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.InputStreamReader;
import java.util.StringTokenizer;

public final class B {

	public static void main(String[] args) throws IOException 
	{
		BufferedReader BR=new BufferedReader(new InputStreamReader(System.in));
		String s=BR.readLine();
		StringTokenizer st=new StringTokenizer(s);
		int m=Integer.parseInt(st.nextToken());
		int n=Integer.parseInt(st.nextToken());
		char arr[][]=new char[4][m];
		for(int i=0;i<m;i++)
		{
			arr[0][i]='.';
			arr[1][i]='.';
			arr[2][i]='.';
			arr[3][i]='.';
		}
		if(n>(2*(m-2)))
			System.out.println("NO");
		else
		{
			int x1=1, y1=1;
			int x2=1, y2=m-2;
			int x3=2, y3=1;
			int x4=2, y4=m-2;
			
			if(n%2==0)
			{
				int c=0;
				for(int i=0;i<n;i=i+2)
				{
					arr[x1][y1]='#';
					arr[x3][y3]='#';
					y1++;
					y3++;
					c=c+2;
					
				}
				if(c==n)
				{
					System.out.println("YES");
					for(int i=0;i<4;i++)
					{
						for(int j=0;j<m;j++)
						{
							System.out.print(arr[i][j]);
						}
						System.out.println();
					}
				}
				else
				{
					System.out.println("NO");
				}
			}
			else
			{
				int c=1;
				int x=1;
				int y=(int)(m-1)/2;
				arr[x][y]='#';
				int q1=y-1;
				int q2=y+1;
				
				for(int i=1;i<n;i=i+2)
				{
					if(q1>0 && q2<m-1)
					{
						arr[x][q1]='#';
						arr[x][q2]='#';
						c=c+2;
						q1--;
						q2++;
					}
					if(q1==0 && q2==m-1 && x==1)
					{
						x=2;
						q1=y-1;
						q2=y+1;
					}
				}
				
				/*
				for(int i=0;i<n;i++)
				{
					//System.out.println("/");
					if(y1<=y2)
						{
						if(y2==(m-y1-1))
						{	
							arr[x1][y1]='#';
							y1++;
							//System.out.println("/");
						}
						else
						{
							arr[x2][y2]='#';
							y2--;
						}
						c++;
						}
					else
					{
						if(y4==(m-y3-1))
						{	
							arr[x3][y3]='#';
							y3++;
						}
						else
						{
							arr[x4][y4]='#';
							y4--;
						}
						c++;
					}
				}*/
				if(c==n)
				{
					System.out.println("YES");
					for(int i=0;i<4;i++)
					{
						for(int j=0;j<m;j++)
						{
							System.out.print(arr[i][j]);
						}
						System.out.println();
					}
				}
				else
				{
					System.out.println("NO");
				
					for(int i=0;i<4;i++)
					{
						for(int j=0;j<m;j++)
						{
							System.out.print(arr[i][j]);
						}
						System.out.println();
					}
				}
			}
			
		}
			
		

	}

}
