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 (Clang 3.8.0) (judge verdict: Accepted)

#include <algorithm>
#include <climits>
#include <cmath>
#include <cstdio>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<vector<ll>> vvl;
#define REP(var, a, b) for (int var = (a); var < (b); var++)
#define rep(var, n) for (int var = 0; var < (n); ++var)
#define ALL(c) (c).begin(), (c).end()
#define rALL(c) (c).rbegin(), (c).rend()
ll MOD = 1000000007;
ll INF = 1000000000;

int main() {
  //
  ll h, w;
  cin >> h >> w;
  if (h % 3 == 0 || w % 3 == 0) {
    cout << 0 << endl;
    return 0;
  }
  ll ans = INT_MAX;
  REP(i, h / 3, h / 3 + 2) {
    REP(j, w / 2, w / 2 + 2) {
      ll s1 = i * w;
      ll s2 = (h - i) * j;
      ll s3 = (h - i) * (w - j);
      ans = min(max(s1, max(s2, s3)) - min(s1, min(s2, s3)), ans);
    }
  }
  REP(j, w / 3, w / 3 + 2) {
    REP(i, h / 2, h / 2 + 2) {
      ll s1 = j * h;
      ll s2 = (w - j) * i;
      ll s3 = (h - i) * (w - j);
      // cout << i << ":" << j << ":" << s1 << "," << s2 << "," << s3 << endl;
      ans = min(max(s1, max(s2, s3)) - min(s1, min(s2, s3)), ans);
    }
  }
  ans = min(min(ans, w), h);
  cout << ans << endl;
  return 0;
}