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<cmath>

using namespace std;

int main() {
  long long H, W;

  cin >> H >> W;

  long long mins, maxs;
  long long mind = 10000000000000;
  for (int w = 1; w <= W; w++) {
    long long o_mind = mind;
    maxs = w * H;
    mins = w * H;
    long long difw = W - w;
    if (difw >= 2) {
      maxs = fmax(maxs, (difw / 2) * H);
      mins = fmin(mins, (difw / 2) * H);
      maxs = fmax(maxs, (difw - (difw / 2)) * H);
      mins = fmin(mins, (difw - (difw / 2)) * H);
      mind = fmin(mind, maxs - mins);
    }

    maxs = w * H;
    mins = w * H;
    if (difw >= 1 && H >= 2) {
      maxs = fmax(maxs, H / 2 * difw);
      mins = fmin(mins, H / 2 * difw);
      maxs = fmax(maxs, (H - (H / 2)) * difw);
      mins = fmin(mins, (H - (H / 2)) * difw);
      mind = fmin(mind, maxs - mins);
    }

  }

  for (int h = 1; h <= H; h++) {
    maxs = h * W;
    mins = h * W;
    long long difh = H - h;
    if (difh >= 2) {
      maxs = fmax(maxs, difh / 2 * W);
      mins = fmin(mins, difh / 2 * W);
      maxs = fmax(maxs, (difh - (difh / 2)) * W);
      mins = fmin(mins, (difh - (difh / 2)) * W);
      mind = fmin(mind, maxs - mins);
    }

    maxs = h * W;
    mins = h * W;
    if (H - h >= 1 && W >= 2) {
      maxs = fmax(maxs, W / 2 * (H - h));
      mins = fmin(mins, W / 2 * (H - h));
      maxs = fmax(maxs, (W - (W / 2)) * (H - h));
      mins = fmin(mins, (W - (W / 2)) * (H - h));
      mind = fmin(mind, maxs - mins);
    }
  }

  cout << mind << endl;
  return 0;
}