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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

int main()
{
	long long H, W;
	scanf("%lld %lld", &H, &W);
	if (H % 3 == 0 || W % 3 == 0) {
		printf("0\n");
		fflush(stdout);
		return 0;
	}

	long long min = (H < W)? H: W;
	if ((H + 1) / 2 * (W - W / 3) - H * (W / 3) < min) min = (H + 1) / 2 * (W - W / 3) - H * (W / 3);
	if ((W + 1) / 2 * (H - H / 3) - W * (H / 3) < min) min = (W + 1) / 2 * (H - H / 3) - W * (H / 3);
	if (H * (W / 3 + 1) - (H / 2) * (W - W / 3 - 1) < min) min = H * (W / 3 + 1) - (H / 2) * (W - W / 3 - 1);
	if (W * (H / 3 + 1) - (W / 2) * (H - H / 3 - 1) < min) min = W * (H / 3 + 1) - (W / 2) * (H - H / 3 - 1);

	printf("%lld\n", min);
	fflush(stdout);
	return 0;
}