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 ll=long long;
using ld=long double;
using namespace std;
int main(){
  ll h,w,ans=0,tmp=0;
  cin>>h>>w;
  if(w>h)swap(h,w);
  ll a=ceil((ld)h/3)*w,b=(h-ceil((ld)h/3))*(w/2),c=(h-ceil((ld)h/3))*(w-w/2);
  ll a2=(h/3)*w,b2=(h-(h/3))*(w/2),c2=(h-(h/3))*(w-w/2);
  ans=min(max(a,c)-b,max(a2,max(b2,c2))-min(a2,min(b2,c2)));
  if(h%3==0 ||w%3==0)cout<<"0";
  else cout<<ans;
}