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 OCaml (4.02.3) (judge verdict: Accepted)

open Printf
open Scanf

let id x = x

let n, k = scanf "%d %d" (fun n k -> n, k)

let cond v = v mod k = 0

let rec gcd m n =
  if m < n then gcd n m
  else if n = 0 then m
  else gcd n (m mod n)

let lcm m n = m * n / gcd m n

let rec step_loop st ed step f =
  if st <= ed then begin
    f st; step_loop (st + step) ed step f
  end else ()

let () =
  let count = ref 0 in
  for a = 1 to n do
    let m1 = a mod k in
    let m2 = (k - m1) mod k in
    if m1 = m2 then
      if m1 = 0 then begin
        count := !count + (n / k) * (n / k);
      end else begin
        let v = (n - m1) / k + 1 in
        count := !count + v * v
      end;
  done;
  printf "%d\n" !count