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 <iostream>

using namespace std;

long smax=0;
long smin=0;
long res_min=1e13;

void divide2(int H,int W){
  if(H%2==0 || W%2==0){
    smin=(long)H*(long)W/2;
    smax=(long)H*(long)W/2;
  }else{
    if(H>W){
      int half=H/2;
      smin=(long)half*(long)W;
      smax=smin+W;
    }else{
      int half=W/2;
      smin=(long)half*(long)H;
      smax=smin+H;
    }
  }
}

void divide3(int H,int W){
  if(H%3==0||W%3==0){
    smin=0;
    smax=0;
    res_min=0;
  }else{
    for(int i=H/3;i<=H/3+1;i++){
      divide2(H-i,W);
      long tmp=(long)i*(long)W;
      smax=smax>tmp?smax:tmp;
      smin=tmp>smin?smin:tmp;
      if(res_min>(smax-smin))
	res_min=smax-smin;
    }
    for(int i=W/3;i<=W/3+1;i++){
      divide2(H,W-i);
      long tmp=(long)i*(long)H;
      smax=smax>tmp?smax:tmp;
      smin=tmp>smin?smin:tmp;
      if(res_min>(smax-smin))
	res_min=smax-smin;
    }
  }
}

int main(){
  int H=0,W=0;
  cin>>H>>W;
  divide3(H,W);
  cout<<res_min<<endl;
  return 0;
}