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 (Clang 3.8.0) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <limits.h>
#include <math.h>
/*
#define min(a, b, c) (a < b ? (a < c ? a : ((b < c) ? b : c)) : (b < c ? b : (a < c ? a : c )))
#define max(a, b, c) (a > b ? (a > c ? a : ((b > c) ? b : c)) : (b > c ? b : (a > c ? a : c )))
*/
#define min(a, b) (a < b ? a : b)
#define max(a, b) (a > b ? a : b)

long diffS(int h, int w, long s) {
	int i;
	long a, b, minDiff = LONG_MAX, diffh, diffw;
	a = (long)(h+1)/2*w;
	b = (long)h*w - a;
	diffh = max(a, s) - min(b, s);
//	printf("%ld %ld %ld diff:%ld\n", s, a, b, diffh);
	a = (long)(w+1)/2*h;
	b = (long)w*h - a;
	diffw = max(a, s) - min(b, s);
//	printf("%ld %ld %ld diff:%ld\n", s, a, b, diffw);
/*	for (i = 0; i <= (h+1)/2; i++) {
		a = (long)i * w;
		b = (long)(h - i) * w;
		diff = max(a, b, s) - min(a, b, s);
		if (minDiff > diff) {
			minDiff = diff;
		}
	}
	for (i = 0; i <= (w+1)/2; i++) {
		a = (long)i * h;
		b = (long)(w - i) * h;
		diff = max(a, b, s) - min(a, b, s);
		if (minDiff > diff) {
			minDiff = diff;
		}
	}
*/
	return min(diffh, diffw);
}

int main(void) {
	int H, W, i;
	long diff, minDiff = LONG_MAX;
	scanf("%d %d", &H, &W);
	for (i = 1; i <= (H+1)/2; i++) {
		diff = diffS(H - i, W, (long)i * W);
		if (minDiff > diff) {
			minDiff = diff;
		}
	}
	for (i = 1; i <= (W+1)/2; i++) {
		diff = diffS(H, W - i, (long)i * H);
		if (minDiff > diff) {
			minDiff = diff;
		}
	}
	printf("%ld\n", minDiff);
	return 0;
}