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>
using namespace std;

long h, w;
long h2, w2;
long long ll, ss;
long long _min;
long long s[3] = {0,0,0};
long long a[3] = {0,0,0};

int main(){
    cin >> h >> w;
    _min = h * w;
    if(h % 3 == 0 || w % 3 == 0){
        cout << 0 << endl;
        return 0;
    }
    h2 = h / 2;
    w2 = w / 2;
    int debug[2] = {0,0};
    for(int i = 1; i <= h2 + 1; i++){
        s[0] = i * w;
        s[1] = (h - i) * w2;
        s[2] = (h - i) * (w - w2);
        if(s[0] < s[2]){
            ll = s[2];
            if(s[0] > s[1]){
                ss = s[1];
            }else{
                ss = s[0];
            }
        }else{
            ll = s[0];
            ss = s[1];
        }
        if(_min > ll - ss){
            _min = ll - ss;
            a[0] = s[0];
            a[1] = s[1];
            a[2] = s[2];
            debug[0] =h - i;
            debug[1] = (w - w2) ;//* (h - i);
        }
    }
    for(int i = 1; i <= w2 + 1; i++){
        s[0] = i * h;
        s[1] = (w - i) * h2;
        s[2] = (w - i) * (h - h2);
        if(s[0] < s[2]){
            ll = s[2];
            if(s[0] > s[1]){
                ss = s[1];
            }else{
                ss = s[0];
            }
        }else{
            ll = s[0];
            ss = s[1];
        }
        if(_min > ll - ss){
            _min = ll- ss;
            a[0] = ll;
            a[1] = ss;
        }
    }
    cout << _min << endl;
    //cout << a[0] << " " << a[1] << " " << a[2] << endl;
    //cout << debug[0] << " " << debug[1] << " " << a[2] << endl;
}