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 Ruby (2.3.3) (judge verdict: Wrong Answer)

# Here your code !



a,b=gets.split


a=a.to_i
b=b.to_i
n=0

if a>=b
    c=a
    d=b
else c=b
    d=a
end


k=c-c/3
l=k-1

if a%3==0 || b%3==0
     puts 0
     
elsif c%3==1  && d%2==0

     puts (c/3*d-k*d/2).abs
elsif c%3==1  && d%2==1
      puts [c/3*d,k*((d+1)/2),k*((d+1)/2)].max-[c/3*d,k*((d+1)/2),k*((d+1)/2)].min

elsif c%3==2  && d%2==0
        puts ((c/3+1)*d-l*d/2).abs
   
   
elsif c%3==2  && d%2==1
        puts [(c/3+1)*d,(c-c/3-1)*((d+1)/2),(c-c/3-1)*((d-1)/2)].max-[(c/3+1)*d,(c-c/3-1)*((d+1)/2),(c-c/3-1)*((d-1)/2)].min
        
end