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>
#define MAX(x, y) ((x) > (y) ? (x) : (y))
#define MIN(x, y) ((x) > (y) ? (y) : (x))
#define ABS(x) ((x) > 0 ? (x) ? -(x))

long int f(long int h, long int w){
  long a, b, c, x = 0, y[2] = {h - (h/2), h/2};
  a = 0; b = y[0] * w; c = y[1] * w;
  while(a < b){
    a += h;
    b -= y[0];
    c -= y[1];
    x++;
  }
  long min1 = a - c;
  long min2 = (b + y[0]) - MIN(a - h, c + y[1]);
  return MIN(min1, min2);
}

int
main(int argc, char *argv[])
{
  long h, w;
  scanf("%ld %ld", &h, &w);
  long ans;
  if((h % 3)*(w % 3) == 0) ans = 0;
  else{
    ans = MIN(f(h, w), f(w, h));
  }
  printf("%ld\n", ans);

  return 0;
}