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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <algorithm>

using namespace std;

typedef long long ll;

int main() {
	ll h, w;
	cin >> h >> w;
	if (h % 3 == 0 || w % 3 == 0)
		cout << 0 << endl;
	else {
		ll ans = 99999999;
		for (ll i = 1; i < h; i++) {
			ll t = max(i*w, (h - i)*(w / 2 + w % 2)) - min(i*w, (h - i)*(w / 2));
			ans = min(ans, t);
		}
		for (ll i = 1; i < w; i++) {
			ll t = max(i*h, (w - i)*(h / 2 + h % 2)) - min(i*h, (w - i)*(h / 2));
			ans = min(ans, t);
		}
		cout << ans << endl;
	}
	return 0;
}