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.Applicative
import Control.Monad

compute :: Int -> Int
compute n = n^3

solver :: Int -> Int -> Int
solver n k
    | odd k     = compute $ length [x | x <- [1..n], x `mod` k == 0]
    | otherwise = h + j
        where m  = k `div` 2
              xs = [x | x <- [1..n], x `mod` k == m]
              ys = [y | y <- [1..n], y `mod` k == 0]
              h  = compute $ length xs
              j  = compute $ length ys

main :: IO ()
main = do
    [n, k] <- (map read) . words <$> getLine
    print $ solver n k