Problem: You are given two integers A and B.

Print a grid where each square is painted white or black that satisfies the following conditions, in the format specified in Output section:

* Let the size of the grid be h \times w (h vertical, w horizontal). Both h and w are at most 100.
* The set of the squares painted white is divided into exactly A connected components.
* The set of the squares painted black is divided into exactly B connected components.



It can be proved that there always exist one or more solutions under the conditions specified in Constraints section. If there are multiple solutions, any of them may be printed.

Constraints

* 1 \leq A \leq 500
* 1 \leq B \leq 500

Input

Input is given from Standard Input in the following format:


A B


Output

Output should be in the following format:

* In the first line, print integers h and w representing the size of the grid you constructed, with a space in between.
* Then, print h more lines. The i-th (1 \leq i \leq h) of these lines should contain a string s_i as follows:
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted white, the j-th character in s_i should be `.`.
* If the square at the i-th row and j-th column (1 \leq j \leq w) in the grid is painted black, the j-th character in s_i should be `#`.

Examples

Input

2 3


Output

3 3
##.
..#
#.#


Input

7 8


Output

3 5
.#.#
.#.#.
.#.#


Input

1 1


Output

4 2
..
.


Input

3 14


Output

8 18
..................
..................
....##.......####.
....#.#.....#.....
...#...#....#.....
..#.###.#...#.....
.#.......#..#.....
.........#..####.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Main {

	public static void main(String[] args) throws IOException {
		MyScanner sc = new MyScanner(System.in);
		int a = sc.nextInt();
		int b = sc.nextInt();
		char[][] map = new char[100][99];
		for(int i=0; i<100; i++) {
			Arrays.fill(map[i], '.');
		}
		fillA(map, a);
		if(a==1) {
			fillB(map, b+1);	
		} else {
			fillB(map, b);
		}
		PrintWriter pw = new PrintWriter(System.out);
		pw.println(100 + " " + 99);
		for(int i=0; i<100; i++) {
			for(int j=0; j<99; j++) {
				pw.print(map[i][j]);
			}
			pw.println();
		}
		pw.close();
	}
	
	static void fillA(char[][] map, int a) {
		for(int i=0; i<100; i+=3) {
			for(int j=0; j<99; j+=3) {
				if(a-1>0) {
					fillBlock(map, i, j);
					a--;
				} else if(a-1==0) {
					return;
				} else {
					assert false;
				}
			}
		}
	}
	
	static void fillBlock(char[][] map, int i, int j) {
		for(int ii=i; ii<i+3; ii++) {
			for(int jj=j; jj<j+3; jj++) {
				map[ii][jj] = '#';
			}
		}
		map[i+1][j+1]='.';
	}
	
	static void fillB(char[][] map, int b) {
		for(int i=99; i>=50; i-=2) {
			for(int j=0; j<99; j+=2) {
				if(b-1>0) {
					if(j%2==0) {
						map[i][j] = '#';
						b--;
					}
				} else if(b-1==0) {
					return;
				} else {
					assert false;
				}
			}
		}
	}

	static class MyScanner
	{
		BufferedReader br;
		StringTokenizer st;
		public MyScanner(InputStream s)
		{
			br=new BufferedReader(new InputStreamReader(s));
		}
		public String nextLine() throws IOException
		{
			return br.readLine();
		}
		public String next() throws IOException
		{
			while(st==null || !st.hasMoreTokens())
				st=new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public int nextInt() throws IOException
		{
			return Integer.parseInt(next());
			
		}
		public double nextDouble() throws IOException
		{
			return Double.parseDouble(next());
		}
		public boolean ready() throws IOException
		{
			return br.ready();
		}
		public long nextLong() throws IOException
		{
			return Long.parseLong(next());
		}
	}
}