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: Wrong Answer)

#include <stdio.h>

long long int min(long long int a, long long int b) { return a < b ? a : b; }
long long int max(long long int a, long long int b) { return a > b ? a : b; }
long long int abs(long long int a) { return a > 0 ? a : -a; }

int main(void) {
	long long int H, W, i, tmp, ans;
	scanf("%lld%lld", &H, &W);

	ans = H * W;
	if (H % 3 == 0 || W % 3 == 0) {
		ans = 0;
	}
	else if (H == 1 || W == 1) {
		ans = 1;
	}
	else {
		for (i = 1; i < W / 2 + 1; i++) {
			if (H % 2 == 0)
				tmp = abs(i * H - H / 2 * (W - i));
			else 
				tmp = max(abs(i * H - H / 2 * (W - i)), abs(i * H - (H / 2 + 1) * (W - i)));
			ans = min(tmp, ans);
		}
	}

	printf("%lld\n", ans);
	return 0;
}