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>
#include<stdlib.h>
#include<string.h>
#include<math.h>
 
#define sl(x) scanf("%ld", &x)
#define ss(x) scanf("%s", x)
#define pl(x) printf("%ld\n", x)
#define pd(x) printf("%lf\n", x)
#define ps(x) printf("%s\n", x)
 
#define INF 1000000000000000000
#define MOD 1000000007
 
#define MIN(a,b) (((a)<(b))?(a):(b))
#define MAX(a,b) (((a)>(b))?(a):(b))

int compare_long(const void *a, const void *b) {
	return *(long*)a - *(long*)b;
}
 
int main() {
	long H, W;
	long tmp;
	long low, mid, high;
	long min, max;
	long ans = INF;
	long i, j;
	
	sl(H); sl(W);
	for(i=0;i<2;i++) {
		low = 1; high = H; mid = (low + high) / 2;
		while(1) {
			if(mid * W <= H * W / 3 && (mid + 1) * W > H * W / 3) {
				break;
			}
			if(mid * W < H * W / 3) {
				low = mid + 1;
				mid = (low + high) / 2;
			} else {
				high = mid - 1;
				mid = (low + high) / 2;
			}
		}
		for(j=0;j<2;j++) {
			min = max = mid * W;
			if((H - mid) % 2 && W % 2) {
				if(H - mid > W) {
					min = MIN(min, (H - mid) / 2 * W);
					max = MAX(max, ((H - mid) / 2 + 1) * W);
				} else {
					min = MIN(min, (H - mid) * (W / 2));
					max = MAX(max, (H - mid) * (W / 2 + 1));
				}
			} else {
				min = MIN(min, (H - mid) * W / 2);
				max = MAX(max, (H - mid) * W / 2);
			}
			ans = MIN(ans, max - min);
			mid++;
		}
		tmp = H; H = W; W = tmp;
	}
	
	pl(ans);
	
	return 0;
}