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 pan(i,n) for(int i=0;i<n;i++)
#define pans(i,n,a) for(int i=a;i<n;i++)
#define ll long long int
#define vi vector<ll>
#define vl vector<ll>
#define pb push_back
#define INF 1000000007
#define PI 3.141592653
#define inf 100007
#define pll pair<ll,ll>
#define pii pair<int,int>
ll gcd(ll a, ll b) { return a % b == 0 ? b : gcd(b, a % b); }
ll lcm(ll a, ll b) { return (a / gcd(a, b)) * b; }

int main(){
    int h,w;
    cin>>h>>w;
    int ans=inf;
    if(h%3==0 || w%3==0) ans=0;
    else{
        if(h>=w){
            pans(i,h+1,1){
                int a=w*i,b=(h-i)*(w/2),c=(h-i)*(w-(w/2));
                int mx=max({a,b,c}),mn=min({a,b,c});
                ans=min(ans,mx-mn);
            }
        }
        else{
            for(int i=1;i<=w;i++){
                int a=h*i,b=(w-i)*floor(h/2),c=(w-i)*(ceil(h/2));
                int mx=max({a,b,c}),mn=min({a,b,c});
                ans=min(ans,mx-mn);
            }
        }
    }
    cout<<ans;
}