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 <bits/stdc++.h>
using namespace std;

int n, k, t, t2;

int main() {
	cin >> n >> k;
	for (int i = 1; i <= n; i++){
		if(i % k == k / 2)
			t++;
		if(i % k == 0)
			t2++;
	}
	long long ans = t;
	if(t >= 1)
		ans += (1LL * t * (t - 1) * 3);
	if(t >= 2)
		ans += (1LL * t * (t - 1) * (t - 2));
	if(k % 2 == 1)	
		ans = 0;
	ans += t2;
	if(t2 >= 1)
		ans += (1LL * t2 * (t2 - 1) * 3);
	if(t2 >= 2)
		ans += (1LL * t2 * (t2 - 1) * (t2 - 2));
	cout << ans;
	return 0;
}