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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>

int main()
{
  int h, w, h1, h2, w1, w2;
  int answer = 0;
  int x1, x3;
  int m, n;
  scanf("%d %d", &m, &n);
  if(m >= n)
  {
    h = m;
    w = n;
  }
  else
  {
    h = n;
    w = m;
  }
  if(h % 3 == 0 || w % 3 == 0)
  {
    answer = 0;
  }
  else
  {
    //1
    h1 = h / 3;
    if(h % 3 == 2) h1++;
    x1 = h1 * w;

    //3
    h2 = h - h1;
    w1 = w / 2;
    if(w % 2 != 0)
    {
      w1 = w1 + 1;
    }

    w2 = w - w1;
    x3 = h2 * w2;

    //
    if(x1 > x3)
    {
      answer = x1 -x3;
    }
    else if(x3 > x1)
    {
      answer = x3 - x1;
    }
    else
    {
      answer = 0;
    }
  }
  printf("%d\n", answer);
  return 0;
}