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)

def min_diff(h, w)
  min_diff = h * w
  # pattern 1
  if h % 3 == 0
    return 0
  else
    min_diff = [min_diff, w].min
  end

  # pattern 2
  1.upto(h-1).each do |hh|
    if w.even?
      diff = (hh * w - (h - hh) * (w / 2)).abs
      min_diff = [min_diff, diff].min
    else
      areas = [hh * w, (h - hh) * (w - 1) / 2, (h - hh) * (w + 1)/ 2]
      diff = areas.max - areas.min
      min_diff = [min_diff, diff].min
    end
  end

  min_diff
end

puts [min_diff(h, w), min_diff(w, h)].min