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>

int main() {
	int64_t h, w;
	std::cin >> h >> w;

	if (h % 3 == 0 || w % 3 == 0) {
		std::cout << 0 << std::endl;
		return 0;
	}
	if (h == 2 || w == 2) {
		std::cout << 1 << std::endl;
		return 0;
	}

	if (w < h) {
		std::swap(w, h);
	}

	int64_t min = 1e18;
	{
		int64_t A = (w + 2) / 3 * h;
		int64_t B = (w - (w + 2) / 3) * (h / 2);
		min = std::min(min, A - B);
	}
	{
		int64_t A = (w - w / 3) * ((h + 1) / 2);
		int64_t B = w / 3 * h;
		min = std::min(min, A - B);
	}
	std::cout << min << std::endl;
}