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;

namespace ARC102
{
    class C
    {
        static void Main(string[] args)
        {
            int[] input = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int N = input[0];
            int K = input[1];

            long[] num = new long[K];
            for (int i = 1; i <= N; i++) num[i % K]++;

            long res = 0;
            for (int a = 0; a < K; a++)
            {
                int b = (K - a) % K;
                int c = (K - a) % K;

                if ((b + c) % K != 0) continue;
                res += num[a] * num[b] * num[c];

            }
            Console.WriteLine(res);
        }
    }
}