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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
fscanf(STDIN, "%d %d", $h, $w);
if ($h % 3 == 0 || $w % 3 == 0) {
	$x = 0;
} else {
	$x = min($h, $w);
	for ($i = 0; $i < 2; $i++) {
		$w1 = floor($w / 3);
		$w2 = $w1 + 1;
		$h1 = floor($h / 2);
		$h2 = ceil($h / 2);
		$s1 = ($w - $w1) * max($h1, $h2)  - $w1 * $h;
		$s2 = $w2 * $h - ($w - $w2) * min($h1, $h2);
		$x = min($x, $s1, $s2);
		if ($h == $w) break;
		list($h, $w) = [$w, $h];
	}
}
echo $x;