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<sstream>
#include<ios>
#include<iomanip>
#include<vector>
#include<list>
#include<algorithm>
#include<cstdlib>
#include<cmath>
#include<queue>
#include<map>
#include<string>
#include<numeric>
#include<set>
using namespace std;

int main(){
  int H, W;
  cin >> H >> W;

  if(H%3 == 0 or W%3 == 0){
    cout << 0 << endl;
    return 0;
  }

  int w = W/3 + 1;
  while((3*(H/2)+2*(H%2))*w >= W*((H/2)+(H%2)))
    w--;

  int diff1 = W*((H/2) + (H%2)) - 3*w*(H/2) - 2*w*(H%2);
  w++;
  int diff2 = 3*w*(H/2) + w*(H%2) - W*(H/2);

  int h = H/3 + 1;
  while((3*(W/2)+2*(W%2))*h >= H*((W/2)+(W%2)))
    h--;

  int diff3 = H*((W/2) + (W%2)) - 3*h*(W/2) - 2*h*(W%2);
  h++;
  int diff4 = 3*h*(W/2) + h*(W%2) - H*(W/2);

  int ans = min(min(H, W), min(min(diff1, diff2), min(diff3, diff4)));

  cout << ans << endl;
  
  return 0;
}