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.lang.*;
import java.math.*;
import java.util.*;

public class B {
	public static void main(String[] args) {
        FastReader fr = new FastReader();
        int n = fr.nextInt();
        int k = fr.nextInt();
        StringBuilder sb = new StringBuilder();
        if(k%2==0){
            sb.append("YES\n");
            boolean[][] bool = new boolean[4][n];
            for(int i = 0; i < k/2; i++){
                bool[1][i+1] = true;
                bool[2][i+1] = true;
            }
            for(int j = 0; j < 4; j++){
                for(int kk = 0; kk < n; kk++){
                    if(bool[j][kk]) sb.append("#");
                    else sb.append(".");
                }
                sb.append("\n");
            }
        }else if(k == n-2){
            sb.append("YES\n");
            boolean[][] bool = new boolean[4][n];
            for(int i = 0; i < k; i++){
                bool[1][i+1] = true;
            }
            for(int j = 0; j < 4; j++){
                for(int kk = 0; kk < n; kk++){
                    if(bool[j][kk]) sb.append("#");
                    else sb.append(".");
                }
                sb.append("\n");
            }
        }else if(k > n-1){
            sb.append("YES\n");
            boolean[][] bool = new boolean[4][n];
            for(int i = 0; i < n-2; i++){
                bool[1][i+1] = true;
            }
            for(int i = n-2; i < k-1; i++){
                bool[2][i-(n-2)+1] = true;
            }
            bool[2][n-2] = true;
            for(int j = 0; j < 4; j++){
                for(int kk = 0; kk < n; kk++){
                    if(bool[j][kk]) sb.append("#");
                    else sb.append(".");
                }
                sb.append("\n");
            }
        }else if(k > 4){
            sb.append("YES\n");
            boolean[][] bool = new boolean[4][n];
            for(int i = 0; i < (k+1)/2; i++){
                bool[1][i+1] = true;
            }
            for(int i = (k+1)/2; i < k-1; i++){
                bool[2][i-(k+1)/2+1] = true;
            }
            bool[2][(k+1)/2] = true;
            for(int j = 0; j < 4; j++){
                for(int kk = 0; kk < n; kk++){
                    if(bool[j][kk]) sb.append("#");
                    else sb.append(".");
                }
                sb.append("\n");
            }
        }else if(k == 1){
            sb.append("YES\n");
            boolean[][] bool = new boolean[4][n];
            bool[2][n/2] = true;
            for(int j = 0; j < 4; j++){
                for(int kk = 0; kk < n; kk++){
                    if(bool[j][kk]) sb.append("#");
                    else sb.append(".");
                }
                sb.append("\n");
            }
        }else if(k == 3){
            sb.append("YES\n");
            boolean[][] bool = new boolean[4][n];
            bool[2][n/2] = true;
            bool[2][n/2-1] = true;
            bool[2][n/2+1] = true;
            for(int j = 0; j < 4; j++){
                for(int kk = 0; kk < n; kk++){
                    if(bool[j][kk]) sb.append("#");
                    else sb.append(".");
                }
                sb.append("\n");
            }
        }else{
            sb.append("NO\n");
        }
        System.out.print(sb);
	}
}

class FastReader{
	BufferedReader br;
	StringTokenizer st;

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

	String next(){
		while(st==null || !st.hasMoreTokens()){
			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;
	}
}

//source: http://www.geeksforgeeks.org/fast-io-in-java-in-competitive-programming/