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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

import itertools as itr

N, K = tuple(int(i) for i in input().split())

n = int(N/K)
c1 = list(itr.product(range(n), repeat=3))
c1 = len(c1)

k_2 = K/2

if N < k_2:
    print(0)
elif K%2 != 0:
    print(c1)
else:

    if N < n*K + k_2:
        c2 = list(itr.product(range(n), repeat=3))
    else:
        c2 = list(itr.product(range(n+1), repeat=3))

    c2 = len(c2)
    print(c1 + c2)