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 Ruby (2.7.1) (judge verdict: Accepted)

a = gets.split(" ")

N = a[0].to_i
K = a[1].to_i

num_div = []
for i in 1..K do
  num_div[i-1] = 0
end
for i in 1..N do
  j = i % K
  num_div[j] += 1
end

ans = 0
for i in 0..K-1 do
  res = (K - i) % K
  if (res * 2) % K == 0 then
    ans += num_div[i] * (num_div[res] ** 2)
  end
end
puts ans