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>
#include <algorithm>
using namespace std;

long long solve(long long h, long long w) {
    long long result = h * w;
    for (long long i = 1; i < h; i++) {
        long long cut1[3], cut2[3];
        cut1[0] = i * w;
        auto rest = h - i;
        cut1[1] = rest / 2 * w;
        cut1[2] = (rest - (rest / 2)) * w;
        cut2[0] = cut1[0];
        cut2[1] = w / 2 * rest;
        cut2[2] = (w - (w / 2)) * rest;
        auto p1 = minmax_element(cut1, cut1 + 3), p2 = minmax_element(cut2, cut2 + 3);
        result = min({result, *p1.second - *p1.first, *p2.second - *p2.first});
    }
    return result;
}

int main() {
    long long h, w;
    cin >> h >> w;
    long long result = solve(h, w);
    result = min(result, solve(w, h));
    cout << result;
    return 0;
}