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.to_i

a = []

(1..9).each{|x| a << x.to_s}
(1..9).each{|x| a << x.to_s + "9"}
(1..9).each{|x| a << x.to_s + "99"}
(2..10).each{|len|
    base = "9" * len
    list = [(1..9).map{|i| i.to_s + "9"} + (10...len*10).map{|x| x.to_s}].flatten.sort.uniq
    list.each{|x| a << x.to_s + base}
}
len = 11
loop {
    break if a.size >= k
    base = "9" * len
    (10..99).each{|x| a << x.to_s + base}
    len += 1
}

puts a[0...k]