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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
using namespace std;
typedef long long ll;
int main(){
    ll m, n, c1, c2, c3, c4, c5, c6, km, kn;
    cin >> m >> n;
    c1 = (m % 3 > 0) * n;
    c2 = (n % 3 > 0) * m;
    km = m / 3;
    kn = n / 3;
    c3 = max(km * n, (m - km) * (n / 2 + n % 2)) - min(km * n, (m - km) * (n / 2));
    c4 = max(kn * m, (n - kn) * (m / 2 + m % 2)) - min(kn * m, (n - kn) * (m / 2));
    km += (m % 3 > 0);
    kn += (n % 3 > 0);
    c5 = max(km * n, (m - km) * (n / 2 + n % 2)) - min(km * n, (m - km) * (n / 2));
    c6 = max(kn * m, (n - kn) * (m / 2 + m % 2)) - min(kn * m, (n - kn) * (m / 2));
    cout << min(c1, min(c2, min(c3, min(c4, min(c5, c6)))));
    return 0;
}