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: Wrong Answer)

//

#include <stdio.h>

int main(void){
    long H,W;
    //h*wのチョコレート
    //hは縦幅、wは横幅
    scanf("%ld %ld",&H,&W);
    long smax,smin,diff,ans=100000000000;
    long sa,sb,sc;
    long h,w;
    if(H%3==0||W%3==0){
        printf("0\n");
        return 0;
    }
    for(h=1;h<H;h++){
        sa=h*W;
        w=(long)W/2;
        sb=(H-h)*w;
        sc=(H-h)*(W-w);
        //printf("%ld %ld %ld\n",sa,sb,sc);
        smax=sa;
        if(sb>smax)smax=sb;
        if(sc>smax)smax=sc;
        smin=sa;
        if(sb<smin)smin=sb;
        if(sc<smin)smin=sc;
        diff=smax-smin;
        if(ans>diff)ans=diff;
    }
    for(w=1;w<W;w++){
        sa=H*w;
        h=(long)H/2;
        sb=(W-w)*h;
        sc=(W-w)*(H-h);
        //printf("%ld %ld %ld\n",sa,sb,sc);
        smax=sa;
        if(sb>smax)smax=sb;
        if(sc>smax)smax=sc;
        smin=sa;
        if(sb<smin)smin=sb;
        if(sc<smin)smin=sc;
        diff=smax-smin;
        if(ans>diff)ans=diff;
    }

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