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)

n = gets.chomp.to_i
count = 0
num = 1
digit = 0
while count < n do
  nums = num.to_s.split('')
  digit_num = nums.reverse[digit].to_i
  unless digit_num == 0
    puts num
    num += 10 ** digit
    count += 1
    next
  end
  sum = nums.map(&:to_i).inject(:+)
  if (sum * (10 ** digit) - num < 0)
    num += 9 * (10 ** digit)
    digit += 1
    next
  end
  puts num
  num += 10 ** digit
  count += 1
  next
end