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)

main :: IO ()
main = do
    [h, w] <- map read.words <$> getLine
    print $ solve h w

solve :: Int -> Int -> Int
solve h w
    | mod h 3 == 0 || mod w 3 == 0 = 0
    | otherwise = minimum resH `min` minimum resW
  where
    f x y z
        | even $ x * y = abs $ z - (x * y) `quot` 2
        | s <- (x * y - min x y) `quot` 2
            = maximum [abs (s - z), abs (x * y - s - z), min x y]
    resH = [f h (w - i) (h * i)| i <-[1..w-1]]
    resW = [f w (h - i) (w * i)| i <-[1..h-1]]