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 "bits/stdc++.h"
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 RREP(i,n) for(int i=(n)-1;i>=0;i--)
#define REPS(i,n) for(int i=1;i<=(n);i++)
#define RREPS(i,n) for(int i=(n);i>0;i--)
#define mp make_pair
#define pb(a) push_back(a)
typedef long long ll;

int main(){
  ll H,W;
  cin >> H >> W;
  ll ans = 1e9;
  if(H%3 == 0 || W%3 == 0) ans = 0;
  else if(H == 2 && W == 2) ans = 1;
  else{
    ans = min(H,W);
    for(ll i = 1;i < H;i++){
      ll M = max((H-i)*W,max(i*(W/2),i*(W-W/2)));
      ll m = min((H-i)*W,min(i*(W/2),i*(W-W/2)));
      ans = min(ans,M-m);
    }
    for(ll i = 1;i < W;i++){
      ll M = max((W-i)*H,max(i*(H/2),i*(H-H/2)));
      ll m = min((W-i)*H,min(i*(H/2),i*(H-H/2)));
      ans = min(ans,M-m);
    }
  }
  cout << ans << endl;
  return 0;
}