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)

if h % 3 == 0 || w % 3 == 0
  puts 0
  exit
end

a = nil
h2 = h
w2 = w
if h > w
  _h = (h.to_f / 3).ceil
  a = _h * w
  h2 = h - _h
else
  _w = (w.to_f / 3).ceil
  a = h * _w
  w2 = w - _w
end

if h2 % 2 == 0 || w2 % 2 == 0
  result = a - (h2 * w2) / 2
elsif h2 > w2 
  result = a - (h2 / 2) * w2
else
  result = a - (w2 / 2) * h2
end

a = nil
h2 = h
w2 = w
if h > w
  _h = (h.to_f / 3).floor
  a = _h * w
  h2 = h - _h
else
  _w = (w.to_f / 3).floor
  a = h * _w
  w2 = w - _w
end

if h2 % 2 == 0 || w2 % 2 == 0
  result2 = (a - (h2 * w2) / 2).abs
elsif h2 > w2 
  result2 = (a - (h2 / 2) * w2).abs
else
  result2 = (a - (w2 / 2) * h2).abs
end

if result < result2
  puts result
else
  puts result2
end