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(ll i=0; i<n; i++)
typedef long long ll;
typedef long long unsigned int llu;
ll MOD = 1000000007;
ll INF = 1000000009;

/*
各iについて、
x=h*iとして、残りの面積はh%2==0ならh/2*(w-i)が２つ
h%2!=0ならh/2*(w-i)と(h/2+1)*(w-i)
wについても同じことをやる
*/

void solve(){
    ll h,w;
    cin >> h >> w;
    ll ans = INF;
    for(ll i=1; i<w-1; i++){
        ll x,y,z;
        x=h*i;
        if(h%2==0) {
            y = h/2 * (w-i);
            z = y;
        }
        else{
            y = h/2 * (w-i);
            z = (h+1)/2 * (w-i);
        }
        ll tmp, tmp2;
        tmp = min(x,min(y,z));
        tmp2 = max(x,max(y,z));
        ans = min(ans,tmp2-tmp);
        //cout << i << " " << x << " " << y << " " << z << endl;
    }
    for(ll i=1; i<h-1; i++){
        ll x,y,z;
        x=w*i;
        if(w%2==0) {
            y = w/2 * (h-i);
            z = y;
        }
        else{
            y = w/2 * (h-i);
            z = (w+1)/2 * (h-i);
        }
        ll tmp, tmp2;
        tmp = min(x,min(y,z));
        tmp2 = max(x,max(y,z));
        ans = min(ans,tmp2-tmp);
        //cout << i << " " << x << " " << y << " " << z << endl;
    }
    ans = min(ans,h%3*w);
    ans = min(ans,w%3*h);
    cout << ans << endl;
}

int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);
  solve();
  return 0;
}