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 PYTHON3):

Solution:
import sys
import math
import collections
import bisect
import itertools

# import numpy as np

sys.setrecursionlimit(10 ** 7)
INF = 10 ** 16
MOD = 10 ** 9 + 7
# MOD = 998244353

ni = lambda: int(sys.stdin.readline().rstrip())
ns = lambda: map(int, sys.stdin.readline().rstrip().split())
na = lambda: list(map(int, sys.stdin.readline().rstrip().split()))
na1 = lambda: list(map(lambda x: int(x) - 1, sys.stdin.readline().rstrip().split()))


# ===CODE===

def main():
    w, b = ns()
    l = 100
    mat = [["#" for _ in range(l)] for __ in range(l)]

    if w == 1 and b == 1:
        mat[0][0] = "."

    cnt = 0
    breakflg = False
    tmp = 1 if b > 1 else 0
    flg = False
    for i in range(0, l - 3, 3):
        for j in range(0, l - 3, 3):
            if not flg:
                if cnt < w - tmp:
                    around = "#"
                    center = "."
                else:
                    flg = True
                    break

            if flg:
                if cnt < w - tmp + b - 1:
                    around = "."
                    center = "#"
                else:
                    breakflg = True
                    break




            for n in range(3):
                for m in range(3):
                    mat[i + n][j + m] = center if n == 1 and m == 1 else around
            cnt += 1
        if breakflg:
            break

    print(l, l)
    for mi in mat:
        print(*mi, sep="")


if __name__ == '__main__':
    main()