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)

#define L long long
L n(L a,L b){return a<b?a:b;}
L x(L a,L b){return a>b?a:b;}
L l(L a){return a>0?a:-a;}
#define E(p,q) x(l(b*i-p),l(b*i-q))
L s(L a,L b){
    L i=0,p=1<<30;
    for(;i++<a;p=n(p,n(E((a-i)/2*b,b*(a-i-(a-i)/2)),E(b/2*(a-i),(a-i)*(b-b/2)))));
}
 
int main(void){
    L h,w;
    scanf("%lld%lld",&h,&w);
	printf("%lld",n(s(h,w),s(w,h)));
}