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>
#include<string.h>

#define ll long long

ll min(ll x, ll y){
  if (x>y){
    return y;
  }else{
    return x;
  }
}

ll max(ll x, ll y){
  if (x<y){
    return y;
  }else{
    return x;
  }
}



int main(void){
  ll H,W;

  scanf("%d%d",&H,&W);

  if(H%3==0 || W%3==0){
    printf("0\n");
    return 0;
  }

  ll ans;
  ans = min(H,W);

  ll s1,s2,s3;
  ll mx,mn;
  for(ll r = 1; r < W; r++){
    s1 =   r   *   H    ;
    s2 = (W-r) * (H/2)  ;
    s3 = (W-r) * (H-H/2);

    mx = max(max(s1,s2),s3);
    mn = min(min(s1,s2),s3);

    ans = min(ans,mx-mn);
  }

  int tmp;
  tmp = H; H = W; W = tmp;
  for(ll r = 1; r < W; r++){
    s1 =   r   *   H    ;
    s2 = (W-r) * (H/2)  ;
    s3 = (W-r) * (H-H/2);

    mx = max(max(s1,s2),s3);
    mn = min(min(s1,s2),s3);

    ans = min(ans,mx-mn);
  }

  printf("%lld\n",ans);

  return 0;
}