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)

def f n
  ret = 0
  while n > 0
    ret += n % 10
    n /= 10
  end
  ret
end

def g n
  n.to_f / f(n)
end

K = gets.to_i
ret = []
data = 1
15.times { (2..200).to_a.each {|i| ret.push(data * i - 1)}; data *= 10 }
ret.uniq!
ret.sort!
ans = ret.select.with_index {|num,i| flg = true; ret[i..(i+9)].each {|num2| flg = false if g(num) > g(num2) }; flg }
puts ans[0...K]