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

solve :: Int -> Int -> Int
solve h w 
  | h `mod` 3 == 0 = 0
  | w `mod` 3 == 0 = 0
  | otherwise =
    -- Hで全探査
    let 
      hm = minimum [min (max3 a b1 c1 - min3 a b1 b1)  (max3 a b2 c2 - min3 a b2 c2)| 
         h'<-[1..(h-1)], 
         let a = h' * w,
         let b1 = (h-h')`div`2*w,
         let c1 = ((h-h')`div`2 + (h-h')`mod`2)*w,
         let b2 = (h-h')*(w`div`2),
         let c2 = (h-h')*(w`div`2 + w`mod`2)  ]  
      
      -- Wで全探査
      wm = minimum [min (max3 a b1 c1 - min3 a b1 b1)  (max3 a b2 c2 - min3 a b2 c2)| 
         w'<-[1..(w-1)], 
         let a = h * w',
         let b1 = (w-w')`div`2*h,
         let c1 = ((w-w')`div`2 + (w-w')`mod`2)*h,
         let b2 = (w-w')*(h`div`2),
         let c2 = (w-w')*(h`div`2 + h`mod`2)  ]  
    in 
      min hm wm
    where
      max3 a b c = max (max a b) c
      min3 a b c = min (min a b) c