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)

module Main where

import Control.Applicative
import Control.Monad

main :: IO ()
main = do
    [n, k] <- fmap read . words <$> getLine :: IO [Int]
    let ans = [ (a, b, c)
              | a <- [1 .. n]
              , let s = (a + 1) `div` k
              , let t = (a + n) `div` k
              , q1 <- [s .. t]
              , let b = k * q1 - a
              , b >= 1
              , (a + b) `mod` k == 0
              , q2 <- [s .. t]
              , let c = k * q2 - a
              , c >= 1
              , (b + c) `mod` k == 0
              , (c + a) `mod` k == 0
              ]
    print $ length ans