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 0
end

area = h * w

b = [h, w].max
s = [h, w].min

third = (area / 3.0)
k = [(third / s).floor, (third / s).ceil].min_by {|i| (third - i*s).abs}

s1 = s * k
s2 = s3 = nil

rest = (b - k)

b = [rest, s].max
s = [rest, s].min

if b.even?
  x =  s * (b / 2)
  s2 = s3 = x
else
  x = s * ((b+1) / 2)
  y = s * (b / 2)
  s2 = x
  s3 = y
end

set = [s1,s2,s3]
p [s1,s2,s3]
puts (set.max - set.min).abs