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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

def main():
    h,w = map(int,input().split())
    a=(h%3)*w
    b=(w%3)*h

    m=float('inf')
    for i in range(1,h//2+1):
        s1=i*w
        s2=(w//2)*(h-i)
        s3=(w-(w//2))*(h-i)
        x=max(abs(s1-s2),abs(s2-s3),abs(s3-s1))
        m=min(m,x)
    c=m
    m=float('inf')
    for i in range(1,w//2+1):
        s1=i*h
        s2=(h//2)*(w-i)
        s3=(h-(h//2))*(w-i)
        x=max(abs(s1-s2),abs(s2-s3),abs(s3-s1))
        m=min(m,x)
    d=m
    print(min(a,b,c,d))
    
if __name__ == "__main__":
    main()