int t=1;
    // t=in.nextInt();
    for(int i=0;i<t;i++){
      solver.solve(in, out);
    }
    out.close();
  }

  static class PROBLEM
  {
    public void solve(FastReader in,PrintWriter out)
    {
      int n=in.nextInt();
      int k=in.nextInt();
      out.println("YES");
      char grid[][]=new char[4][n];
      for(int i=0;i<n;i++){
        grid[0][i]=grid[1][i]=grid[2][i]=grid[3][i]='.';
      }
      boolean odd=false;
      if(k%2!=0){odd=true;k--;}
      int xx=1;
      for(int i=1;i<n/2;i++){
        if(k==0)break;
        grid[1][i]=grid[1][n-i-1]='#';
        k-=2;
      }
      if(k>0){
        for(int i=1;i<n/2;i++){
          if(k==0)break;
          grid[2][i]=grid[2][n-i-1]='#';
          k-=2;
        }
      }
      if(k>0){grid[1][n/2]=grid[2][n/2]='#';}
      if(odd)grid[1][n/2]='#';
      for(int i=0;i<4;i++){
        for(int j=0;j<n;j++){
          out.print(grid[i][j]);
        }
        out.println();
      }
    }
  }
  
  static class FastReader 
  {
    BufferedReader br; 
    StringTokenizer st; 

    public FastReader() 
    { 
      br = new BufferedReader(new InputStreamReader(System.in)); 
    } 

    String next() 
    { 
      while (st == null || !st.hasMoreElements()) 
      {
        try
        { 
          st = new StringTokenizer(br.readLine()); 
        } 
        catch (IOException  e) 
        { 
          e.printStackTrace(); 
        } 
      } 
      return st.nextToken(); 
    } 

    int nextInt(){return Integer.parseInt(next());}

    long nextLong(){return Long.parseLong(next());} 

    double nextDouble(){return Double.parseDouble(next());}

    boolean nextBoolean(){return Boolean.parseBoolean(next());}

    String nextLine() 
    { 
      String str = ""; 
      try
      { 
        str = br.readLine(); 
      } 
      catch (IOException e){e.printStackTrace();} 
      return str; 
    } 
  }
}
