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)

K = gets.to_i

N = 10_000_000_000_000_000_000

def calc(i)
  j = i
  tot = 0
  while j > 0
    tot += j % 10
    j /= 10
  end
  i.to_f / tot
end

ans = []
n = N
while n > 1
  x = n / 10000
  x = 1 if x < 1
  localmin = calc(n - 1)
  (n - 1).step(n / 10, -x) do |i|
    tmp = calc(i)
    if tmp <= localmin 
      ans << i   
      localmin = tmp 
    end 
  end 
  n /= 10
end

puts ans.sort.take(K)