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: Wrong Answer)

n, k = gets.split.map(&:to_i)
trios = []

# a % k == x である場合、 b % k == c % k == (k - x)、
# なぜなら (a+b)%k == (a+c)%k == 0だから。
# あれ、でも (b+c)%k == 0でもあるんだから、
# x == 0 か、あるいは x == k/2じゃないとダメじゃね？
# しかも k/2ってことは、これはkが偶数のときのみ有効ってことか。
# kが奇数ならx==0の場合のみ、
# kが偶数ならx==0の場合とx==k/2の場合の2種類。
# これらを考えればいいってことか。

s = 1
while s*k <= n
  a = s*k
  t = 1
  while t*k <= n
    b = t*k
    u = 1
    while u*k <= n
      c = u*k
      trios << [a, b, c]
      u += 1
    end
    t += 1
  end
  s += 1
end
p trios.size

if k.even?
  s = 0
  while s*k <= n
    a = s*k + k/2
    t = 0
    while t*k <= n
      b = t*k + k/2
      u = 0
      while u*k <= n
        c = u*k + k/2
        trios << [a, b, c]
        u += 1
      end
      t += 1
    end
    s += 1
  end
end
p trios.size