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;
using ll = long long;

int main() {
    ll h,w;
    cin>>h>>w;
    ll sdiff=h*w;
    for(int i = 1;i < h;++i) {
        ll s1=w*i;
        ll rh=h-i;
        ll s2,s3;
        if(rh%2==0||w%2==0) {
            s2=rh*w/2;
            s3=rh*w/2;
        }
        else {
            if(rh<w) {
                s2=rh*(w/2);
                s3=rh*(w+1)/2;
            }
            else {
                s2=(rh/2)*w;
                s3=(rh+1)/2*w;
            }
        }
        if(s1>s3)sdiff=min(sdiff,s1-s2);
        else if(s1<s2)sdiff=min(sdiff,s3-s1);
        else sdiff=min(sdiff,s3-s2);
    }
    for(int i = 1;i < w;++i) {
        ll s1=h*i;
        ll rw=w-i;
        ll s2,s3;
        if(rw%2==0||h%2==0) {
            s2=rw*h/2;
            s3=rw*h/2;
        }
        else {
            if(rw<h) {
                s2=rw*(h/2);
                s3=rw*(h+1)/2;
            }
            else {
                s2=(rw/2)*h;
                s3=(rw+1)/2*h;
            }
        }
        if(s1>s3)sdiff=min(sdiff,s1-s2);
        else if(s1<s2)sdiff=min(sdiff,s3-s1);
        else sdiff=min(sdiff,s3-s2);
    }
    cout<<sdiff<<endl;
    return 0;
}