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 = 10 ** 10
(1...h).each do |height|
  half_width, mod = w.divmod(2)
  a = height * w
  b = (h - height) * half_width
  c = (h - height) * (half_width + mod)
  options = [a, b, c]
  gap = options.max - options.min
  ans = gap if ans > gap
end

if h >= 3
  third_height, mod = h.divmod(3)
  min = third_height * w
  max = mod.nonzero? ? (third_height + 1) * w : third_height * w
  gap = max - min
  ans = gap if ans > gap
end

h, w = w, h

(1...h).each do |height|
  half_width, mod = w.divmod(2)
  a = height * w
  b = (h - height) * half_width
  c = (h - height) * (half_width + mod)
  options = [a, b, c]
  gap = options.max - options.min
  ans = gap if ans > gap
end

if h >= 3
  third_height, mod = h.divmod(3)
  min = third_height * w
  max = mod.nonzero? ? (third_height + 1) * w : third_height * w
  gap = max - min
  ans = gap if ans > gap
end

puts ans