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 Solution 
{
  
    
    
    public static void main(String args[])
    {
       MyScanner sc=new MyScanner();
       int n=sc.nextInt();
       int k=sc.nextInt();
       char ch[][]=new char[4][n];
       for(int i=0;i<4;i++)
       {
           for(int j=0;j<n;j++)
           ch[i][j]='.';
       }
       if(k%2==0)
       {
           int lt=k/2;
           for(int i=1;i<=lt;i++)
           {
               ch[1][i]='#';
               ch[2][i]='#';
           }
       }
       else
       {
               int s=(n-2-k)/2+1;
               int e=n-1-s;
               if(k>n-2)
               {
                   s=1;
                   e=n-2;
               }
             for(int i=s;i<=e;i++)
              {
               ch[1][i]='#';
              }
          
           if(k>n-2)
           {
            
            k=k-(n-2);
            int p=1;
            while(k>0)
            {
                ch[2][p]='#';
                ch[2][n-p-1]='#';
                k-=2;
                p++;
            }
               
           }
       }
    
    System.out.println("YES");
    for(int i=0;i<4;i++)
    {
        for(int j=0;j<n;j++)
        System.out.print(ch[i][j]);
        System.out.println();
    }
       
       
    }
	static pair process(String s)
	{
	    Stack<Character> st=new Stack<>();
	    int pc=0;
	    int nc=0;
	    for(int i=0;i<s.length();i++)
	    {
	        char ch=s.charAt(i);
	        if(ch==')'&&st.isEmpty())
	        nc++;
	        else if(ch==')')
	        st.pop();
	        else if(ch=='(')
	        st.push(ch);
	    }
	    pc=st.size();
	    pair pr=new pair();
	    pr.p=pc;
	    pr.n=nc;
	    return pr;
	    
	    
	}
  static class pair
  {
      int p;
      int n;
  }
    
    public static class MyScanner 
    {
        BufferedReader br;
        StringTokenizer st;
 
        public MyScanner() {
            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()); }
         
        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}
