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 Common Lisp (SBCL 1.1.14) (judge verdict: Runtime Error)

(defmacro swap (a b)
  `(let ((temp ,a))
     (setf ,a ,b)
     (setf ,b temp)))

(defun solver ()
  (let ((H (read)) (W (read)) (sabun 100000))
    (if (or (zerop (mod W 3)) (zerop (mod H 3)))
        (format t "0~%")
        (progn
          (when (=> H W) (swap H W))
          (let ((H2 (1- (floor (/ H 2)))))
          (loop for a from 1 to W do
                (loop for b from H2 to (+ H2 2) do
                      (let* ((c1 (* a b))
                             (c2 (* (- W a) H))
                             (c3 (* a (- H b)))
                             (minchoco (min c1 c2 c3))
                             (maxchoco (max c1 c2 c3)))
                        (when (> sabun (- maxchoco minchoco))
                          (setf sabun (- maxchoco minchoco))))))
          (format t "~A~%" sabun))))))

(solver)