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
/*
    Problem URL : http://arc074.contest.atcoder.jp/tasks/arc074_a

    Score  :
    Result :
    Time   : ms
    Memory : KB
 */

ini_set('error_reporting', E_ALL & ~E_NOTICE);

fscanf(STDIN, "%d %d", $H, $W);

$ans = min($H, $W);

if ($H % 3 == 0 || $W % 3 == 0) {
    echo "0\n";
    exit;
} else {
    for ($y = 1; $y < $H; $y++) {
        $a1 = $y * $W;
        if ($W % 2 == 0) {
            $a2 = $a3 = ($H - $y) * ($W / 2);
        } else {
            $a2 = ($H - $y) * floor($W / 2);
            $a3 = ($H - $y) * ceil($W / 2);
        }
        $mmin = min($a1, $a2, $a3);
        $mmax = max($a1, $a2, $a3);
        $ans = min($ans, $mmax - $mmin);
    }
    $tmp = $H;
    $H = $W;
    $W = $tmp;
    for ($y = 1; $y < $H; $y++) {
        $a1 = $y * $W;
        if ($W % 2 == 0) {
            $a2 = $a3 = ($H - $y) * ($W / 2);
        } else {
            $a2 = ($H - $y) * floor($W / 2);
            $a3 = ($H - $y) * ceil($W / 2);
        }
        $mmin = min($a1, $a2, $a3);
        $mmax = max($a1, $a2, $a3);
        $ans = min($ans, $mmax - $mmin);
    }
}

echo $ans . PHP_EOL;