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 main
  knum = ARGF.gets.chomp.to_i

  1.upto(knum) do |k|
    # 累乗数 0, 1, 2, ...
    n = (k-1) / 9

    # ベース数 1, 10, 100, ...
    b = 10**n

    # 剰余数 1, 2, ..., 9, 1, 2, 3, ...
    r = (k-1) % 9 + 1

    # すぬけ数
    s = b * (r + 1) - 1

    puts s
  end
end

if __FILE__ == $0
  main
end