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;
int main () {
  long H, W;
  cin >> H >> W;
  if ((H * W) % 3 == 0) {
    cout << 0 << endl;
    return 0;
  }
  if(H < W) swap(H,W);
  long a, ans = 10000000000;
  long one, two, three;
  for(int i = 1; i < H; i++) {
    one = W * i;
    if(W % 2 == 0) two = (H - i) * (W / 2), three = (H - i) * (W / 2);
    else two = (H - i) * ((W - 1) / 2), three = (H - i) * ((W - 1) / 2 + 1);
    cout << one << ' ' << two << ' ' << three << endl;
    a = max(one,max(two, three)) - min(one,min(two, three));
    ans = min(ans, a);
  }
  cout << ans << endl;
  return 0;
}