Problem:
Score : 300 points

Problem Statement

You are given integers N and K. Find the number of triples (a,b,c) of positive integers not greater than N such that a+b,b+c and c+a are all multiples of K.
The order of a,b,c does matter, and some of them can be the same.

Constraints

1 \leq N,K \leq 2\times 10^5

N and K are integers.

Input

Input is given from Standard Input in the following format:

N K

Output

Print the number of triples (a,b,c) of positive integers not greater than N such that a+b,b+c and c+a are all multiples of K.

Sample Input 1

3 2

Sample Output 1

9

(1,1,1),(1,1,3),(1,3,1),(1,3,3),(2,2,2),(3,1,1),(3,1,3),(3,3,1) and (3,3,3) satisfy the condition.

Sample Input 2

5 3

Sample Output 2

1

Sample Input 3

31415 9265

Sample Output 3

27

Sample Input 4

35897 932

Sample Output 4

114191

Solution in Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

main = map read . words <$> getLine >>= \[n, k] -> print (answer n k)
answer n k = sum
      [case (a == b, b == c, c == a) of 
        (True, True, True)    -> 1
        (False, False, False) -> 6
        _                     -> 3 | 
      ab <- [k, 2 * k .. 2 * n], 
      ca <- [ab, ab + k .. 2 * n], 
      bc <- [ca, ca + k .. 2 * n], 
      let (abc, m) = (ab + bc + ca) `divMod` 2,
      let a = abc - bc, 
      let b = abc - ca, 
      let c = abc - ab,
      m == 0, 0 < a, c <= n]