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.Collections.Generic;
using System.Linq;
using static System.Console;
using static MyUtil;

class MyUtil
{
    public static int[] ReadIntArray()
    {
        return ReadLine().Split().Select(x => int.Parse(x)).ToArray();
    }
}

class Program
{
    public static void Main()
    {
        var tmp = ReadIntArray();
        int n = tmp[0], k = tmp[1];

        long n0 = 0;
        for (int i = 1; i <= n; i++)
        {
            if (i % k == 0){ n0++; }
        }

        long n1 = 0;
        if (k%2 == 0)
        {
            for (int i = 1; i <= n; i++)
            {
                if (i % k == k/2){ n1++; }
            }
        }

        long ans = n0*n0*n0 + n1*n1*n1;
        WriteLine(ans);
    }
}