Problem:
Score : 500 points

Problem Statement

Let S(n) denote the sum of the digits in the decimal notation of n.
For example, S(123) = 1 + 2 + 3 = 6.

We will call an integer n a Snuke number when, for all positive integers m such that m > n, \frac{n}{S(n)} \leq \frac{m}{S(m)} holds.

Given an integer K, list the K smallest Snuke numbers.

Constraints

1 \leq K

The K-th smallest Snuke number is not greater than 10^{15}.

Input

Input is given from Standard Input in the following format:

K

Output

Print K lines. The i-th line should contain the i-th smallest Snuke number.

Sample Input 1

10

Sample Output 1

1
2
3
4
5
6
7
8
9
19

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

K = gets.to_i
cnt = 0
v = 0

0.upto(100) do |cnt9|
  STDERR.puts "cnt9=#{cnt9}"
  # if cnt9 == 11
  #   STDOUT.flush
  #   raise
  # end

  if cnt9 <= 1
    rng = (1..9)
  else
    b = 1
    e = cnt9 * 10
    rng = (b...e)
  end

  sf = '9' * cnt9
  rng.each do |pr|
    nv = "#{pr}#{sf}".to_i
    if v >= nv
      next
    end
    puts v = nv
    cnt += 1
    if cnt == K
      exit
    end
  end
end