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 Calc_ans(int a, int b){
    int S_max,S_min;
    S_max = (a/2)*b;
    a -= a/2;
    S_min = (b > a) ? (b/2)*a : (a/2)*b;
    return S_max - S_min;
}

int main(void){

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

    if(H % 3 == 0 || W % 3 == 0){
        ans = 0;
    }else{
        if(W > H) ans = Calc_ans(W,H);
        else ans = Calc_ans(H,W);
    }

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