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: Accepted)

import sys
## io
IS = lambda: sys.stdin.readline().rstrip()
II = lambda: int(IS())
MII = lambda: list(map(int, IS().split()))
MIIZ = lambda: list(map(lambda x: x-1, MII()))
## dp
INIT_VAL = 0
DP2 = lambda d1, d2: [[INIT_VAL]*d2 for _ in range(d1)]
DP3 = lambda d1, d2, d3: [[[INIT_VAL]*d3 for _ in range(d2)] for _ in range(d1)]

def main():
    n, k = MII()
    cnt = (n//k)**3
    if k%2==0:
        cnt += ((n+(k//2))//k)**3
    print(cnt)

if __name__ == '__main__':
    main()