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 Common Lisp (SBCL 1.1.14) (judge verdict: Wrong Answer)

(defun int-to-digit (n &key (base 10)) ;; (int-to-digit 123) => (1 2 3)
  (if (zerop n)
      `(0)
      (labels ((rec (n list)
                 (if (= n 0)
                     list
                     (rec (floor n base) (cons (rem n base) list)))))
        (rec n nil))))

(defun solver ()
  (let ((k (read)) (count 0) current  (temp 1))
    (loop for i fixnum from 2 do
          (when (= count k) (return))
          (setf current (/ i (apply #'+ (int-to-digit i))))
          (when (<= temp current)
            (format t "~a~%" (1- i)) (incf count))
          (setf temp current))))

(solver)