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)

h,w=gets.split.map(&:to_i)
diff_min = 100000000000
[h/3-2, 1].max.upto([h/3+2, h-1].min) do |i|
  [2*h/3-2, 1].max.upto([2*h/3+2, h-1].min) do |j|
    s1 = w * i
    s2 = w * (h - i - j)
    s3 = w * j
    diff = [s1, s2, s3].max - [s1, s2, s3].min
    diff_min = diff if diff_min > diff
  end
end

[w/3-2, 1].max.upto([w/3+2, w-1].min) do |i|
  [2*w/3-2, 1].max.upto([2*w/3+2, w-1].min) do |j|
    s1 = h * i
    s2 = h * (w - i - j)
    s3 = h * j
    diff = [s1, s2, s3].max - [s1, s2, s3].min
    diff_min = diff if diff_min > diff
  end
end

[h/3-2, 1].max.upto([h/3+2, h-1].min) do |i|
  [w/2-2, 1].max.upto([w/2+2, w-1].min) do |j|
    s1 = w * i
    s2 = j * (h - i)
    s3 = (w - j) * (h - i)
    diff = [s1, s2, s3].max - [s1, s2, s3].min
    diff_min = diff if diff_min > diff
  end
end

[w/3-2, 1].max.upto([w/3+2, w-1].min) do |i|
  [h/2-2, 1].max.upto([h/2+2, h-1].min) do |j|
    s1 = h * i
    s2 = j * (w - i)
    s3 = (h - j) * (w - i)
    diff = [s1, s2, s3].max - [s1, s2, s3].min
    diff_min = diff if diff_min > diff
  end
end
puts diff_min