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)

if (h % 3).zero? || (w % 3).zero?
  p 0
  exit
end

ans = h * w

a0 = h / 3
(a0 - 3..a0 + 3).each do |a|
  next if a < 0
  next if h - a - a < 0
  ds = (h - 3 * a).abs * w
  ans = [ans, ds].min
end

h, w = w, h

a0 = h / 3
(a0 - 3..a0 + 3).each do |a|
  next if a < 0
  next if h - a - a < 0
  ds = (h - 3 * a).abs * w
  ans = [ans, ds].min
end

a0 = h / 3
b0 = w / 2
(a0 - 3..a0 + 3).each do |a|
  (b0 - 3..b0 + 3).each do |b|
    s0 = a * w
    s1 = (h - a) * b
    s2 = (h - a) * (w - b)
    next if s0 < 0
    next if s1 < 0
    next if s2 < 0
    ans = [ans, [s0, s1, s2].max - [s0, s1, s2].min].min
  end
end

h, w = w, h

a0 = h / 3
b0 = w / 2
(a0 - 3..a0 + 3).each do |a|
  (b0 - 3..b0 + 3).each do |b|
    s0 = a * w
    s1 = (h - a) * b
    s2 = (h - a) * (w - b)
    next if s0 < 0
    next if s1 < 0
    next if s2 < 0
    ans = [ans, [s0, s1, s2].max - [s0, s1, s2].min].min
  end
end

p ans