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++ (Clang 10.0.0) (judge verdict: Accepted)

#include <algorithm>
#include <iostream>
#include <math.h>
#include <stdio.h>
#include <string>
#include <stack>
#include <sstream>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <cmath>
#define rep(i, n) for(int i = 0; i < (int)(n); i++)

using namespace std;
typedef unsigned long long int ll;


struct edge{
	int to,cost;
};

typedef vector<vector<edge>> adjList;
typedef pair<int,int> P;
const int INF = 1e9;
vector<int> dist;
adjList graph;

void dijkstra(int n,int s){
	dist = vector<int>(n,INF);
	dist[s] = 0;
	priority_queue<P,vector<P>,greater<P>> que;
	que.push(make_pair(0,s));
	while( ! que.empty()){
		P p = que.top();
		que.pop();
		int v = p.second;
		if(dist[v] < p.first){
			continue;
		}
		for(int i = 0; i < graph[v].size(); i++){
			edge e = graph[v][i];
			if( dist[e.to] > dist[v] + e.cost){
				dist[e.to] = dist[v] + e.cost;
				que.push(make_pair(dist[e.to],e.to));
			}
		}
	}
}


int main()
{
	int n,k;
	cin>>n>>k;
	ll ans = 0;
	ll a;
	if( k % 2 == 0){
		int half = k / 2;
		if( (n % k ) >= half){
			a = (n/k) + 1;
		}else{
			a = n/k;
		}
		ans += a*a*a;
	}
	ll b = n / k;
	ans += b*b*b;
	cout<<ans<<endl;

	return 0;
}