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>

long long int max(long long int a,long long int b,long long int c){
    if(a>=b&&a>=c)return a;
    else if(b>=a&&b>=c)return b;
    return c;
}
long long  int min(long long int a,long long int b,long long int c){
    if(a<=b&&a<=c)return a;
    else if(b<=a&&b<=c)return b;
    return c;
}
int main(void){
    long long int H,W;
    scanf("%lld %lld",&H,&W);
    long long int karix,kariy;
    karix=H/3;kariy=W/3;
    long long int karians[4];
    long long int kari[3];
    long long int ans;
    kari[0]=karix*W;
    kari[1]=(H-karix)*(W/2);
    kari[2]=(H-karix)*W-kari[1];
    if(karix==0)karians[0]=1000000000;
    else karians[0]=max(kari[0],kari[1],kari[2])-min(kari[0],kari[1],kari[2]);
    
    kari[0]+=W;
    kari[1]-=(W/2);
    kari[2]=(H-karix-1)*W-kari[1];;
    karians[1]=max(kari[0],kari[1],kari[2])-min(kari[0],kari[1],kari[2]);
    
    kari[0]=kariy*H;
    kari[1]=(W-kariy)*(H/2);
    kari[2]=(W-kariy)*H-kari[1];
    if(kariy==0)karians[2]=1000000000;
    else karians[2]=max(kari[0],kari[1],kari[2])-min(kari[0],kari[1],kari[2]);
    
    kari[0]+=H;
    kari[1]-=(H/2);
    kari[2]=(W-kariy-1)*H-kari[1];
    karians[3]=max(kari[0],kari[1],kari[2])-min(kari[0],kari[1],kari[2]);
    
    if(H%3==0||W%3==0)printf("0");
    else{
        ans=min(karians[0],karians[1],karians[2]);
        if(ans>karians[3])ans=karians[3];
        printf("%lld",ans);
    }
    return 0;
}