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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <cstdint>
#include <iostream>

using namespace std;

int main()
{
    int n, k;
    cin >> n >> k;

    int count_k = 0;
    int count_half = 0;

    for (int i = 1; i <= n; i += 1) {
        if (i % k == 0) {
            count_k += 1;
        } else if (i % k == k / 2) {
            count_half += 1;
        }
    }

    int64_t res = 1LL * count_k * count_k * count_k;
    if (k % 2 == 0) {
        res += 1LL * count_half * count_half * count_half;
    }

    cout << res << "\n";
    return 0;
}