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<algorithm>
#include<cstdio>
#include<cmath>
#include<math.h>
#include<string>
#include<string.h>
#include<stack>
#include<queue>
#include<vector>
#include<utility>
#include<set>
#include<map>
#include<stdlib.h>
#include<iomanip>

using namespace std;

#define ll long long
#define ld long double
#define EPS 0.0000000001
#define INF 1e9
#define MOD 1000000007
#define rep(i,n) for(i=0;i<n;i++)
#define loop(i,a,n) for(i=a;i<n;i++)
#define all(in) in.begin(),in.end()
#define shosu(x) fixed<<setprecision(x)

typedef vector<int> vi;
typedef pair<int,int> pii;

int main(void) {
  int i,j;
  int h,w;
  cin>>h>>w;
  int ans=INF;
  loop(i,1,w){
    vi v(3);
    v[0]=i*h;
    v[1]=((w+i)/2-i)*h;
    v[2]=h*w-v[0]-v[1];
    sort(all(v));
    ans=min(ans,v[2]-v[0]);
    v[0]=i*h;
    v[1]=(w-i)*(h/2);
    v[2]=h*w-v[0]-v[1];
    sort(all(v));
    ans=min(ans,v[2]-v[0]);
  }
  swap(w,h);
  loop(i,1,w){
    vi v(3);
    v[0]=i*h;
    v[1]=((w+i)/2-i)*h;
    v[2]=h*w-v[0]-v[1];
    sort(all(v));
    ans=min(ans,v[2]-v[0]);
    v[1]=(w-i)*(h/2);
    v[2]=h*w-v[0]-v[1];
    sort(all(v));
    ans=min(ans,v[2]-v[0]);
  }
  cout<<ans<<endl;
}