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:
def examA():
    C = [SI()for _ in range(3)]
    ans = C[0][0]+C[1][1]+C[2][2]
    print(ans)
    return

def examB():
    N, M = LI()
    P = [0]*N
    S = [LSI()for _ in range(M)]
    pena = 0
    ac = set()
    for p,s in S:
        p = int(p)-1
        if s=="WA":
            P[p] += 1
        else:
            if p in ac:
                continue
            ac.add(p)
            pena += P[p]

    print(len(ac),pena)
    return

def examC():
    W, H, N = LI()
    lx, rx, ly, ry = 0, W, 0, H
    A = [LI()for _ in range(N)]
    for x,y,a in A:
        if a==1:
            lx = max(lx,x)
        elif a==2:
            rx = min(rx,x)
        elif a==3:
            ly = max(ly,y)
        elif a==4:
            ry = min(ry,y)
    ans = max(0,rx-lx)*max(0,ry-ly)
    print(ans)
    return

def examD():
    N, H = LI()
    B = [0]*N
    maxa = 0
    ans = 0
    for i in range(N):
        a, B[i] = LI()
        if a>maxa:
            maxa = a
    B.sort(reverse=True)
    for b in B:
        if b<maxa:
            break
        H -= b
        ans += 1
        if H<=0:
            print(ans)
            return
    ans += -(-H//maxa)
    print(ans)
    return

def examE():
    A, B = LI()
    ans = [["#"]*100 for _ in range(50)] + [["."]*100 for _ in range(50)]
    i = 0; j = 0
    for _ in range(A-1):
        ans[i][j] = "."
        j += 2
        if j>=100:
            j = 0; i += 2
    i = 0; j = 0
    for _ in range(B-1):
        ans[99-i][j] = "#"
        j += 2
        if j>=100:
            j = 0; i += 2
    print(100,100)
    for v in ans:
        print("".join(map(str,v)))
    return

def examF():
    ans = 0
    print(ans)
    return

import sys,bisect,itertools,heapq,math,random
from copy import deepcopy
from heapq import heappop,heappush,heapify
from collections import Counter,defaultdict,deque
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
def I(): return int(readline())
def LI(): return list(map(int,readline().split()))
def LSI(): return list(map(str,sys.stdin.readline().split()))
def LS(): return sys.stdin.readline().split()
def SI(): return sys.stdin.readline().strip()
global mod,mod2,inf,alphabet,_ep
mod = 10**9 + 7
mod2 = 998244353
inf = 10**18
_ep = 10**(-12)
alphabet = [chr(ord('a') + i) for i in range(26)]

sys.setrecursionlimit(10**7)

if __name__ == '__main__':
    examE()

"""
142
12 9 1445 0 1
asd dfg hj o o
aidn
"""