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;
int main()
{
    int h,w,a;
    cin>>h>>w;
    int temp;
    if(h>=w)
    {
        temp=h;
        h=w;
        w=temp;
    }
    if(w%3==0||h%3==0)
    {
        cout<<0;
        return 0;
    }
    a=(w+1)/3;
    long long int a1=h*a;
    long long int a2,a3;
    w=w-a;
    if(h>=w)
    {
        temp =h;
        h=w;
        w=temp;
    }
    if(h%2==0)
    {
        a2=h/2*w;
        a3=a2;
    }
    else if(w%2==0)
    {
        a2=w/2*h;
        a3=a2;
    }
    else
    {
        if(h<w)
        {
            a2=w/2*h;
            a3=ceil(w/2.0)*h;
        }
        else
        {
            a2=h/2*w;
            a3=ceil(h/2.0)*w;
        }
    }
    cout<<max(a1,a3)-min(a2,a1);
    return 0;
}