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 <iostream>
#include <algorithm>
#include <numeric>
using namespace std;

typedef long long ll;

int main() {
    ll n, k;
    cin >> n >> k;
    ll a[n];
    for (int i = 1; i <= n; i++)
        a[i - 1] = (ll) i;
    transform(a, a+n, a, [k, n](ll x) {
            ll rem_a = x % k, rem_b = (k + (k - x) % k) % k;
            if (rem_a == rem_b) {
                ll t = (n + rem_a) / k;
                return t * t;
            }
            return 0LL;
            });
    cout << accumulate(a, a+n, 0LL) << endl;
	return 0;
}