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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

long long max(long long a,long long b){
  if(a > b){
    return a;
  }
  return b;
}

long long min(long long a,long long b){
  if(a < b){
    return a;
  }
  return b;
}

int main(void){
  long H,W;
  long long ans;
  long long Sa,Sb,Sc;
  scanf("%ld%ld",&H,&W);

  if(W%3 == 0 || H%3 == 0) ans = 0;
  else ans = min(H,W);

  for(long i = 1;i < H;i++){
    Sa = i*W;
    Sb = (H-i)*(W/2);
    Sc = (H-i)*(W-W/2);

    ans = min(ans,max(Sa,max(Sb,Sc))-min(Sa,min(Sb,Sc)));

    if(i < H-1){
      Sa = i*W;
      Sb = (H-i)/2*W;
      Sc = H*W-Sa-Sb;

      ans = min(ans,max(Sa,max(Sb,Sc))-min(Sa,min(Sb,Sc)));
    }
  }

  long tmp = H;
  H = W;
  W = tmp;

  for(long i = 1;i < H;i++){
    Sa = i*W;
    Sb = (H-i)*(W/2);
    Sc = (H-i)*(W-W/2);

    ans = min(ans,max(Sa,max(Sb,Sc))-min(Sa,min(Sb,Sc)));

    if(i < H-1){
      Sa = i*W;
      Sb = (H-i)/2*W;
      Sc = H*W-Sa-Sb;

      ans = min(ans,max(Sa,max(Sb,Sc))-min(Sa,min(Sb,Sc)));
    }
  }

  printf("%lld\n",ans);
  return 0;
}