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)

# frozen_string_literal: true

def read
  gets.to_i
end

def solve(n)
  Enumerator.new { |y|
    cands = candidates(10**15)
    n = 0
    loop do
      n = cands.select { |i| i > n }.min_by { |i| n_s(i) }
      y << n
    end
  }.take(n)
end

def candidates(n)
  digits = n.succ.to_s.chars.map(&:to_i).reverse
  digits.zip(0..Float::INFINITY).flat_map do |d, p|
    (d...10).map { |c| (c + 1) * 10**p - 1 }
  end
end

def n_s(n)
  Rational(n, n.to_s.chars.map(&:to_i).reduce(:+))
end

puts solve(read)