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 <algorithm>
using namespace std;

long long calc(long long a, long long b, long long c)
{
	long long x = max({ a, b, c });
	long long y = min({ a, b, c });

	return abs(x - y);
}

int main(void)
{
	long long H, W;
	cin >> H >> W;

	if (H % 3 == 0 || W % 3 == 0) {
		cout << "0" << endl;
		return 0;
	}

	long long min = 999999999999;
	long long S1, S2, S3, ans;
	for (int j = 0; j < 2; ++j) {
		for (int i = 1; i < H; ++i) {
			S1 = i * W;
			S2 = (H - i) / 2 * W;
			S3 = (H - i + 1) / 2 * W;
			ans = calc(S1, S2, S3);
			if (min > ans)	min = ans;

			S2 = (H - i) * (W / 2);
			S3 = (H - i) * ((W + 1) / 2);
			ans = calc(S1, S2, S3);
			if (min > ans)	min = ans;
		}
		int tmp = H;
		H = W;
		W = tmp;
	}

	cout << min << endl;

	return 0;
}