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: Accepted)

#include<iostream>
#include<set>
#include <bitset>
#include<queue>
#include<vector>
#include<map>
#include<stack>
#include <cstdio>
#include<algorithm>
#include <sstream>
#include<string>
#include<string.h>
#include <cmath>
#include <iomanip>
#include <string>
#include<list>
#include <limits>
#include <numeric>
#include <type_traits>
#define int long long
#define ll long long
#define mod  1000000007
#define inf 1e17
#define rep(i,j,n) for(int i=j;i<n;i++)
#define P pair<int,int>
double pi = 3.141592653589793;
using namespace std;
//ここから始めよう
signed main(){
    int h,w;cin>>h>>w;
    int ans=1e16;
    ans=min((h%3?1:0)*w,(w%3?1:0)*h);
    rep(i,1,h){
        int a=i*w;
        int b=(h-i)*(w/2);
        int c=(h-i)*(w-(w/2));
        int p=max({a,b,c})-min({a,b,c});ans=min(ans,p);
    }
    rep(i,1,w){
        int a=i*h;
        int b=(w-i)*(h/2);
        int c=(w-i)*(h-(h/2));
        int p=max({a,b,c})-min({a,b,c});ans=min(ans,p);
    }
    cout<<ans<<endl;
    return 0;
}