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)

n, k = gets.chomp.split.map(&:to_i)
cnt = Array.new(k, 0)
res = Array.new(k, 0)

k.times do |i|
  cnt[i] = (n + i) / k
end

k.times do |i|
  j = (- i) % k
  if i == j
    res[i] = cnt[i] ** 3
  elsif (2 * i) % k == 0
    res[i] = ((cnt[i] + 1) * cnt[i] / 2) * cnt[j]
  else
    res[i] = 0
  end
end
puts res.inject(:+)