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: Wrong Answer)

def f(h, w)
  area = h*w

  g=lambda{|h,w|
    return 0 if h%3==0
    h1 = area/3/w
    [h1, h1+1].map{|h1|
      # p [w,h]
      a1 = h1*w
      h23 = h-h1
      # p [h1, a1, h23]
      if w.even?
        (a1 - (area-a1)/2).abs
      else
        [(a1-w/2*h23).abs, (a1-(w/2+1)*h23).abs, h23].max
      end
    }.min
  }
  [g.(h,w), g.(w,h)].min
end

H, W = gets.split.take(2).map(&:to_i)
p f(H, W)