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)

#p [n,k].inspect

alter_k = k%2==1 ? k : k/2

candidates = (1..n).to_a.keep_if {|e| e%alter_k==0 }

if k%2==1
  p candidates.size ** 3 and exit
end

results = []
candidates.each do |a|
  candidates.each do |b|
    candidates.each do |c|
#      results.push([a,b,c]) if (a+b)%k==0 && (b+c)%k==0 && (a+c)%k==0
      results.push([a,b,c]) if a%k == b%k && a%k==c%k
    end
  end
end

p results.size