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<bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef pair<int, int> PII;

const int MM = 1e9 + 7;
const double eps = 1e-8;
const int MAXN = 2e6 + 10;

int n, m;

void prework(){

}

void read(){

}

ll a[1000];

ll gao(ll n, ll m){
	ll ret = 1ll << 60;
	for(int i = 1; i < n; i++){
		a[0] = i * m;
		ll p = n - i;
		ll q = m;
		if (p % 2 == 0 || q % 2 == 0)
			a[1] = a[2] = p * q / 2;
		else{
			if (p > q) swap(p, q);
			a[1] = (q - 1) / 2 * p;
			a[2] = (q + 1) / 2 * p;
		}
		sort(a, a + 3);
		ret = min(ret, a[2] - a[0]);
	}
	return ret;
}

void solve(int casi){
//	cout << "Case #" << casi << ": ";
	cin >> n >> m;
	ll ans = min(gao(m, n), gao(n, m));
	cout << ans << endl;
}

void printans(){

}


int main(){
//	std::ios::sync_with_stdio(false);
	prework();
	int T = 1;
//	cin>>T;
	for(int i = 1; i <= T; i++){
		read();
		solve(i);
		printans();
	}
	return 0;
}