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)


ans = Float::INFINITY

1.upto(H - 1) do |h|
  areaA = h * W
  w = (W / 2).ceil
  areaB = (H - h) * w
  areaC = (H - h) * (W - w)

  ans = [ans, [areaA, areaB, areaC].minmax.inject(:-).abs].min

  c = ((H - h) / 2).ceil
  areaD = c * W
  areaE = (H - h - c) * W

  ans = [ans, [areaA, areaD, areaE].minmax.inject(:-).abs].min
end

1.upto(W - 1) do |w|
  areaA = w * H
  h = (H / 2).ceil
  areaB = (W - w) * h
  areaC = (W - w) * (H - h)

  ans = [ans, [areaA, areaB, areaC].minmax.inject(:-).abs].min

  c = ((W - w) / 2).ceil
  areaD = c * H
  areaE = (W - w - c) * H

  ans = [ans, [areaA, areaD, areaE].minmax.inject(:-).abs].min
end

puts ans