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 <bits/stdc++.h>

using namespace std;

typedef long long ll;

ll result = LLONG_MAX;

ll max(ll a, ll b, ll c) {return max(a, max(b, c));}
ll min(ll a, ll b, ll c) {return min(a, min(b, c));}

int main() {
  ll h, w;
	cin >> h >> w;

  result = min(result, h%3*w);
	if (result == 0) {
    cout << 0 << endl;
		return 0;
	}
	result = min(result, w%3*h);
	if (result == 0) {
    cout << 0 << endl;
		return 0;
	}

	for (int i = 1; i < w; i++) {
    result = min(result, max(h*i, (w-i)*(h/2), (w-i)*(h/2+h%2)) - min(h*i, (w-i)*(h/2), (w-i)*(h/2+h%2)));
		if (result == 0) {
      cout << 0 << endl;
			return 0;
		}
	}

	for (int i = 1; i < h; i++) {
    result = min(result, max(w*i, (h-i)*(w/2), (h-i)*(w/2+w%2)) - min(w*i, (h-i)*(w/2), (h-i)*(w/2+w%2)));
		if (result == 0) {
      cout << 0 << endl;
			return 0;
		}
	}

	cout << result << endl;

	return 0;
}