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 = map(int , input().split())
h_ans = 100000
w_ans = 100000

for h in range(1,H):
    Sa = h * W
    Sb = (H - h) * (W // 2)
    Sc = (H - h) * (W - ( W //2 ))
    if max(Sa,Sb,Sc) - min(Sa,Sb,Sc) < h_ans:
        h_ans = max(Sa,Sb,Sc) - min(Sa,Sb,Sc)
        
for h in range(1,H):
    Sa = h * W
    Sb = (H - h)//2 * W
    Sc = (H - (h + (H-h)//2)) * W
    if max(Sa,Sb,Sc) - min(Sa,Sb,Sc) < h_ans:
        h_ans = max(Sa,Sb,Sc) - min(Sa,Sb,Sc)
    
for w in range(1,W):
    Sa = H * w
    Sb = (H // 2) * (W - w)
    Sc = (H - (H //2)) * (W - w)
    if max(Sa,Sb,Sc) - min(Sa,Sb,Sc) < w_ans:
        w_ans = max(Sa,Sb,Sc) - min(Sa,Sb,Sc)
    
for w in range(1,W):
    Sa = H * w
    Sb = H * (W -w)//2
    Sc = H * (W - (w + (W -w)//2) ) 
    if max(Sa,Sb,Sc) - min(Sa,Sb,Sc) < w_ans:
        w_ans = max(Sa,Sb,Sc) - min(Sa,Sb,Sc)
    
        
print((min(h_ans,w_ans)))