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 Scala (2.11.7) (judge verdict: Accepted)

import java.io.{InputStream, OutputStream, PrintStream}
import java.util.Scanner

import scala.annotation.tailrec

object Main {

  def main(args: Array[String]): Unit = {
    val solver = new Solver(System.in, System.out)
    solver.solve()
  }

  class Solver(in: InputStream, out: OutputStream) {
    lazy val input = new Scanner(in)

    lazy val output = new PrintStream(out)

    def solve(): Unit = {
      val Array(n, k) = input.nextLine().split(" ").map(_.toInt)

      if (k % 2 == 1) {
        val p = 1.to(n).count { i =>
          i % k == 0
        }
        output.println(Math.pow(p, 3).toLong)
      } else {
        val p = 1.to(n).count { i =>
          i % k == k / 2
        }
        val q = 1.to(n).count { i =>
          i % k == 0
        }
        output.println(Math.pow(p, 3).toLong + Math.pow(q, 3).toLong)
      }

    }

    @tailrec
    final def gcd(m: Int, n: Int): Int = {
      val (x, y) = if (m > n) (m, n) else (n, m)
      if (y != 0) gcd(y, x % y)
      else x
    }

  }

}