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<cstdio>
#include <iostream>
#include<algorithm>
#include<string>
#include<queue>
#include<vector>
#include<functional>
#include<cmath>
#include<map>
#include<stack>
#include<set>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> P;
const ll MOD = 1000000007;

int H, W;

int main()
{
	ll ans = 1e9;
	cin >> H >> W;

	ll s = H * W;
	for (ll i = 1; i < H; i++) {
		ll Sa = i * W;
		ll Sb = (H - i)*(W / 2);
		ll Sc = s - Sa - Sb;
		ll diff = max(abs(Sa - Sc), max(abs(Sa - Sb), abs(Sb - Sc)));
		ans = min(diff, ans);
	}
	swap(H,W);
	for (ll i = 1; i < H; i++) {
		ll Sa = i * W;
		ll Sb = (H - i)*(W / 2);
		ll Sc = s - Sa - Sb;
		ll diff = max(abs(Sa - Sc), max(abs(Sa - Sb), abs(Sb - Sc)));
		ans = min(diff, ans);
	}
	cout << ans << endl;
	return	0;
}