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 <bits/stdc++.h>

using namespace std;

typedef long long ll;

const int INF = 1000000000;

int main()
{
  ll H, W; scanf("%lld %lld", &H, &W);
  if (H % 3 == 0 or W % 3 == 0) {
    printf("0\n");
    return 0;
  }
  if (H > W) { swap(H, W); }
  ll a, b, c;
  ll ans = INF;
  for (int i = 1; i <= (W + 2) / 3; ++i) {
    ll ww = W - i;
    a = H * i;
    b = (H / 2) * ww;
    c = (H - (H / 2)) * ww;
    ll diff = max(a, max(b, c)) - min(a, min(b, c));
    ans = min(ans, diff);
  }
  for (int i = 1; i <= (H + 2) / 3; ++i) {
    ll hh = H - i;
    a = i * W;
    b = hh * (W / 2);
    c = hh * (W - (W / 2));
    ll diff = max(a, max(b, c)) - min(a, min(b, c));
    ans = min(ans, diff);
  }
  printf("%lld\n", ans);
  return 0;
}