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)
ans  = []

#同じ方向に三等分するときの面積の差は(hを3で割ったあまり)*w
ans << (h % 3) * w
ans << (w % 3) * w

#Ｔ字型に三等分するときは愚直に
temp = []
for i in 1 .. (h + 1) / 2
  temp  = [i * w, (w / 2) * (h - i), ((w + 1) / 2) * (h - i)].sort
  ans  << (temp.max - temp.min).abs
end
for i in 1 .. (w + 1) / 2
  temp  = [i * h, (h / 2) * (w - i), ((h + 1) / 2) * (w - i)].sort
  ans  << (temp.max - temp.min).abs
end

puts ans.min