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 Data.List

main = do
  [h, w] <- map read . words <$> getLine :: IO [Int]
  let ws = map (solve h w) [1..w-1]
      hs = map (solve w h) [1..h-1]
  print $ min (minimum ws) (minimum hs)

solve :: Int -> Int -> Int -> Int
solve h w wa = let wb = (w - wa) `div` 2
                   x = wa * h
                   y1 = wb * h
                   z1 = (w - wa - wb) * h
                   y2 = (w - wa) * (h `div` 2)
                   z2 = (w - wa) * ((-) h $ h `div` 2)
                   mi1 = minimum [x, y1, z1]
                   ma1 = maximum [x, y1, z1]
                   mi2 = minimum [x, y2, z2]
                   ma2 = maximum [x, y2, z2]
               in if w - wa >= 2 then min (ma1 - mi1) (ma2 - mi2)
                                 else ma2 - mi2