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;
ll mod = 1000000007;

int main(){
  ll h,w;
  cin >> h >> w;
  
  ll ans,ans1,ans2,ans3,ans4;
  ll hemain=h%3,wemain=w%3;
  ll hart1=(h-hemain)/3,wart1=(w-wemain)/3;
  ll hart2=h/2,wart2=w/2;
  ll hact,wact;
  
  if(hemain==0 || wemain==0){
   cout << 0 << endl;
   return 0;
  }
  
  ans1=w;
  ans2=h;
  ans=min(ans1,ans2);
  
  if(hemain==2){
    hact=hart1+1;
    ans3=w*hact-wart2*(h-hact);
  }
  else{
    hact=hart1;
    ans3=w*hact-(w-wart2)*(h-hact);
  }
  
  if(ans3<0)ans3*=-1;
  ans=min(ans,ans3);
  
  
  if(wemain==2){
    wact=wart1+1;
    ans4=h*wact-hart2*(w-wact);
  }
  
  else{
    wact=wart1;
    ans4=h*wact-(h-hart2)*(w-wact);
  }
  if(ans4<0)ans4*=-1;
  ans=min(ans,ans4);
  
  
  
  cout << ans << endl;
  
  
  
  
}