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>

int main(void) {
	int H, W, max, min, S;
	int x, y, i, s;

	scanf("%d %d", &H, &W);
	S = H*W;

	if ((H % 3 == 0) || (W % 3 == 0)) {
		printf("0\n");
		return 0;
	}
	if (H > W) {
		x = W;
		y = H;
	}
	else {
		x = H;
		y = W;
	}
	for (i = 1; i <= y; i++) {
		if ((x*i) >= (S/3)) {
			max = x*i;
			if (x > (y - i)) {
				s = x;
				x = y - i;
				y = s;
			}
			S = S - max;
			break;
		}
	}

	if ((x % 2 == 0) || (y % 2 == 0)) {
		min = S / 2;
		if (max < min) {
			s = min;
			min = max;
			max = s;
		}
		printf("%d\n", max - min);
		return 0;
	}

	for (i = 1; i <= y; i++) {
		if ((x*i) >= (S/2)) {
			s = x*i;
			min = S - s;
			break;
		}
	}

	if (max < s) {
		i = s;
		s = max;
		max = i;
	}
	
	printf("%d\n", max - min);

	return 0;
}