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 PHP (5.6.30) (judge verdict: Wrong Answer)

<?php
	$a = explode(" ",trim(fgets(STDIN)));
	$a1 = $a[0] / 2;
	$a2 = $a[1] / 2;
	$s1;
	$s2;
	$min = 100000;
	if($a[0]%3 == 0 || $a[1]%3 == 0){
		echo "0";
	}
	else{
		for($n = $a1;$n < $a[0];++$n){
			for($m = $a2;$m < $a[1];++$m){
				$s1[0] = $m * $n;
				$s1[1] = ($a[1] - $m) * $n;
				$s1[2] = ($a[0] - $n) * $a[1];
				$s2[0] = $m * $n;
				$s2[1] = ($a[1] - $m) * $a[0];
				$s2[2] = ($a[0] - $n) * $m;
				
				if((max($s1)-min($s1)) < $min){
					$min = (max($s1)-min($s1));
				}
				if((max($s2)-min($s2)) < $min){
					$min = (max($s2)-min($s2));
				}
			}
		}
		echo $min;
	}
?>