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: Accepted)

($H,$W)=glob<>;
$%=1e16;
for(1,2){
	$t=($H/3|0);
	for($t-1,$t,$t+1){
		if($_>0){
			@_=sort{$a-$b}$_*$W,($H-$_)*($W>>1),($H-$_)*($W-($W>>1));
			$%-=$-=$%-($_[2]-$_[0]);
			@_=sort{$a-$b}$_*$W,($H-$_>>1)*$W,($H-$_-($H-$_>>1))*$W;
			$%-=$-=$%-($_[2]-$_[0]);
		}
	}
	($H,$W)=($W,$H);
}
print$%,$/