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;
#define pb push_back

#define ll long long 
#define mod 1000000007

int main()
{
	ll n,k;
	cin>>n>>k;
	if(n%3LL==0 || k%3LL==0)
	{
		cout<<0<<endl;
		return 0;
	}
	ll s1,s2,d1,d2,s3=INT_MAX,d3=INT_MAX;
	for(ll i=1;i<k;i++)
	{
		ll q1=i*n;
		ll q2=n/2*(k-i);
		ll q3=(n-n/2)*(k-i);
		 s1=max(q1,max(q2,q3));
		 s2=min(q1,min(q2,q3));
		 s3=min(s3,s1-s2);
	}
	//ll re1=s1-s2;
	swap(n,k);
	for(ll i=1;i<k;i++)
	{
		ll q1=i*n;
		ll q2=n/2*(k-i);
		ll q3=(n-n/2)*(k-i);
		 d1=max(q1,max(q2,q3));
		 d2=min(q1,min(q2,q3));
		 d3=min(d3,d1-d2);
	}
	//ll re2=d1-d2;
	cout<<min(s3,d3);
}