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<cstdio>
#include<cmath>
#include<cstring>
#include<string>
#include<stack>
#include<queue>
#include<vector>
#include<algorithm>
#include<iomanip>
typedef long long int ll;
using namespace std;
#define FOR(i,a,b) for (int i=(a);i<(b);i++)
#define REP(i,n) for (int i=0;i<(n);i++)
#define EREP(i,n) for (int i=1;i<=(n);i++)
#define ALL(a) (a).begin(),(a).end()
#define EVEL 1

#ifndef EVEL
#define DEB(X) cout << #X << ":" <<X<<" " ;
#define TF(f) f ? cout<<"true  " : cout<<"false ";
#define END cout<<"\n";
#else
#define DEB(X) {}
#define TF(f) {}
#define END {}
#endif
const int MOD = 1000000007;
const ll INF = 200000000000;


    ll W,H;
    ll ans=INF;
    bool f=false;
int main(){
    ios_base::sync_with_stdio(false);
    cin>>H>>W;
    if(H%3==0||W%3==0){
        cout<<"0";
        f=true;
    }else{
        EREP(i,W){
            ll S1=i*H,S2,S3;
            if(H%2==0){
                 S2=S3=H/2*(W-i);
            }else{
                 S2=H/2*(W-i);
                 S3=(H/2+1)*(W-i);
            }
            ans=min((max(S1,S3)-min(S1,S2)),ans);
            DEB(i)DEB(ans)DEB((max(S1,S3)-min(S1,S2)))END
        }
        END
        EREP(i,H){
            ll S1=i*W,S2,S3;
            if(W%2==0){
                 S2=S3=W/2*(H-i);
            }else{
                 S2=W/2*(H-i);
                 S3=(W/2+1)*(H-i);
            }
            ans=min((max(S1,S3)-min(S1,S2)),ans);
            DEB(i)DEB(ans)DEB((max(S1,S3)-min(S1,S2)))END
        }
    }
    if(!f)cout<<ans;
    return 0;
}