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 <vector>
#include <algorithm>
#include <numeric>
#include <cstdint>
#include <map>

using namespace std;

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

    int series = n/k;
    int64_t count = 0;
    for(int i = 0; i < k; ++i)
    {
        if(2*(k-i) % k == 0)
        {
            int x = i;
            int y = (k-i) % k;
            int64_t ser_x = (x + series * k) <= n ? series + 1: series;
            int64_t ser_y = (y + series * k) <= n ? series + 1: series;
            if(x == 0) ser_x -= 1;
            if(y == 0) ser_y -= 1;
            //cout << x << ',' << y << ',' << y << '\n';
            //cout << '*' << ser_x << '\n';
            //cout << '*' << ser_y << '\n';
            //cout << '*' << ser_y << '\n';
            count += ser_x * ser_y * ser_y;
        }
    }
    cout << count << '\n';
 
    return 0;
}