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<string>
#include<vector>
#include<iomanip>
#include<algorithm>
#include<queue>
#include<stack>
#include<list>
#include<map>
#include<deque>
#include<math.h>
using namespace std;
#define ll long long

int main(){
    ll H,W;
    cin >> H >> W;
    ll ans;
    if(H%3==0||W%3==0)ans=0;else ans=min(H,W);
    for(ll h=1;h<=H-1;h++){
        ll w=W/2;
        ll a=h*W;
        ll b=(H-h)*w;
        ll c=(H-h)*(W-w);
        ans=min(ans,abs(a-b));
        ans=min(ans,abs(b-c));
        ans=min(ans,abs(c-a));
    }
    cout << ans;
    return 0;
}