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;
ll n, m;
ll ans;

ll maxT(ll a, ll b) {
	if(a >= b) return a;
	else return b;
}

ll minT(ll a, ll b) {
	if(a <= b) return a;
	else return b;
}

int main() {
	cin >> n >> m;
	ll p = maxT(n, m) / 2;
	ll s1 = p * minT(n, m); //最大面积
	ll tmp = maxT(n, m) - p;
	ll s2 = tmp * (minT(n, m) / 2); //最小面积
	ans = s1 - s2; //最小化最值差
	if((n * m) % 3 == 0) ans = 0; 
	cout << ans << endl;
}