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

def sunuke(num)
  num.to_f/num.to_s.chars.map(&:to_i).inject(:+)
end

list = []
pos = 0
counter = 1
res = loop.lazy.flat_map do
  num = (list.last||0) + counter * 10**pos
  if sunuke(num) <= sunuke(num + (counter * 10**pos))
    counter += 1
    range = num.to_s.size >= pos ? (0..8) : (0..9)
    list = range.map { |i| num + i * 10**pos}
  else
    pos += 1
    counter = 1
    []
  end
end

puts res.first(k+1)