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: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

#define   ll     long long int

void sortt(ll &a, ll &b, ll &c)
{
    if (a < b) swap(a, b);
    if (b < c) swap(c, b);
    if (a < b) swap(a, b);
}

ll func(ll h, ll w)
{
    ll i, j, k, s = 1e15;
    ll first, second, third;
    ll w_second = w / 2;
    ll w_third = w - w_second;

    for (i = 1; i < h; i++) {
        first = i * w;
        j = h - i;
        second = j * w_second;
        third = j * w_third;
        sortt(first, second, third);
        s = min(s, first - third);
    }
    return s;
}

int main( )
{
    ll h, w;
    cin >> h >> w;
    if (h % 3 == 0 || w % 3 == 0) {
        cout << "0\n";
        return 0;
    }
    cout << min(func(h, w), func(w, h)) << '\n';
    return 0;
}