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: Wrong Answer)

(defmacro defsolver (name vars &body body)
  `(defun ,name ()
     (let (,@(mapcar #'list
		    vars
		    (mapcar (constantly '(read))
			    vars)))
       ,@body)))

(defsolver prob-c (h w)
  (cond ((and (= h 2)
	      (= w 2))
	 (format t "1"))
	((or (= (mod h 3) 0)
	     (= (mod w 3) 0))
	 (format t "0"))
	(t
	 (format t "~a" (+ h w)))))

(prob-c)