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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

class Program
{
    static void Main(string[] args)
    {
        var inputs = Console.ReadLine().Split(' ');
        var N = int.Parse(inputs[0]);
        var K = int.Parse(inputs[1]);

        var kCount = 0;
        var halfKCount = 0;
        for (int i = 1; i <= N; i++)
        {
            if (i % K == 0)
            {
                kCount++;
            }

            if (K % 2 == 0 && i % K == K / 2)
            {
                halfKCount++;
            }
        }

        var ans = 0L;
        if (K % 2 == 0)
        {
            ans = pow(kCount, 3) + pow(halfKCount, 3);
        }
        else
        {
            ans = pow(kCount, 3);
        }
        Console.WriteLine(ans);
    }

    static long pow(long baseValue, long n)
    {
        var ans = 1L;
        for (long i = 1; i <= n; i++)
        {
            ans *= baseValue;
        }

        return ans;
    }
}