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.*;
import java.util.*;

public class Main {

	private static Scanner sc;
	private static Printer pr;

	private static void solve() {
		int a = sc.nextInt();
		int b = sc.nextInt();

		boolean swap = false;
		if (a < b) {
			swap = true;
			int tmp = a;
			a = b;
			b = tmp;
		}

		if (a == 1 && b == 1) {
			pr.printf("%d %d\n", 1, 2);
			pr.println("#.");
		} else if (b == 1) {
			int w = 50;
			int h = (a + 49) / 50;

			StringBuilder ans = new StringBuilder();
			int cnt = 0;
			for (int i = 0; i < h; i++) {
				for (int j = 0; j < 2 * w; j++) {
					if (j % 2 == 0 || cnt >= a) {
						ans.append('#');
					} else {
						ans.append('.');
						cnt++;
					}
				}
				ans.append("\n");
				for (int j = 0; j < 2 * w; j++) {
					ans.append('#');
				}
				ans.append("\n");
			}

			pr.printf("%d %d\n", 2 * h, 2 * w);
			if (swap) {
				pr.print(ans.toString().replace('.', 'x').replace('#', '.').replace('x', '#'));
			} else {
				pr.print(ans);
			}
		} else {
			int aa = a - 1;
			int hh = 0;

			int w = 50;
			int h = (aa + 49) / 50;
			hh += 2 * h;

			StringBuilder ans = new StringBuilder();
			int cnt = 0;
			for (int i = 0; i < h; i++) {
				for (int j = 0; j < 2 * w; j++) {
					if (j % 2 == 0 || cnt >= aa) {
						ans.append('#');
					} else {
						ans.append('.');
						cnt++;
					}
				}
				ans.append("\n");
				for (int j = 0; j < 2 * w; j++) {
					ans.append('#');
				}
				ans.append("\n");
			}

			for (int j = 0; j < 2 * w; j++) {
				ans.append('.');
			}
			ans.append("\n");
			hh++;

			aa = b - 1;

			w = 50;
			h = (aa + 49) / 50;
			hh += 2 * h;

			cnt = 0;
			for (int i = 0; i < h; i++) {
				for (int j = 0; j < 2 * w; j++) {
					if (j % 2 == 0 || cnt >= aa) {
						ans.append('.');
					} else {
						ans.append('#');
						cnt++;
					}
				}
				ans.append("\n");
				for (int j = 0; j < 2 * w; j++) {
					ans.append('.');
				}
				ans.append("\n");
			}

			pr.printf("%d %d\n", hh, 2 * w);
			if (swap) {
				pr.print(ans.toString().replace('.', 'x').replace('#', '.').replace('x', '#'));
			} else {
				pr.print(ans);
			}

		}
	}

	// ---------------------------------------------------
	public static void main(String[] args) {
		sc = new Scanner(INPUT == null ? System.in : new ByteArrayInputStream(INPUT.getBytes()));
		pr = new Printer(System.out);

		solve();

//		pr.close();
		pr.flush();
//		sc.close();
	}

	static String INPUT = null;

	@SuppressWarnings("unused")
	private static class Scanner {
		BufferedReader br;

		Scanner (InputStream in) {
			br = new BufferedReader(new InputStreamReader(in));
		}

		private boolean isPrintable(int ch) {
			return ch >= '!' && ch <= '~';
		}

		private boolean isCRLF(int ch) {
			return ch == '\n' || ch == '\r' || ch == -1;
		}

		private int nextPrintable() {
			try {
				int ch;
				while (!isPrintable(ch = br.read())) {
					if (ch == -1) {
						throw new NoSuchElementException();
					}
				}

				return ch;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		String next() {
			try {
				int ch = nextPrintable();
				StringBuilder sb = new StringBuilder();
				do {
					sb.appendCodePoint(ch);
				} while (isPrintable(ch = br.read()));

				return sb.toString();
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		int nextInt() {
			try {
				// parseInt from Integer.parseInt()
				boolean negative = false;
				int res = 0;
				int limit = -Integer.MAX_VALUE;
				int radix = 10;

				int fc = nextPrintable();
				if (fc < '0') {
					if (fc == '-') {
						negative = true;
						limit = Integer.MIN_VALUE;
					} else if (fc != '+') {
						throw new NumberFormatException();
					}
					fc = br.read();
				}
				int multmin = limit / radix;

				int ch = fc;
				do {
					int digit = ch - '0';
					if (digit < 0 || digit >= radix) {
						throw new NumberFormatException();
					}
					if (res < multmin) {
						throw new NumberFormatException();
					}
					res *= radix;
					if (res < limit + digit) {
						throw new NumberFormatException();
					}
					res -= digit;

				} while (isPrintable(ch = br.read()));

				return negative ? res : -res;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		long nextLong() {
			try {
				// parseLong from Long.parseLong()
				boolean negative = false;
				long res = 0;
				long limit = -Long.MAX_VALUE;
				int radix = 10;

				int fc = nextPrintable();
				if (fc < '0') {
					if (fc == '-') {
						negative = true;
						limit = Long.MIN_VALUE;
					} else if (fc != '+') {
						throw new NumberFormatException();
					}
					fc = br.read();
				}
				long multmin = limit / radix;

				int ch = fc;
				do {
					int digit = ch - '0';
					if (digit < 0 || digit >= radix) {
						throw new NumberFormatException();
					}
					if (res < multmin) {
						throw new NumberFormatException();
					}
					res *= radix;
					if (res < limit + digit) {
						throw new NumberFormatException();
					}
					res -= digit;

				} while (isPrintable(ch = br.read()));

				return negative ? res : -res;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		float nextFloat() {
			return Float.parseFloat(next());
		}

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

		String nextLine() {
			try {
				int ch;
				while (isCRLF(ch = br.read())) {
					if (ch == -1) {
						throw new NoSuchElementException();
					}
				}
				StringBuilder sb = new StringBuilder();
				do {
					sb.appendCodePoint(ch);
				} while (!isCRLF(ch = br.read()));

				return sb.toString();
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		void close() {
			try {
				br.close();
			} catch (IOException e) {
//				throw new NoSuchElementException();
			}
		}
	}

	private static class Printer extends PrintWriter {
		Printer(OutputStream out) {
			super(out);
		}
	}
}