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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

using namespace std;
typedef long long int ll;
typedef pair<int, int> ii;

struct fastio {
    fastio() {
        ios::sync_with_stdio(false);
        cout << setprecision(10) << fixed;
        cin.tie(0);
    }
};

fastio _fast_io;

const int N = 1e5 + 5;
int n, k, ans;

int main() {
    cin >> n >> k;
    if (k % 2 == 0) {
        ll a = (n - k / 2) / k + (k / 2 <= n ? 1 : 0);
        ll b = n / k;
        cout << a * a * a + b * b * b << endl;
    } else {
        ll a = n / k;
        cout << a * a * a << endl;
    }
    return 0;
}