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)

#
# File    : D.rb
# Author  : Kazune Takahashi
# Created : 2018-6-23 21:14:41
# Powered by Visual Studio Code
#

k = gets.to_i

a = []

for i in 0...200
  for n in 1...10
    x = n * 10 ** i + 10 ** i - 1
    if x > 0
      a << x
    end
    if a.size == k
      break
    end
  end
end

for i in 0...k
  puts a[i]
end