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:
#!/usr/bin/env python3
#ARC93 D

import sys
import math
from bisect import bisect_right as br
from bisect import bisect_left as bl
sys.setrecursionlimit(1000000000)
from heapq import heappush, heappop,heappushpop
from collections import defaultdict
from itertools import accumulate
from collections import Counter
from collections import deque
from operator import itemgetter
from itertools import permutations
mod = 10**9 + 7
inf = float('inf')
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))

a,b = LI()
lst = []
for _ in range(50):
    lst.append(['#']*100)
for _ in range(50):
    lst.append(['.']*100)
print(100,100)
cnt = 0
flg = True
if cnt != a-1:
    for i in range(25-1):
        for j in range(25-1):
            lst[2*i][2*j] = '.'
            cnt += 1
            if cnt == a-1:
                flg = False
                break
        if not flg:
            break
cnt = 0
flg = True
if cnt != b-1:
    for i in range(25+1,50)[::-1]:
        for j in range(25+1,50)[::-1]:
            lst[2*i+1][2*j+1] = '#'
            cnt += 1
            if cnt == b-1:
                flg = False
                break
        if not flg:
            break
for i in range(100):
    print(''.join(lst[i]))