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)

# 合同式の変形を行うと a ≡ b ≡ c (mod k) ということに注目

# key: kで割ったあまり, value: 個数
hash = {}
(1..n).each do |i|
  r = i % k
  # 2倍してkの倍数にならないものは除外
  next if (r * 2) % k != 0
  hash[r] ||= 0
  hash[r] += 1
end

result = 0
hash.each do |k, v|
  # a, b, cが取りうる組み合わせ
  result += v ** 3
end

puts result