Problem:
Score : 400 points

Problem Statement

There is a bar of chocolate with a height of H blocks and a width of W blocks.
Snuke is dividing this bar into exactly three pieces.
He can only cut the bar along borders of blocks, and the shape of each piece must be a rectangle.

Snuke is trying to divide the bar as evenly as possible.
More specifically, he is trying to minimize S_{max} - S_{min}, where S_{max} is the area (the number of blocks contained) of the largest piece, and S_{min} is the area of the smallest piece.
Find the minimum possible value of S_{max} - S_{min}.

Constraints

2 ≤ H, W ≤ 10^5

Input

Input is given from Standard Input in the following format:

H W

Output

Print the minimum possible value of S_{max} - S_{min}.

Sample Input 1

3 5

Sample Output 1

0

In the division below, S_{max} - S_{min} = 5 - 5 = 0.

Sample Input 2

4 5

Sample Output 2

2

In the division below, S_{max} - S_{min} = 8 - 6 = 2.

Sample Input 3

5 5

Sample Output 3

4

In the division below, S_{max} - S_{min} = 10 - 6 = 4.

Sample Input 4

100000 2

Sample Output 4

1

Sample Input 5

100000 100000

Sample Output 5

50000

Solution in Ruby (2.3.3) (judge verdict: Accepted)

def bisect(h, w)
  [[(h/2)*w, (h-h/2)*w],
   [h*(w/2), h*(w-w/2)]]
end

def trisect(h, w)
  res = []

  hh = h/3
  if hh > 0
    res += bisect(h - hh, w).map { |pair| [hh*w, *pair] }
  end
  if h%3 > 0
    hh += 1
    res += bisect(h - hh, w).map { |pair| [hh*w, *pair] }
  end
  ww = w/3
  if ww > 0
    res += bisect(h, w - ww).map { |pair| [h*ww, *pair] }
  end
  if w%3 > 0
    ww += 1
    res += bisect(h, w - ww).map { |pair| [h*ww, *pair] }
  end

  res
end

h, w = gets.split.map(&:to_i)
choices = trisect(h, w)
p choices.map { |tri| tri.max - tri.min }.min