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)

ret = []
i = "1"

while (i.length <= 16)
  ret << i
  if (i[0] == "9")
    i = "1" + i
  else
    i = (i[0].to_i + 1).to_s + i[1..-1]
  end
end

puts ret[0...gets.chomp.to_i]