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: Runtime Error)

#!/usr/bin/env ruby

k = gets.chomp.to_i
sunu = 1
sunus = []
while (sunus.size < k)
  keta = sunu.to_s.split(//).size
  nine = keta - 1
  sunukari =  sunu if sunu.to_s =~ /^.9{#{nine}}$/
  last = sunus[-1]
  sunus << sunu if (last / last.to_s.split(//).map(&:to_i).inject{|sum, n| sum + n}) <= (sunukari / sunukari.to_s.split(//).map(&:to_i).inject{|sum, n| sum + n})
  sunu += 1
end

puts sunus[k - 1]