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)

k = gets.chomp.to_i
ary = [1,2,3,4,5,6,7,8,9]
if k <= 9
  k.times do |i|
    puts ary[i]
  end
else
  ary.each do |i|
    puts i
  end
  (k/9-1).times do
    9.times do |i|
      ary[i] = ary[i]*10+9
      puts ary[i]
    end
  end
  (k%9).times do |i|
    ary[i] = ary[i]*10+9
    puts ary[i]
  end
end