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>
#define ll long long
using namespace std;
ll h,w,ans=0x7fffffffffffffff,a,b,c,d,e;
ll f(ll h,ll w)
{
	for (int i=0;i<=h/2;++i)
	{
		a=w*i;
		b=w/2*(h-i);
		c=(h-i)/2*w;
		d=h*w-a-b;
		e=h*w-a-c;
		ans=min(ans,min(max(a,max(b,d))-min(a,min(b,d)),max(a,max(c,e))-min(a,min(c,e))));
	}
}
int main()
{
	cin>>h>>w;
	f(h,w);
	f(w,h);
	cout<<ans;
	return 0;
}