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 REP(i,n) for(int i = 0; i < (n); i++)
#define P(x) cout << (x) << "\n"

#define MOD 1000000007 // 1e9+7
#define PI acos(-1.0)
#define ll long long int // 10^18
#define INF 1000000001 // 1e9+1

int dx[4]={1,-1,0,0};
int dy[4]={0,0,1,-1};
//---------------------------

int main(){
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);

  // ifstream in("input.txt");
  // cin.rdbuf(in.rdbuf());

  ll h,w;cin>>h>>w;
  ll ans=0;
  if(h%3!=0 && w%3!=0){
    if(w<h){
      swap(h,w);
    }
    ans=h;
    for(ll i=1;i<w;i++){
      ll s0=h*(w-i);
      ll s1=(h/2)*i;
      ll s2=((h+1)/2)*i;
      ll mx=max(s0, max(s1, s2));
      ll mn=min(s0, min(s1, s2));
      ans=min(ans, mx-mn);
    }
  }
  P(ans);
  return 0;
}