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)

# 1~9, 19, 199, 1999, 19999,...
k = gets.chomp.to_i
if k<18
  puts k
elsif k<198
  puts k+1
elsif k<1998
  puts k+1+1
elsif k<19998
  puts k+1+1+1
elsif k<199998
  puts k+1+1+1
elsif k<1999998
  puts k+1+1+1+1
elsif k<19999998
  puts k+1+1+1+1+1
elsif k<199999998
  puts k+1+1+1+1+1+1
elsif k<1999999998
  puts k+1+1+1+1+1+1+1
elsif k<19999999998
  puts k+1+1+1+1+1+1+1+1
elsif k<199999999998
  puts k+1+1+1+1+1+1+1+1+1
elsif k<1999999999998
  puts k+1+1+1+1+1+1+1+1+1+1
elsif k<19999999999998
  puts k+1+1+1+1+1+1+1+1+1+1+1
elsif k<199999999999998
  puts k+1+1+1+1+1+1+1+1+1+1+1+1
end