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 <iostream>
#include <fstream>
#include <vector>
#include <map>
#include <unordered_map>
#include <string>
#include <cmath>
#include <cstdio>
#include <algorithm>
#include <functional>
#include <numeric>
#include <iomanip>
#include <queue>
using namespace std;

typedef int64_t ll;
const ll INF = 1000000000000000000;
#define fori(i, a, b) for (ll i = (a); i < (b); ++i)
#define ford(i, a, b) for (ll i = (b - 1); (a) <= i; --i)
#define rep(i, n) fori(i, 0, n)
#define vll vector<ll>
#define all(v) v.begin(), v.end()



int main() {
	ll H, W;
	cin >> H >> W;
	if (H % 3 == 0 || W % 3 == 0) {
		cout << 0 << endl;
		return 0;
	}

	ll val1 = INF;
	ll a1 = (H / 2) * W, a2 = (H - H / 2) * W, a3 = 0;
	rep(i, W) {
		a1 -= H / 2;
		a2 -= H - H / 2;
		a3 += H;
		val1 = min(val1, max({ a1, a2, a3 }) - min({ a1, a2, a3 }));
	}

	ll val2 = INF;
	a1 = (W / 2) * H, a2 = (W - W / 2) * H, a3 = 0;
	rep(i, H) {
		a1 -= W / 2;
		a2 -= W - W / 2;
		a3 += W;
		val2 = min(val1, max({ a1, a2, a3 }) - min({ a1, a2, a3 }));
	}

	cout << min(val1, val2) << endl;
}