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
list($h, $w) = ints();
if ($h % 3 === 0 || $w % 3 === 0) exit('0');
$min = PHP_INT_MAX;

$min = min($min, $w * (intdiv($h, 3) + 1) - $w * intdiv($h, 3));
$min = min($min, $h * (intdiv($w, 3) + 1) - $h * intdiv($w, 3));

$s = [intdiv($w, 3) * $h, intdiv($h, 2) * ($w - intdiv($w, 3)), ($h - intdiv($h, 2)) * ($w - intdiv($w, 3))];
$min = min($min, max($s) - min($s));
$s = [(intdiv($w, 3) + 1) * $h, intdiv($h, 2) * ($w - (intdiv($w, 3) + 1)), ($h - intdiv($h, 2)) * ($w - (intdiv($w, 3) + 1))];
$min = min($min, max($s) - min($s));
$s = [intdiv($h, 3) * $w, intdiv($w, 2) * ($h - intdiv($h, 3)), ($w - intdiv($w, 2)) * ($h - intdiv($h, 3))];
$min = min($min, max($s) - min($s));
$s = [(intdiv($h, 3) + 1) * $w, intdiv($w, 2) * ($h - (intdiv($h, 3) + 1)), ($w - intdiv($w, 2)) * ($h - (intdiv($h, 3) + 1))];
$min = min($min, max($s) - min($s));
echo $min;
function ints()
{
    return array_map('intval', explode(' ', trim(fgets(STDIN))));
}