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.List
import Data.Char
strToInt s = (read :: String -> Int) s
strToInteger s = (read :: String -> Integer) s
strToDouble s = (read :: String -> Double) s

main :: IO ()
main = do
    -- スペース区切り整数の入力
    [h, w] <- map strToInt . words <$> getLine
    -- 出力
    putStrLn . show $ min (solve h w) (solve w h)

solve :: Int -> Int -> Int
solve h w = if ((h `mod` 3) == 0 || (w `mod` 3) == 0)
            then 0
            else min ver hor where
                ver = minimum [let chocor = map (* w) [k, (h-k) `div` 2, (h-k) - (h-k) `div` 2] in (maximum chocor - minimum chocor) | k <- [1..h-1]]
                hor = minimum [let chocos = [k * w, (h-k) * (w `div` 2), (h-k) * (w - w `div` 2)] in (maximum chocos - minimum chocos) | k <- [1..h-1]]