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>
#include <string>
#include <algorithm>
#include <vector>
#include <cmath>
#include <queue>
#include <map>
#include <unordered_map>
#include <set>
#include <functional>
using namespace std;

typedef long long ll;

int main() {
	ll h, w; cin >> h >> w;
	ll ans = 1e9;
	for (ll i = 1; i < h; ++i) {
		ans = min(ans, max(i*w, (h - i + 1) / 2 * w) - min(i*w, (h - i) / 2 * w));
		ans = min(ans, max(i*w, (w + 1) / 2 * (h - i)) - min(i*w, w / 2 * (h - i)));
	}
	for (ll i = 1; i < w; ++i) {
		ans = min(ans, max(i*h, (w - i + 1) / 2 * h) - min(i*h, (w - i) / 2 * h));
		ans = min(ans, max(i*h, (h + 1) / 2 * (w - i)) - min(i*h, h / 2 * (w - i)));
	}
	cout << ans << endl;
	return 0;
}