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 OCaml (4.02.3) (judge verdict: Accepted)

let diff3 a b c = max a (max b c) - min a (min b c)
let calc a b =
  let sub_calc s0 a' b' =
    let d0 = diff3 s0 (a'/2*b') ((a'-a'/2)*b') in
    let d1 = diff3 s0 (b'/2*a') ((b'-b'/2)*a') in
    min d0 d1
  in
  [ sub_calc (a/3*b) (a-a/3) b;
    sub_calc ((a+3)/3*b) (a-(a+3)/3) b;
    sub_calc (b/3*a) a (b-b/3);
    sub_calc ((b+3)/3*a) a (b-(b+3)/3);
  ] |> List.fold_left min 1010101010101010
let h, w = Scanf.scanf "%d %d" (fun x y -> x, y)
let () = calc h w |> Printf.printf "%d\n"