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)


solve :: Int -> Int -> Int
solve a b =
  let c = round(fromIntegral a/3)
      d = a - c
      e = b `div` 2
      f = b - e
      g = d `div` 2
      h = d - g
      ls1 = [ c*b, e*d, f*d ]
      ls2 = [ c*b, g*b, h*b ]
  in min (maximum ls1 - minimum ls1) (maximum ls2 - minimum ls2)

main = do
  [h, w] <- map read.words <$> getLine :: IO [Int]
  if h`mod`3 == 0 || w`mod`3 == 3
    then print 0
    else print $ min (solve h w) (solve w h)