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 3.8.0) (judge verdict: Accepted)

#include <stdio.h>

typedef long long ll;

int main()
{
    ll n, k;

    ll a, b, c;
    ll ans = 0;

    scanf("%lld %lld", &n, &k);

    for (a = 1; a <= n; a++) {
        ll mod_k = a % k;

        b = k - mod_k;
        c = k - b;

        if ((a + b) % k == 0 && (b + c) % k == 0 && (a + c) % k == 0 &&
            a <= n && b <= n && c <= n) {

            ans += ((n - b) / k + 1) * ((n - c) / k + 1);

            if (b == 0) ans -= (n - c) / k + 1;
            if (c == 0) ans -= (n - b) / k + 1;
            //ans++;
        }
    }

    printf("%lld\n", ans);

    return 0;
}