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: Wrong Answer)

{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE UnboxedTuples #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE ViewPatterns #-}
{-# LANGUAGE TupleSections #-}
{-# LANGUAGE MultiWayIf #-}

import Control.Monad
import Control.Monad.ST
import Control.Monad.State
import Control.Monad.Primitive
import Control.Applicative
import Control.Arrow
import Data.List
import Data.Array
import Data.Array.IO
import Data.Array.ST
import Data.IORef
import Data.STRef
import Data.Maybe
import Data.Bits
import Data.Ord
import Data.Ratio
import Data.Int
import Data.Char
import qualified Data.ByteString.Char8 as BS
import qualified Data.Set as Set
import qualified Data.Vector as V
import qualified Data.Vector.Mutable as VM
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import Data.Tuple
import Data.Function
import Text.Printf
import Debug.Trace
import Numeric

modifyArray arr i f = readArray arr i >>= \x -> writeArray arr i (f x)

listToTuple2 [a,b] = (a,b)
listToTuple3 [a,b,c] = (a,b,c)
listToTuple4 [a,b,c,d] = (a,b,c,d)
listToTuple5 [a,b,c,d,e] = (a,b,c,d,e)

readIntBS = fst . fromJust . BS.readInt

for = flip map

infixr 1 ?
(?) :: Bool -> (a,a) -> a
(?) b t = (if b then fst else snd) t

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

  print $ sum [((n`div`k+1) - (b0`div`k) -1) * ((n`div`k+1) - (c0`div`k) - 1) | a <- [1..n], (2*a) `mod` k == 0, let b0 = k * (floor $ a % k) - a, let c0 = k * (floor $ (-a) % k) + a]
  
  
  return ()