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)

# require 'pry'
# binding.pry

h, w=gets.chomp.split.map(&:to_i)

if h%3==0 or w%3==0
  puts 0
else
  dif=10**12
  hh=h/2
  (1...w).each do |j|
    x=hh*j
    y=(h-hh)*j
    z=h*(w-j)
    d=[x, y, z].max-[x, y, z].min
    dif=[dif, d].min
  end
  dif=[dif, h].min

  h, w=w, h
  hh=h/2
  (1...w).each do |j|
    x=hh*j
    y=(h-hh)*j
    z=h*(w-j)
    d=[x, y, z].max-[x, y, z].min
    dif=[dif, d].min
  end
  dif=[dif, h].min
  
  puts dif
end

=begin
x+y+z=h*w (x<=y<=z)
a*b+c*d+e*f=h*w
=end