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.chomp.split.map(&:to_i)
max = 0
mid = 0
min = 0
if h % 3 == 0 then
  max = mid = min = (h / 3) * w
elsif w % 3 == 0
  max = mid = min = (w / 3) * h
else
  if h > w then #縦 > 横
    tate = (h / 3.0).ceil
    max = tate * w
    h = h - tate
  else
    yoko = (w / 3.0).ceil
    max = yoko * h
    w = w - yoko
  end

  if h > w then #縦 > 横
    tate = (h / 2.0).ceil
    mid = tate * w
    h = h - tate
    min = h * w
  else
  yoko = (w / 2.0).ceil
  mid = yoko * h
  w = w - yoko
  min = h * w
end
end
#puts "max=#{max} mid=#{mid} min=#{min}"
puts "#{[max,mid,min].max - [max,mid,min].min}"