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: Accepted)

N,K = gets.chomp.split(" ").map(&:to_i)

combis = (1..N).to_a.map{|num| num%K}
count = 0

count = Hash.new(0)
combis.each do |elem|
  count[elem] += 1
end
ans = {}
count.each{|key, value|
  if (key+key)%K == 0
    ans[key] = value
  end
}
ans_count = 0
ans.each{|key, value|
  ans_count += value**3
}

p ans_count