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){
    echo 0;exit;
}
$minDiff = min($H,$W);
foreach([[$H,$W],[$W,$H]] as list($w, $h)){
    $small = floor($w / 3.0) * $h;
    $large = ($w - floor($w / 3.0)) * ceil($h/2.0);
    $minDiff = min($minDiff, $large-$small);

    $large = ceil($w / 3.0) * $h;
    $small = ($w - ceil($w / 3.0)) * floor($h/2.0);
    $minDiff = min($minDiff, $large-$small);
}
echo $minDiff;