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)

n=gets.to_i
c=0
n.times{|i|
  if c<9 then c+=1
  elsif c<99 then c+=10
  elsif c<999 then c+=100
  elsif c<9999 then c+=1000
  elsif c<99999 then c+=10000
  elsif c<999999 then c+=100000
  elsif c<9999999 then c+=1000000
  elsif c<99999999 then c+=10000000
  elsif c<999999999 then c+=100000000
  elsif c<9999999999 then c+=1000000000
  elsif c<99999999999 then c+=10000000000
  elsif c<999999999999 then c+=100000000000
  elsif c<9999999999999 then c+=1000000000000
  elsif c<99999999999999 then c+=10000000000000
  elsif c<999999999999999 then c+=100000000000000
  elsif c<9999999999999999 then c+=1000000000000000
  end
  p c
}