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;

namespace Algorithm
{
    class Program
    {
        static void Main(string[] args)
        {
            var line = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int N = line[0], K = line[1];

            var dict = new Dictionary<long, long>();
            dict[K] = 0;

            for (var i = 1; i <= N; i++)
            {
                if (dict.ContainsKey(i % K))
                    dict[i % K]++;
                else
                    dict[i % K] = 1;
            }

            var ret = 0L;

            for (var a = 0; a < K; a++)
            {
                var b = (K - a) % K;
                var c = (K - a) % K;
                if ((b + c) % K != 0) continue;
                if (!dict.ContainsKey(a) || !dict.ContainsKey(b)) continue;

                ret += dict[a] * dict[b] * dict[c];
            }

            Console.WriteLine(ret);
        }
    }
}