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.Closeable;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Map.Entry;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class Main {
	
	public static void main(String[] args) throws IOException {
		try(final Scanner sc = new Scanner(System.in)){
			final int A = sc.nextInt();
			final int B = sc.nextInt();
			
			//final int W = 100;
			final int W = 100;
			final int H = 100;
			final int half_H = 50;
			ArrayList<ArrayList<Character>> board = new ArrayList<ArrayList<Character>>();
			for(int i = 0; i < H; i++){
				board.add(new ArrayList<Character>());
			}
			
			// A
			for(int i = 0; i < half_H; i++){
				for(int j = 0; j < W; j++){ board.get(i).add('#'); }
			}
			// B
			for(int i = half_H; i < H; i++){
				for(int j = 0; j < W; j++){ board.get(i).add('.'); }
			}
			
			
			
			int curr_A = 1;
			int curr_B = 1;
			
			LOOP_A:
			for(int i = 0; curr_A < A && i < half_H; i += 2){
				for(int j = 1; j < W; j += 2){
					board.get(i).set(j, '.');
					curr_A++;
					
					if(curr_A == A){ break LOOP_A; }
				}
			}
			
			LOOP_B:
			for(int i = H - 1; curr_B < B && i >= half_H; i -= 2){
				for(int j = 1; j < W; j += 2){
					board.get(i).set(j, '#');
					curr_B++;
					
					if(curr_B == B){ break LOOP_B; }
				}
			}
			
			
			try(final PrintWriter pw = new PrintWriter(System.out)){
				pw.println(H + " " + W);
				for(ArrayList<Character> line : board){
					for(int i = 0; i < W; i++){
						pw.print(line.get(i));
					}
					pw.println();
				}				
			}
		}
	}

	public static class Scanner implements Closeable {
		private BufferedReader br;
		private StringTokenizer tok;

		public Scanner(InputStream is) throws IOException {
			br = new BufferedReader(new InputStreamReader(is));
		}

		private void getLine() throws IOException {
			while (!hasNext()) {
				tok = new StringTokenizer(br.readLine());
			}
		}

		private boolean hasNext() {
			return tok != null && tok.hasMoreTokens();
		}

		public String next() throws IOException {
			getLine();
			return tok.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public int[] nextIntArray(int n) throws IOException {
			final int[] ret = new int[n];
			for (int i = 0; i < n; i++) {
				ret[i] = this.nextInt();
			}
			return ret;
		}

		public long[] nextLongArray(int n) throws IOException {
			final long[] ret = new long[n];
			for (int i = 0; i < n; i++) {
				ret[i] = this.nextLong();
			}
			return ret;
		}

		public void close() throws IOException {
			br.close();
		}
	}
}