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)

ret_sub :: Integer -> Integer -> Integer -> Integer -> Integer
ret_sub num id n k =
    if (id > n) then
        num
    else
        if (mod (((mod (-id) k) + k)*2) k == 0) then
            let a = div n k + if (mod n k >= mod (-id) k && mod (-id) k /= 0) then 1 else 0 in
            ret_sub (num + a*a) (id + 1) n k
        else
            ret_sub num (id + 1) n k


ret :: Integer -> Integer -> Integer
ret n k = ret_sub 0 1 n k


main = do
    hoge <- getLine
    let [n, k] = map read $ words hoge
    putStrLn $ show $ ret n k