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;
#define INF 2147483647
#define INFF 9223372036854775807
#define ll long long
#define REP(i,n) for(long long i=0;i<n;i++)
#define REPP(i,m,n) for(long long i=m;i<n;i++)
#define ALL(N) (N.begin(),N.end())
#define de cout << "line : " << __LINE__ << " debug" << endl;
#define pb push_back
#define pq priority_queue
#define Dcout(N) cout << setprecision(20) << N << endl;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

int main() {
    cin.tie(0);    
	ios::sync_with_stdio(false);
    ll H,W;
    cin >> H >> W;
    if(H % 3 == 0 || W % 3 == 0){
        cout << 0 << endl;
        return 0;
    }
  	if(H > W) swap(H,W);
    ll A = H/2*W;
    ll B = (H-H/2)*W;
    ll C = 0;
    ll minv = INFF;
    while(A >= 0){
        minv = min(minv,abs(max({A,B,C})-min({A,B,C})));
        A -= H/2;
        B -= (H-H/2);
        C += H;
    }
    cout << minv << endl;
}