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 <bits/stdc++.h>
using namespace std;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

using pll = pair<long long, long long>;
pll sub(long long h, long long w) {
    if (h % 2 == 0 || w % 2 == 0) return {h*w/2, h*w/2};
    if (h > w) swap(h, w);
    return {h * (w+1)/2, h * (w-1)/2};
}


int main() {
    long long H, W;
    cin >> H >> W;
    long long res = H * W;

    for (long long h = 1; h < H; ++h) {
        vector<long long> a(3);
        a[0] = h * W;
        auto p = sub(H-h, W);
        a[1] = p.first, a[2] = p.second;
        sort(a.begin(), a.end());
        chmin(res, a.back() - a[0]);
    }
    for (long long w = 1; w < W; ++w) {
        vector<long long> a(3);
        a[0] = H * w;
        auto p = sub(H, W-w);
        a[1] = p.first, a[2] = p.second;
        sort(a.begin(), a.end());
        chmin(res, a.back() - a[0]);
    }
    cout << res << endl;
}