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: Runtime Error)

#
# File    : C.rb
# Author  : Kazune Takahashi
# Created : 2018-6-23 21:01:02
# Powered by Visual Studio Code
#

n, k = gets.chomp.split(" ").map{|i| i.to_i}
a = gets.chomp.split(" ").map{|i| i.to_i}

ind = 0

for i in 0...a.size
  if (a[i] == 1)
    ind = i
    break
  end
end

if n == k
  puts 1
else
  puts 1 + (n - k + k - 2) / (k - 1)
end