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)

def sumDigit(num, sum)
  if num == 0 then return sum end
  d, m = num.divmod(10)
  return sumDigit(d, m + sum)
end

k = gets.to_i

n = 0
while(k > 0)
  temp = Hash.new
  s = n == 0 ? 1 : 100
  (s..999).each{|i|
    j = (i + 1) * (10 ** n) - 1  #ex) 10099....9
    temp[j] = j / sumDigit(i, 9 * n).to_f
  }

  sorted = temp.sort_by {|k, v| [v, k]}
  bef = 0
  sorted.each{|k, v|
    if k - bef > 1 then sorted.reject!{|key, value| bef < key && key < k} end
    bef = k
  }
  sorted.each{|key, value|
    print("#{key}\n")
    k -= 1
    exit if k == 0
  }

  n += 1
end