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 Python (3.4.3) (judge verdict: Wrong Answer)

from sys import stdin
def main():
    #入力
    readline=stdin.readline
    h,w=map(int,readline().split())

    if h*w%3==0:
        ans=0
    else:
        ans=float("inf")
        #縦方向に全探索
        s1=w//2*h
        s2=h*w-s1
        for i in range(1,h):
            s3=i*w
            s1-=w//2
            s2-=w-w//2
            ans=min(ans,max(s1,s2,s3)-min(s1,s2,s3))

        #横方向に全探索
        s1=h//2*w
        s2=h*w-s1
        for j in range(1,w):
            s3=j*h
            s1-=h//2
            s2-=h-h//2
            ans=min(ans,max(s1,s2,s3)-min(s1,s2,s3))

    print(ans)

if __name__=="__main__":
    main()