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<string>
#include<map>
#include<iomanip>
#include<vector>
#define rep(i,a,b) for(int i=a;i<b;i++)
using namespace std;
using ll = long long;
const int M = 100010;

ll c(ll z){
	return z*(z-1)*(z-2);
}
ll d(ll z){
	return z*(z-1)*3;
}

ll box(ll y){
	if(y==1)return 1;
	else if(y==2)return 8;
	else return y+d(y)+c(y);
}


int main(void){
	ll x[2*M]={},ans=0;
	ll n,k;

	cin>>n>>k;
	rep(i,1,n+1)x[i%k]++;
	if(k%2)cout<<box(x[0])<<endl;
	else cout<<box(x[k/2])+box(x[0])<<endl;

}