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)

def geti; gets.to_i end
def getis; gets.split.map &:to_i end
def getin n;  n.times.map{geti}  end
def getisn n; n.times.map{getis} end
YES = "YES"; NO = "NO"; Yes = "Yes"; No = "No";

h,w = getis
ans = 1e99
2.times do
  w.times do |i|
    a = h * i
    [(h / 2) * (w - i), h * i].map do |b|
      x = [a, b, h * w - a - b]
      ans = [ans, x.max - x.min].min
    end
  end
  h,w = w,h
end
p ans

__END__

n = geti
puts n % n.to_s.chars.map(&:to_i).reduce(:+) == 0 ? Yes : No

n,a,b = getis
p [n*a,b].min

a,b,c = getis
p [a,b,c].any?(&:even?) ? 0 : [a*b,b*c,c*a].min

a,b=getis
puts a > 0 ? 'Positive' : b >= 0 ? 'Zero' : (b - a) % 2 == 1 ? 'Positive' : 'Negative'