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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Control.Applicative
import Control.Monad
import Data.Functor
import Data.List

type Rect = (Int, Int)

rarea :: Rect -> Int
rarea (h, w) = h * w

rsplit :: Rect -> [(Rect, Rect)]
rsplit (h, w) = [((y, w), (h-y, w)) | y <- [0..h`div`2]] ++ [((h, x), (h, w-x)) | x <- [0..w`div`2]]

eqsplit :: Rect -> [(Rect, Rect)]
eqsplit (h, w) = let (y, x) = (div h 2, div w 2) in [((y, w), (h-y, w)), ((h, x), (h, w-x))]

f :: Rect -> Rect -> Rect -> Int
f p q r = let l = map rarea [p, q, r] in maximum l - minimum l

solve :: [Int] -> Int
solve [h, w] = minimum $ concatMap (\(p, q) -> map (uncurry $ f p) (eqsplit q)) $ rsplit (h, w)

main = solve <$> (map read . words <$> getLine) >>= print