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;

int main(){
	cin.tie(0),ios::sync_with_stdio(false);
	int n,k; cin>>n>>k;
	vector<int>v(k,0);
	for(int i=1;i<=n;++i)++v.at(i%k);
	int64_t ans=0;
	for(int a=1;a<=n;++a){
		int b=(k-a%k)%k,c=(k-b%k)%k;
		if((c+a)%k)continue;
		ans+=1L*v.at(b)*v.at(c);
	}
	cout<<ans<<"\n"s;
}