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)

line = gets
data = line.split(" ")
h = data[0].to_i
w = data[1].to_i
def cmin(s1, s2)
  min = s1 * s2
  if s2 % 2 == 0
    (1..(s1/2)).each do |i|
      s3 = s1 - i
      diff = (s2 * i) - ((s2/2) * s3)
      min = diff.abs if min > diff.abs
    end
  else
    area = Array.new(3)
    (1..(s1/2)).each do |i|
      s3 = s1 - i
      area[0] = s2 * i
      if s3 % 2 == 0
        area[1] = s2 * (s3/2)
        area[2] = s2 * (s3/2)
      elsif s2 < s3
        area[1] = s2 * (s3/2)
        area[2] = s2 * (s3 - s3/2)
      else
        area[1] = (s2/2) * s3
        area[2] = (s2 - s2/2) * s3
      end
      diff = area.max - area.min
      min = diff if min > diff
    end
  end
  return min
end
if h % 3 == 0 or w % 3 == 0
  puts 0
else
  min = cmin(h, w)
  if h != w
    result = cmin(w, h)
    min = result if min > result
  end
  p min
end