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 <vector>
#include <queue>
#include <algorithm>
#include <iostream>
#include <string>
#include <tuple>
#include <set>
#include <map>
#include <complex>
#include <iomanip>
#include <cmath>
using namespace std;
typedef long long ll;

ll maxLL(ll a, ll b)
{
  if (a > b) return a;
  else return b;
}

ll minLL(ll a, ll b)
{
  if (a < b) return a;
  else return b;
}

ll calc(int h, int w)
{
  int exH, exW;
  ll s1, s2, s3;
  ll max = h * w;
  ll min = h * w;
  for (int i = 1; i < h; i++) {
    s1 = w * i;
    exH = (h - i) / 2;
    s2 = w * exH;
    s3 = max - s1 - s2;
    ll tmp = maxLL(maxLL(s1, s2), s3) - minLL(minLL(s1, s2), s3);
    if (tmp < min) min = tmp;
  }
  for (int i = 1; i < h; i++) {
    s1 = w * i;
    exW = w / 2;
    s2 = (h - i) * exW;
    s3 = max - s1 - s2;
    ll tmp = maxLL(maxLL(s1, s2), s3) - minLL(minLL(s1, s2), s3);
    if (tmp < min) min = tmp;
  }
  return min;
}

int main()
{
  int h, w;
  cin >> h >> w;
  ll ans = minLL(calc(h, w), calc(w, h));
  cout << ans << endl;
}