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 <bits/stdc++.h>
#define fi first
#define se second
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rrep(i, n) for (int i = 1; i <= (n); ++i)
#define drep(i, n) for (int i = (n)-1; i >= 0; --i)
#define srep(i, s, t) for (int i = s; i < t; ++i)
#define rng(a) a.begin(), a.end()
#define rrng(a) a.rbegin(), a.rend()
#define maxs(x, y) (x = max(x, y))
#define mins(x, y) (x = min(x, y))
#define limit(x, l, r) max(l, min(x, r))
#define lims(x, l, r) (x = max(l, min(x, r)))
#define isin(x, l, r) ((l) <= (x) && (x) < (r))
#define pb push_back
#define eb emplace_back
#define sz(x) (int)(x).size()
#define pcnt __builtin_popcountll
#define uni(x) x.erase(unique(rng(x)), x.end())
#define show(x) cout << #x << " = " << x << endl;
#define PQ(T) priority_queue<T, v(T), greater<T>>
#define bn(x) ((1 << x) - 1)
#define dup(x, y) (((x) + (y)-1) / (y))
#define newline puts("")
#define v(T) vector<T>
#define vv(T) v(v(T))
using namespace std;
typedef long long int ll;
typedef unsigned uint;
typedef unsigned long long ull;
typedef pair<int, int> P;
typedef tuple<int, int, int> T;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<P> vp;
typedef vector<T> vt;
const ll inf = 1001001001001LL;

int main() { 
  ll h,w;
  cin >> h >> w;
  if(h%3 ==0 || w %3 == 0){
    cout<<0<<endl;
    return 0;
  }
  ll a,b,c;
  ll ans = inf;
  vl t(3);
  rep(k,2){
    srep(x,1,w+1){
      t[0] = h*x;
      ll xx = (w-x)/2;
      if(xx==0)continue;
      t[1] = xx*h;
      t[2] =(w-xx-x)*h;
      sort(t.begin(),t.end());
      ans = min(ans,t[2]-t[0]);

      t[0] = h*x;
      ll y = h/2;
      if(y==0)continue;
      t[1] = (w-x)*y;
      t[2] =(w-x)*(h-y);
      sort(t.begin(),t.end());
      ans = min(ans,t[2]-t[0]);
    }
    swap(h,w);
  }
  if(ans==inf){
    cout<<1<<endl;
    return 0;
  }
  cout<<ans<<endl;
  return 0;
}