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())
ans = 10**15
import sys
if h%3==0 or w%3==0:
  print(0)
  sys.exit()
h0 = 1
while h0 <h:
  s1=h0*w
  if (h-h0)%2==0:
    s2=w*(h-h0)//2
    s3=s2
  else:
    s2=w*(h-h0)//2
    s3=w*(h-h0)//2+w
  ans1 = max(s1,s2,s3)-min(s1,s2,s3)
  if w%2==0:
    s4=(h-h0)*(w//2)
    s5=s4
  else:
    s4=(h-h0)*(w//2)
    s5=(h-h0)*(w//2)+(h-h0)
  ans2 = max(s1,s4,s5)-min(s1,s4,s5)
  ans = min(ans,ans1,ans2)
  h0 += 1
w0 = 1
while w0 <w:
  s6=w0*h
  if (w-w0)%2==0:
    s7=h*(w-w0)//2
    s8=s7
  else:
    s7=h*(w-w0)//2
    s8=h*(w-w0)//2+h
  ans3 = max(s6,s7,s8)-min(s6,s7,s8)
  if h%2==0:
    s9=(w-w0)*(h//2)
    s10=s9
  else:
    s9=(w-w0)*(h//2)
    s10=(w-w0)*(h//2)+(w-w0)
  ans4 = max(s6,s9,s10)-min(s6,s9,s10)
  ans = min(ans,ans3,ans4)
  w0 += 1
print(ans)