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: Time Limit Exceeded)

#include<iostream>
#include<math.h>

using namespace std;

int main(){
    int h, w;
    cin >> h >> w;
    int a, b, c = h*w;

    double object = double(h)*double(w)/3;
    int i=0;
    while(h*i<=object-1)i++;
    i--;
    if(object-(h*i) > (h*(i+1))-object)i++;
    int j=0;
    while(w*j<=object-1)j++;
    j--;
    if(object-(w*j) > (w*(j+1))-object)j++;
    if(fabs(h*i-object)>fabs(w*j-object)){
        a = w*j;
        h -= j;
    }else{
        a = h*i;
        w -= i;
    }

    i=0;
    while(h*i<=object-1)i++;
    i--;
    if(object-(h*i) > (h*(i+1))-object)i++;
    j=0;
    while(w*j<=object-1)j++;
    j--;
    if(object-(w*j) > (w*(j+1))-object)j++;
    if(fabs(h*i-object)>fabs(w*j-object)){
        b = w*j;
        h -= j;
    }else{
        b = h*i;
        w -= i;
    }
    c -= a+b;
    cout << abs(c-a) << endl;;
}