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;

int mindiff(int H,int W){
  int ret = 1000000000;
  int w = W / 3;
  int rW = W % 3;
  int h = H / 2;
  int rH = H % 2;
  for(int i = 0; i <= rW; i++){
    int S1 = (w + i) * H;
    int S2 = (2*w + rW - i) * (h + rH);
    int S3 = (2*w + rW - i) * h;
    ret = min(ret,max(S1,max(S2,S3)) - min(S1, min(S2,S3)));
  }
  return ret;
}

int main(){
  int H, W;
  cin >> H >> W;
  cout << min(mindiff(H,W), mindiff(W,H)) << endl;
}