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: Accepted)

def areadifference(h , w):
    ans = 0
    count1 = 10000000000
    count2 = 10000000000
    if h % 3 == 0 or w % 3 == 0:
        return ans

    for i in range(1 , h + 1):
        hcount = max( i * w , (((h - i)//2) * w) , ((-(-(h - i)//2)) * w)) - min( i * w , (((h - i)//2) * w) , ((-(-(h - i)//2)) * w))
        wcount = max( i * w , ((h - i) * (w//2)) , ((h - i) * (-(-w//2)))) - min( i * w , ((h - i) * (w//2)) , ((h - i) * (-(-w//2))))
        count1 = min(count1 , hcount , wcount)

    for i in range(1 , w + 1):
        hcount = max( i * h , (((w - i)//2) * h) , ((-(-(w - i)//2)) * h)) - min( i * h , (((w - i)//2) * h) , ((-(-(w - i)//2)) * h))
        wcount = max( i * h , ((w - i) * (h//2)) , ((w - i) * (-(-h//2)))) - min( i * h , ((w - i) * (h//2)) , ((w - i) * (-(-h//2))))
        count2 = min(count2 , hcount , wcount)

    ans = min(count1 , count2)

    return ans

def main():
    h , w = map(int , input().split())
    print(areadifference(h , w))

if __name__ == '__main__':
    main()