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 (2.3.3) (judge verdict: Time Limit Exceeded)

n, k = gets.split.map(&:to_i)
count = 0
(k..2*n).step(k).each do |ab|
  next if ab % k != 0
  (k..2*n).step(k).each do |bc|
    next if bc % k != 0
    (k..2*n).step(k).each do |ca|
      next if ca % k != 0
      c = (ab - bc - ca)
      a = (bc - ca - ab)
      b = (ca - ab - bc)
      next if c.odd? || a.odd? || b.odd?
      c /= (-2)
      a /= (-2)
      b /= (-2)
      count += 1 if [a, b, c].all? { |e| e > 0 && e <= n }
    end
  end
end
puts count