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 calc(n)
  n.to_f / n.to_s.split("").map{|m| m.to_i }.inject(:+)
end
n = gets.chomp.to_i
order = cnt = 1
n.times {|m|
  puts cnt
  if calc(cnt + 10 ** (order - 1)) > calc(cnt + 10 ** order)
    order += 1
  end
  cnt += 10 ** (order - 1)
}