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 rep(i, n) for (int i = 0; i < (int)(n); i++)
using ll=long long;
using vi = vector<int>;
using Graph = vector<vi>;
using P = pair<int,int>;
const int MOD=(int)1e9+7;
const int INF=(int)1e9;
const ll LINF=(ll)1e18;

ll solve(ll h,ll w){
    ll res=LINF;
    ll men = h*w;
    for(int i=0;i<=h;i++){
        ll S1 = w*i;
        ll S2 = (h-i+1)/2LL;
        ll S3 = men - S1 - S2;
        if(min({S1,S2,S3})<0) continue;
        ll tmp = max({S1,S2,S3}) - min({S1,S2,S3});
        res = min(res,tmp);
    }
    for(int i=0;i<=h;i++){
        ll S1 = w*i;
        ll S2 = (h-i) * (w+1)/2;
        ll S3 = men - S1 - S2;
        if(min({S1,S2,S3})<0) continue;
        ll tmp = max({S1,S2,S3}) - min({S1,S2,S3});
        res = min(res,tmp);
    }
    return res;
}

int main(){
    ll h,w;
    cin >> h >> w;
    cout << min(solve(h,w),solve(w,h)) << endl;
}