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 int long long int
#define pb push_back
#define mp make_pair
#define all(x) x.begin(), x.end()
#define tr(it, a) for(auto it = a.begin(); it != a.end(); it++)
typedef vector<int>         vi;
const int mod = 1000000007;






int32_t main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    float a,b,d;
    float ans=INT_MAX;
    float r,c;
    cin>>r>>c;
    int total  = r*c;

         for(int i =1;i <r;i++){
            a = c*i;
            float left_rows = r-i;
            b = floor(left_rows/2)*c;
            d = ceil(left_rows/2)*c;
            ans = min(ans,max({a,b,d})-min({a,b,d}));

            a = c*i;
            b = floor(c/2)*(r-i);
            d=ceil(c/2)*(r-i);
            ans = min(ans,max({a,b,d})-min({a,b,d}));

         }
         for(int i =1;i <c;i++){
             a = r*i;
            float left_rows = c-i;
            b = floor(left_rows/2)*r;
            d = ceil(left_rows/2)*r;
            ans = min(ans,max({a,b,d})-min({a,b,d}));

            a = r*i;
            b = floor(r/2)*(c-i);
            d=ceil(r/2)*(c-i);;
           ans = min(ans,max({a,b,d})-min({a,b,d}));

        }
    int ans1 = ans;
    cout<<ans1<<endl;


















}