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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.util.NoSuchElementException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		Scanner in = new Scanner(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskD solver = new TaskD();
		solver.solve(1, in, out);
		out.close();
	}

	static class TaskD {
		public void solve(int testNumber, Scanner sc, PrintWriter out) {

			int a = sc.nextInt();
			int b = sc.nextInt();

			int w = 99, h = 100;
			boolean[][] block = new boolean[h][w];
			for (int i = h / 2; i < h; i++) {
				for (int j = 0; j < w; j++) {
					block[i][j] = true;
				}
			}

			for (int i = 0; i < a - 1; i++) {
				block[(i / (w / 2)) * 2 + 1][(i % (w / 2)) * 2 + 1] = true;
			}
			for (int i = 0; i < b - 1; i++) {
				block[(i / (w / 2)) * 2 + h / 2 + 1][(i % (w / 2)) * 2 + 1] = false;
			}

			out.println(h + " " + w);
			for (int i = 0; i < h; i++) {
				for (int j = 0; j < w; j++) {
					out.print(block[i][j] ? '.' : '#');
				}
				out.println();
			}

		}

	}

	static class Scanner {
		private final InputStream in;
		private final byte[] buffer;
		private int ptr;
		private int buflen;

		public Scanner(InputStream in) {
			this.in = in;
			this.buffer = new byte[1024];
			this.ptr = 0;
			this.buflen = 0;
		}

		private boolean hasNextByte() {
			if (ptr < buflen) return true;
			else {
				ptr = 0;
				try {
					buflen = in.read(buffer);
				} catch (IOException e) {
					e.printStackTrace();
				}
				if (buflen <= 0) return false;
			}
			return true;
		}

		private byte readByte() {
			if (hasNextByte()) return buffer[ptr++];
			return -1;
		}

		private boolean isPrintableChar(byte c) {
			return '!' <= c && c <= '~';
		}

		private void skipUnprintable() {
			while (hasNextByte() && !isPrintableChar(buffer[ptr])) {
				ptr++;
			}
		}

		public boolean hasNext() {
			skipUnprintable();
			return hasNextByte();
		}

		public int nextInt() {
			if (!hasNext()) throw new NoSuchElementException();
			int n = 0;
			boolean minus = false;
			byte b = readByte();
			if (b == '-') {
				minus = true;
				b = readByte();
			}
			if (b < '0' || '9' < b) throw new NumberFormatException();
			while (true) {
				if ('0' <= b && b <= '9') {
					n *= 10;
					n += b - '0';
				} else if (b == -1 || !isPrintableChar(b)) {
					return minus ? -n : n;
				} else {
					throw new NumberFormatException();
				}
				b = readByte();
			}
		}

	}
}