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: Accepted)

K = gets.to_i

def get_snuke_num(digit)
  res = []
  base = 10 ** (digit - 2)
  geta = ('9' * (digit - 2)).to_i

  min_s = Float::INFINITY

  999.downto(10) do |i|
    s = i * base + geta
    v = s / s.to_s.chars.map(&:to_i).inject(:+).to_f
    next if min_s < v
    min_s = v

    res << s
  end

  res.reverse
end

snuke_nums = [*1..9]

keta = 2
while snuke_nums.size <= K
  snuke_nums += get_snuke_num(keta)
  snuke_nums.uniq!
  keta += 1
end

puts snuke_nums.take(K)