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.Monad
import Control.Applicative
import Data.List
import Data.Array

strToInt s = (read :: String -> Int)

acut :: Int -> Int -> Int
acut h w 
  | h `mod` 3 == 0 = 0
  | otherwise = w

bcut :: Int -> Int -> Int
bcut h w = minimum [bcutsub h w c | c <-[1..(h-1)]]


bcutsub :: Int -> Int -> Int -> Int
bcutsub h w l = maximum [abs(a-b),abs(b-c),abs(c-a)]
                where a = (h-l) * (w `div` 2)
                      b = w * (h-l) - a
                      c = w * l



main = do

    [h,w] <- (map read . words) <$> getLine
    
    print (minimum [(acut h w) , (bcut h w) , (acut w h) , (bcut w h)])