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: Accepted)

def score(n)
  Rational(n, s(n))
end
def s(n)
  n.to_s.chars.map(&:to_i).inject(:+)
end
def f(n)
  r = n+1
  s = score(r)
  15.times.map{|i|10**i}.each do |i|
    m = n+i
    next if s <= score(m)
    s = score(m)
    r = m
  end
  r
end
n=1
gets.to_i.times do
  p n
  n = f(n)
end