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: Accepted)

import Control.Monad

main :: IO ()
main = do
  (n:k:_) <- fmap (map read . words) getLine :: IO [Int]
  print $ solve' n k

solve :: Int -> Int -> Int
solve n k = length $ filter (validate k) (replicateM 3 [1..n])
  where validate k a = (a !! 0 + a !! 1) `mod` k == 0 && (a !! 1 + a !! 2) `mod` k == 0 && (a !! 2 + a !! 0) `mod` k == 0

solve' n k
  | k `mod` 2 == 1 = m^3 -- odd
  | otherwise = m^3 + p^3
    where
      m = n `div` k
      p = if n `mod` k < k `div` 2
          then m
          else m + 1