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: Accepted)

#include <iostream>
using namespace std;

int main(){
	using ll = long long;
	ll h, w;
	cin >> h >> w;
	ll ans = 1ll << 60;
	for(ll i = 1; i <= (h + 2) / 3; i++){
		ll a = w * i, b = (h - i) * (w / 2 + (w & 1)), c = h * w - a - b;
		ans = min(ans, max(a, max(b, c)) - min(a, min(b, c)));
		b = w * ((h - i) / 2 + ((h - i) & 1)), c = h * w - a - b;
		ans = min(ans, max(a, max(b, c)) - min(a, min(b, c)));
	}
	for(ll i = 1; i <= (w + 2) / 3; i++){
		ll a = h * i, b = (w - i) * (h / 2 + (h & 1)), c = h * w - a - b;
		ans = min(ans, max(a, max(b, c)) - min(a, min(b, c)));
		b = h * ((w - i) / 2 + ((w - i) & 1)), c = h * w - a - b;
		ans = min(ans, max(a, max(b, c)) - min(a, min(b, c)));
	}
	cout << ans << endl;
}