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<iostream>
#include<vector>
#include<string>
#include<cmath>
#include<algorithm>
#include <numeric>
#include<map>
 
using namespace std;
using ll=long long;
#define rep(i,n) for(int i=0;i<n;i++)
#define ALL(a) (a).begin(),(a).end()

int main(){
    ll h, w;
    cin >> h >> w;

    ll s = h*w;

    if(s % 3 == 0){
        cout << 0;
        return 0;
    }

    ll hans = 1000000000000;
    for(int i = 1; i < h; i++){
        ll s1 = i*w;
        ll s2, s3;
        if(w%2 == 0)s2 = s3 = (h-i)*(w/2);
        else {
            s2 = (h-i)*(w/2);
            s3 = (h-i)*(w/2 + 1);
        }
        // cout << "s1:" << s1 << " s2:" << s2 << " s3:" << s3 << endl;
        hans = min(hans, (max(s1, max(s2, s3))-min(s1, min(s2, s3))));
    }
    ll wans = 1000000000000;
    for(int i = 1; i < w; i++){
        ll s1 = i*h;
        ll s2, s3;
        if(h%2 == 0)s2 = s3 = (w-i)*(h/2);
        else {
            s2 = (w-i)*(h/2);
            s3 = (w-i)*(h/2 + 1);
        }
        wans = min(wans, (max(s1, max(s2, s3))-min(s1, min(s2, s3))));
    }

    cout << min(hans, wans);
}