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>
#define all(x) (x).begin(), (x).end()
using namespace std;
typedef long long ll;
typedef pair<int, int> P;
const int INF = 1e9;
const ll LINF = 1e18;
const int MOD = 1e9 + 7;

int main() {
  ll h, w;
  cin >> h >> w;
  int ans = 0;
  if (h % 3 == 0 || w % 3 == 0)
    ans = 0;
  else if (h == w && h % 2 == 0 && w % 2 == 0)
    ans = h / 2;
  else if (h % 2 == 0 && w % 2 == 0 && (h % 5 == 0 || w % 5 == 0))
    ans = 1;
  else if (h % 2 == 0)
    ans = w / 2 * h - (h / 2) * (w + 1) / 2;
  else if (w & 2 == 0)
    ans = h / 2 * w - (w / 2) * (h + 1) / 2;
  else
    ans = ((h + 1) / 2 * (w + 1) / 2) - (h / 2 * w / 2);
  cout << ans << endl;
}