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;

struct Fast {Fast(){std::cin.tie(0);ios::sync_with_stdio(false);}} fast;

typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef queue<int> qi;
typedef stack<int> si;
typedef deque<int> dqi;

#define reps(i, a, b) for (int i = a; i < b; ++i)
#define rep(i, n) reps(i, 0, n)
#define REPS(i, a, b) reps(i, a, b)
#define REP(i, n) rep(i, n)
#define deps(i, a, b) for (int i = a; i >= b; --i)
#define dep(i, n) deps(i, n, 0)
#define DEPS(i, a, b) deps(i, a, b)
#define DEP(i, n) dep(i, n)

#define pf push_front
#define pb push_back
#define mp make_pair
#define fst first
#define FST fst
#define sec second
#define SEC sec
#define sz(obj) ((int)(obj).size())
#define all(v) (v).begin(), (v).end()
#define ALL(v) all(v)

const int INF = 999999999;
const int MOD = 1e9 + 7;
const int dx[] = {0, 1, 0, -1}, dy[] = {1, 0, -1, 0};

inline bool inside(int y, int x, int H, int W) {return y >= 0 && x >= 0 && y < H && x < W;}
inline int in() {int x; std::cin >> x; return x;}
template <typename T>
void print(std::vector<T>& v, char c = ' ') {
  REP(i, v.size()) {
    if (i != 0) std::cout << c;
    std::cout << v[i];
  }
  std::cout << endl;
}
template <typename T> void print(T x) { std::cout << x << '\n'; }

signed main()
{
  int H, W;
  cin >> H >> W;

  if (H % 3 == 0 or W % 3 == 0) {
    cout << 0 << endl;
    return 0;
  }

  long long int h = min(H, W), w = max(H, W), wl = w/2;
  long long int ans = LLONG_MAX;

  for (int i = 1; i < h; i++) {
    vector<long long> v = {i*w, (h - i)*wl, (h - i)*(w - wl)};
    ans = min(ans, *max_element(v.begin(), v.end()) - *min_element(v.begin(), v.end()));
    int hl = (h - i)/2;
    v = {i*w, hl*w, (h - hl)*wl};
    ans = min(ans, *max_element(v.begin(), v.end()) - *min_element(v.begin(), v.end()));
  }
  h = max(H, W), w = min(H, W), wl = w/2;

  for (int i = 1; i < h; i++) {
    vector<long long> v = {i*w, (h - i)*wl, (h - i)*(w - wl)};
    ans = min(ans, *max_element(v.begin(), v.end()) - *min_element(v.begin(), v.end()));
    int hl = (h - i)/2;
    v = {i*w, hl*w, (h - hl)*wl};
    ans = min(ans, *max_element(v.begin(), v.end()) - *min_element(v.begin(), v.end()));
  }
  cout << ans << endl;

  return (0);
}