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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define itn int
#define REP(i, n) for (ll i = 0; i < n; i++)
#define IREP(i, n) for (ll i = n - 1; i >= 0; i--)
#define FOR(i, a, b) for (ll i = a; i < b; i++)
#define all(v) v.begin(), v.end()
#define SENTINEL 2000000000
#define NIL -1
using namespace std;
typedef long long ll;


const ll MAX = 510000;
const ll INF = 1LL << 60;
const ll MOD = 1000000007;
template <class T>inline bool chmin(T &a, T b){if(a>b){a=b;return true;}return false;}
template <class T>inline bool chmax(T &a, T b){if(a<b){a=b;return true;}return false;}

bool isOK(int mid,ll a,ll b){
    if(mid*a*2<=(b-mid)*a){
        return true;
    }
    return false;
}
int main()
{
    ll h, w;
    cin >> h >> w;
    if((h*w)%3==0){
        cout << 0 << endl;
        return 0;
    }
    ll ans=min(w,h);
    int left,right;
    left=0;right=h;
    while (right - left > 1)
    {
        int mid = left + (right - left) / 2;

        if (isOK(mid,w,h))
            left = mid;
        else
            right = mid;
    }
    ans = min({ans, max((left - 1) * w, (h - left + 1) * int(w / 2) + (w % 2 == 0 ? 0 : (h - left + 1))) - min((left - 1) * w, (h - left + 1) * int(w / 2))});
    ans = min({ans, max((left)*w, (h - left) * int(w / 2) + (w % 2 == 0 ? 0 : (h - left))) - min((left)*w, (h - left) * int(w / 2))});
    ans = min({ans, max((left + 1) * w, (h - left - 1) * int(w / 2) + (w % 2 == 0 ? 0 : (h - left - 1))) - min((left + 1) * w, (h - left - 1) * int(w / 2))});
    left = 0;
    right = w;
    while (right - left > 1)
    {
        int mid = left + (right - left) / 2;

        if (isOK(mid, h,w))
            left = mid;
        else
            right = mid;
    }
    ans = min({ans, max((left - 1) * h, (w - left + 1) * int(h/2) + (h % 2 == 0 ? 0 : (w - left + 1))) - min((left - 1) * h, (w - left + 1) * int(h/2))});
    ans = min({ans, max((left)*h, (w - left) * int(h/2) + (h % 2 == 0 ? 0 : (w - left))) - min((left)*h, (w - left) * int(h/2))});
    ans = min({ans, max((left + 1) * h, (w - left - 1) * int(h/2) + (h % 2 == 0 ? 0 : (w - left - 1))) - min((left + 1) * h, (w - left - 1) * int(h/2))});
    cout << ans << endl;
}