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<iostream>
#include<algorithm>
#include<queue>
#include<string>
#include<vector>
#include<stdio.h>
using namespace std;

int main(){
    long long h,w;
    cin>>h>>w;
    long long n=h/2;
    long long m=h-h/2;
    long long a=w/2;
    long long b=w-w/2;
    long long lastmin=10000000;
    long long callmax,realmax,callmin,realmin,cmax,rmax,cmin,rmin;
    if(h%3==0||w%3==0){
        cout<<0<<endl;
    }
    else{
        for(int i=1;i<h;i++){
            callmax=max(i*w,(h-i)*a);
            realmax=max(callmax,(h-i)*b);
            callmin=min(i*w,(h-i)*a);
            realmin=min(callmin,(h-i)*b);
            lastmin=min(lastmin,realmax-realmin);
        }
        for(int i=1;i<w; i++){
            cmax=max(i*h,(w-i)*n);
            rmax=max(cmax,(w-i)*m);
            cmin=min(i*h,(w-i)*n);
            rmin=min(cmin,(w-i)*m);
            lastmin=min(lastmin,rmax-rmin);
        }
        cout<<lastmin<<endl;
    }
    return 0;
}