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: Wrong Answer)

main = do
 [h,w] <- map read . words <$> getLine
 print (cb h w)

cb h w
 | mod h 3 == 0 || mod w 3 == 0 = 0
 | h==1 || w==1 = 1
 | otherwise = min (maximum [s1,s2,s3] - minimum [s1,s2,s3]) (maximum [s1',s2',s3'] - minimum [s1',s2',s3'])
 where
  s1 = (div (max h w) 3 + 1) * (min h w)
  s2 = (div (min h w) 2) * (max h w - (div (max h w) 3 + 1))
  s3 = ((min h w) - (div (min h w) 2)) * (max h w - (div (max h w) 3 + 1))
  s1' = (div (max h w) 3) * (min h w)
  s2' = (div (min h w) 2) * (max h w - (div (max h w) 3))
  s3' = ((min h w) - (div (min h w) 2)) * (max h w - (div (max h w) 3))