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 = do
  l <- getLine
  let [n,k] = map read $ words l
  print $ abc108c n k

abc108c n k = sum
  [ count a b c
  | a <- [1..n]
  , b <- [a..n]
  , mod (a+b) k == 0
  , c <- [b..n]
  , mod (b+c) k == 0
  , mod (c+a) k == 0
  ]

count a b c
  | a == b && b == c = 1
  | a == b || b == c || c == a = 3
  | True = 6