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)

h, w = gets.split.map(&:to_i)
ans = []

if h % 3 == 0 || w % 3 == 0
  ans = [0]
else
  # 縦2分割する(1:2)
  hikaeme_left = (w / 3.0).floor # 左小さめ
  rest = w - hikaeme_left
  # -> さらに縦分割
  if rest >= 2
    a = [hikaeme_left * h, (rest / 2.0).floor * h, (rest / 2.0).ceil * h]
    ans << a.max - a.min
  end
  # -> 大きい方を横分割
  if h >= 2
    b = [hikaeme_left * h, rest * (h / 2.0).floor, rest * (h / 2.0).ceil]
    ans << b.max - b.min
  end

  # 同様に
  donyoku_left = (w / 3.0).ceil # 左でかめ
  restx = w - donyoku_left
  if restx >= 2
    c = [donyoku_left * h, (restx / 2.0).floor * h, (restx / 2.0).ceil * h]
    ans << c.max - c.min
  end
  if h >= 2
    d = [donyoku_left * h, restx * (h / 2.0).floor, restx * (h / 2.0).ceil]
    ans << d.max - d.min
  end

  # 縦横逆転して
  w, h = [h, w] # swap

  # 縦2分割する(1:2)
  hikaeme_left = (w / 3.0).floor # 左小さめ
  rest = w - hikaeme_left
  # -> さらに縦分割
  if rest >= 2
    a = [hikaeme_left * h, (rest / 2.0).floor * h, (rest / 2.0).ceil * h]
    ans << a.max - a.min
  end
  # -> 大きい方を横分割
  if h >= 2
    b = [hikaeme_left * h, rest * (h / 2.0).floor, rest * (h / 2.0).ceil]
    ans << b.max - b.min
  end

  # 同様に
  donyoku_left = (w / 3.0).ceil # 左でかめ
  restx = w - donyoku_left
  if restx >= 2
    c = [donyoku_left * h, (restx / 2.0).floor * h, (restx / 2.0).ceil * h]
    ans << c.max - c.min
  end
  if h >= 2
    d = [donyoku_left * h, restx * (h / 2.0).floor, restx * (h / 2.0).ceil]
    ans << d.max - d.min
  end

end

puts ans.min