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.chomp.split(' ').map(&:to_i)
if h % 3 == 0 || w % 3 == 0
  puts 0
else
  candidate1 = [
    [w * (h / 3), w / 2 * (h - h / 3), (w - w / 2) * (h - h / 3)],
    [w * (h / 3 + 1), w / 2 * (h - h / 3 - 1), (w - w / 2) * (h - h / 3 - 1)],
    [w * (h / 3), (w / 2 + 1) * (h - h / 3), (w - w / 2 - 1) * (h - h / 3)],
    [w * (h / 3 + 1), (w / 2 + 1) * (h - h / 3 - 1), (w - w / 2 - 1) * (h - h / 3 - 1)],
    [h * (w / 3), h / 2 * (w - w / 3), (h - h / 2) * (w - w / 3)],
    [h * (w / 3 + 1), h / 2 * (w - w / 3 - 1), (h - h / 2) * (w - w / 3 - 1)],
    [h * (w / 3), (h / 2 + 1) * (w - w / 3), (h - h / 2 - 1) * (w - w / 3)],
    [h * (w / 3 + 1), (h / 2 + 1) * (w - w / 3 - 1), (h - h / 2 - 1) * (w - w / 3 - 1)],
  ].map { |c| c.max - c.min }.min
  candidate2 = [h, w].min
  puts [candidate1, candidate2].min
end