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 <stdlib.h>

long long int area(long int h, long int w, unsigned long long int min)
{
    long int i;
    unsigned long long int S[3],max=min;
    for(i=1;i<=h-1;i++){
        S[0]=i*w;
        S[1]=(h-i)*(w/2);
        S[2]=(h-i)*(w-w/2);
        if(llabs(S[0]-S[1])>=llabs(S[1]-S[2]) && llabs(S[0]-S[1])>=llabs(S[0]-S[2])) max=llabs(S[0]-S[1]);
        else if(llabs(S[1]-S[2])>=llabs(S[0]-S[1]) && llabs(S[1]-S[2])>=llabs(S[0]-S[2])) max=llabs(S[1]-S[2]);
        else max=llabs(S[0]-S[2]);
        
        if(min>max) min=max;
        
        S[1]=(h-i)/2*w;
        S[2]=(h-i-(h-i)/2)*w;
        if(llabs(S[0]-S[1])>=llabs(S[1]-S[2]) && llabs(S[0]-S[1])>=llabs(S[0]-S[2])) max=llabs(S[0]-S[1]);
        else if(llabs(S[1]-S[2])>=llabs(S[0]-S[1]) && llabs(S[1]-S[2])>=llabs(S[0]-S[2])) max=llabs(S[1]-S[2]);
        else max=llabs(S[0]-S[2]);
        
        if(min>max) min=max;
    }
    return min;
}

int main()
{
    long int H,W;
    scanf("%ld %ld",&H,&W);
    unsigned long long int min=H*W;
    if(min%3==0) puts("0");
    else{
        min=area(H,W,min);
        min=area(W,H,min);
        printf("%lld\n",min);
    }
    return 0;
}