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 Perl (v5.18.2) (judge verdict: Wrong Answer)

#!/usr/bin/perl -w

while(<>) {
    ($h, $w) = split /\s/, $_;
}

if($h % 3 == 0 || $w % 3 == 0) {
    print "0\n";
    exit;
}

$m = 0;
if($h % 2 == 0 && $w % 2 == 0) {
    if($h > $w) {
        $x = $h;
        $y = $w;
    } else {
        $x = $h;
        $y = $w;
    }
    $m = 1;
} elsif($h % 2 == 0) {
    $x = $w;
    $y = $h;
    $m = 1;
} elsif ($w % 2 == 0) {
    $x = $h;
    $y = $w;
    $m = 1;
} elsif ($w % 3 == 1) {
    $x = $h;
    $y = $w;
} else {
    $x = $w;
    $y = $h;
}

if($m == 1) {
    if($x % 3 == 1) {
        $l = sprintf("%d", $x / 3) * $y;
        $s = (sprintf("%d", $x / 3) * 2 + 1) * $y / 2;
    } elsif($x % 3 == 2) {
        $l = (sprintf("%d", $x / 3) + 1) * $y;
        $s = (sprintf("%d", $x / 3) * 2 + 1) * $y / 2;
    }
    print abs($l - $s), "\n";
} else {
    if($x % 3 == 1) {
        $l = sprintf("%d", $x / 3) * $y;
        $s = (sprintf("%d", $x / 3) * 2 + 1) * sprintf("%d", $y / 2);
    } elsif($x % 3 == 2) {
        $l = (sprintf("%d", $x / 3) + 1) * $y;
        $s = (sprintf("%d", $x / 3) * 2 + 1) * sprintf("%d", $y / 2);
    }
    print $l - $s, "\n";
}