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: Accepted)

H,W = map(int,input().split())
#l = sorted([int(input()) for i in range(N)],reverse=True)
def three(h,w):
    ans = h*w
    for i in range(h//3,h//3+2):
        A = w*i
        B = w*((h-i)//2)
        C = w*((h-i+1)//2)
        ans = min(ans,max(A,B,C)-min(A,B,C))
    return ans
def onetwo(h,w):
    ans = h*w
    for i in range(h//3,h//3+2):
        A = w*i
        B = (h-i)*(w//2)
        C = (h-i)*((w+1)//2)
        ans = min(ans,max(A,B,C)-min(A,B,C))
    return ans
print(min(three(H,W),three(W,H),onetwo(H,W),onetwo(W,H)))