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 <cstdio>
#include <cstdint>
#include <vector>
#include <algorithm>
#include <tuple>

int f(intmax_t H, intmax_t W) {
  intmax_t res = std::min(H, W);
  for (intmax_t i = 1; i < H; ++i) {
    intmax_t a = i * W;
    intmax_t b = intmax_t(H-i) * (W / 2);
    intmax_t c = intmax_t(H) * W - (a+b);

    intmax_t min, max;
    std::tie(min, max) = std::minmax({a, b, c});
    res = std::min(res, max-min);
  }
  return res;
}

int main() {
  int H, W;
  scanf("%d %d", &H, &W);

  if (H % 3 == 0 || W % 3 == 0) return puts("0"), 0;
  printf("%d\n", std::min({H, W, f(H, W), f(W, H)}));
}