Problem:
Score : 500 points

Problem Statement

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.

Notes

Two squares painted white, c_1 and c_2, are called connected when the square c_2 can be reached from the square c_1 passing only white squares by repeatedly moving up, down, left or right to an adjacent square.

A set of squares painted white, S, forms a connected component when the following conditions are met:

Any two squares in S are connected.

No pair of a square painted white that is not included in S and a square included in S is connected.

A connected component of squares painted black is defined similarly.

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 #.

Sample Input 1

2 3

Sample Output 1

3 3
##.
..#
#.#

This output corresponds to the grid below:

Sample Input 2

7 8

Sample Output 2

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

Sample Input 3

1 1

Sample Output 3

4 2
..
#.
##
##

Sample Input 4

3 14

Sample Output 4

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

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.UncheckedIOException;
import java.util.StringTokenizer;

class Main{
	static int[][] area;
	static int White,Black;
	static int zone;
	public static void main(String[] args) {
		SC sc=new SC(System.in);
		int A=sc.nextInt();
		int B=sc.nextInt();
		area=new int[100][100];
		for(int i=0; i<100; i++) {
			for(int j=0; j<100; j++) {
				area[i][j]=0;
			}
		}
		if(A==B && A==1) {
			pl("1 2");
			pl(".#");
			System.exit(0);
		}
		pl("100 100");
		if(A>=B) {	//白のほうが多い
			White=A;
			Black=B;
			zone=1;
			Black--;
			White--;
			fill(zone);
			zone+=2;
			dot(zone);
			StringBuilder sb=new StringBuilder();
			for(int i=0; i<100; i++) {
				sb=new StringBuilder();
				for(int j=0; j<100; j++) {
					if(area[i][j]==0) {
						sb.append(".");
					}
					else {
						sb.append("#");
					}
				}
				pl(sb.toString());
			}
		}
		else if(A<B) {	//跡で反転させる
			int tmp=B;
			B=A;
			A=tmp;
			White=A;
			Black=B;
			zone=1;
			Black--;
			White--;
			fill(zone);
			zone+=2;
			dot(zone);
			StringBuilder sb=new StringBuilder();
			for(int i=0; i<100; i++) {
				sb=new StringBuilder();
				for(int j=0; j<100; j++) {
					if(area[i][j]==0) {
						sb.append("#");
					}
					else {
						sb.append(".");
					}
				}
				pl(sb.toString());
			}
		}
	}
	public static void fill(int i) {
		for(int j=0; j<100; j++) {
			area[i][j]=1;	//黒でぬる
		}
		White--;
		if(White<=49) {
			for(int j=1; j<=White; j++) {
				area[i-1][j*2-1]=1;
			}
			White=0;
		}
		else if(White>49) {
			for(int j=1; j<=97; j+=2) {
				area[i-1][j]=1;
			}
			White-=49;
			if(White>0) {
				zone+=2;
				fill(i+2);
			}
		}
	}
	public static void dot(int i) {

		if(Black<=50) {
			for(int j=0; j<Black; j++) {
				area[i][j*2]=1;
			}
			Black=0;
		}

		else if(Black>50) {
			for(int j=0; j<100; j+=2) {
				area[i][j]=1;
			}
			Black-=50;
			if(Black>0) {
				dot(i+2);
			}
		}
	}
	public static void pl(Object o) {
		System.out.println(o);
	}
	public static void pl() {
		System.out.println();
	}
	public static void p(Object o) {
		System.out.print(o);
	}
	static class SC {
		private BufferedReader reader = null;
		private StringTokenizer tokenizer = null;
		public SC(InputStream in) {
			reader = new BufferedReader(new InputStreamReader(in));
		}
		public String next() {
			if (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new UncheckedIOException(e);
				}
			}
			return tokenizer.nextToken();
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new UncheckedIOException(e);
			}
		}
	}
}