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)

H,W = list(map(int,input().split()))

ans = float('inf')
a,b,c = H//3*W,(H-H//3)*(W//2),(H-H//3)*(W-W//2)
ans = min(ans,max(a,b,c)-min(a,b,c))
a,b,c = (H+2)//3*W,(H-(H+2)//3)*(W//2),(H-(H+2)//3)*(W-W//2)
ans = min(ans,max(a,b,c)-min(a,b,c))
a,b,c = W//3*H,(W-W//3)*(H//2),(W-W//3)*(H-H//2)
ans = min(ans,max(a,b,c)-min(a,b,c))
a,b,c = (W+2)//3*H,(W-(W+2)//3)*(H//2),(W-(W+2)//3)*(H-H//2)
ans = min(ans,max(a,b,c)-min(a,b,c))
a,b,c = H//3*W,H//3*W,(H//3+1)*W
ans = min(ans,max(a,b,c)-min(a,b,c))
a,b,c = W//3*H,W//3*H,(W//3+1)*H
ans = min(ans,max(a,b,c)-min(a,b,c))

print(ans)