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: Time Limit Exceeded)

import Control.Applicative
import Data.List
import Data.Int
import Debug.Trace

count :: [Int64] -> Int64
count [h, w] =
    let calc :: Int64 -> Int64 -> Int64
        calc ver hor =
            let left = h * ver 
                top = ver * (h - hor)
                bottom = (w - ver) * (h - hor)
                [a, _, b] = sort [left, top, bottom]
                in  b - a
        horizon :: Int64 -> Int64 -> Int64
        horizon ver hor
            | hor > div w 2 = h * w 
            | otherwise = min (horizon ver (hor + 1)) (calc ver hor)
        vertex :: Int64 -> Int64
        vertex ver
            | ver > div h 2 = h * w
            | otherwise = min (vertex (ver + 1)) (horizon ver 1)
        in if (mod h 3) == 0 || (mod w 3) == 0 then 0 else vertex 1
        

main = print =<< count . reverse . sort . (map (\a -> read a :: Int64)) . words <$> getLine