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: Accepted)

;; -*- coding: utf-8 -*-
(eval-when (:compile-toplevel :load-toplevel :execute)
  (sb-int:defconstant-eqx OPT
    #+swank '(optimize (speed 3) (safety 2))
    #-swank '(optimize (speed 3) (safety 0) (debug 0))
    #'equal)
  #+swank (ql:quickload '(:cl-debug-print :fiveam) :silent t)
  #-swank (set-dispatch-macro-character
           ;; enclose the form with VALUES to avoid being captured by LOOP macro
           #\# #\> (lambda (s c p) (declare (ignore c p)) `(values ,(read s nil nil t)))))
#+swank (cl-syntax:use-syntax cl-debug-print:debug-print-syntax)
#-swank (disable-debugger) ; for CS Academy

;; BEGIN_INSERTED_CONTENTS
(declaim (inline integer-length*))
(defun integer-length* (x &optional (radix 10))
  "Returns the length of the integer X when displayed in RADIX. (Returns 0 when
X = 0. Ignores the negative sign.)"
  (declare (integer x)
           ((integer 2 #.most-positive-fixnum) radix))
  (loop for length of-type (integer 0 #.most-positive-fixnum) from 0
        for y = (abs x) then (floor y radix)
        until (zerop y)
        finally (return length)))

(declaim (inline digit-sum))
(defun digit-sum (x &optional (radix 10))
  "Returns the sum of the each digit of X w.r.t. RADIX. (Returns 0 when X =
0. Ignores the negative sign.)"
  (declare (integer x)
           ((integer 2 #.most-positive-fixnum) radix))
  (let ((sum 0)
        (x (abs x)))
    (declare (unsigned-byte x)
             ((integer 0 #.most-positive-fixnum) sum))
    (loop
      (when (zerop x)
        (return sum))
      (multiple-value-bind (quot rem) (floor x radix)
        (incf sum rem)
        (setq x quot)))))

(defmacro dbg (&rest forms)
  #+swank
  (if (= (length forms) 1)
      `(format *error-output* "~A => ~A~%" ',(car forms) ,(car forms))
      `(format *error-output* "~A => ~A~%" ',forms `(,,@forms)))
  #-swank (declare (ignore forms)))

(defmacro define-int-types (&rest bits)
  `(progn
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "UINT~A" b)) () '(unsigned-byte ,b))) bits)
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "INT~A" b)) () '(signed-byte ,b))) bits)))
(define-int-types 2 4 7 8 15 16 31 32 62 63 64)

(declaim (inline println))
(defun println (obj &optional (stream *standard-output*))
  (let ((*read-default-float-format* 'double-float))
    (prog1 (princ obj stream) (terpri stream))))

(defconstant +mod+ 1000000007)

;;;
;;; Body
;;;

(declaim (inline frob))
(defun frob (function x mask-width)
  (declare (uint62 x)
           (uint8 mask-width)
           (function function))
  (let* ((tens (expt 10 mask-width))
         (nines (- tens 1))
         (upper-base (floor x tens))
         (upper-limit (* 20 (ceiling (+ 1 upper-base) 20))))
    (declare (uint62 tens nines upper-base upper-limit))
    (loop for upper from upper-base below upper-limit
          do (funcall function (+ (* upper tens) nines)))))

(defun calc-next-snuke (n)
  (declare #.OPT
           (uint62 n))
  (let ((width (integer-length* n))
        (min-val most-positive-fixnum)
        (res 0))
    (declare (rational min-val)
             (uint62 res))
    (loop for mask-width from 0 below width
          do (frob (lambda (x)
                     (declare (uint62 x))
                     (let ((val (/ x (digit-sum x))))
                       ;; (dbg x val)
                       (when (or (< val min-val)
                                 (and (= val min-val)
                                      (< x res)))
                         (setq res x
                               min-val val))))
                   n
                   mask-width))
    (assert (not (zerop res)))
    res))

(defun main ()
  (let* ((k (read))
         (val 1))
    (dotimes (_ k)
      (println val)
      (setq val (calc-next-snuke (+ val 1))))))

#-swank (main)

;;;
;;; Test and benchmark
;;;

#+swank
(defun io-equal (in-string out-string &key (function #'main) (test #'equal))
  "Passes IN-STRING to *STANDARD-INPUT*, executes FUNCTION, and returns true if
the string output to *STANDARD-OUTPUT* is equal to OUT-STRING."
  (labels ((ensure-last-lf (s)
             (if (eql (uiop:last-char s) #\Linefeed)
                 s
                 (uiop:strcat s uiop:+lf+))))
    (funcall test
             (ensure-last-lf out-string)
             (with-output-to-string (out)
               (let ((*standard-output* out))
                 (with-input-from-string (*standard-input* (ensure-last-lf in-string))
                   (funcall function)))))))

#+swank
(defun get-clipbrd ()
  (with-output-to-string (out)
    (run-program "C:/msys64/usr/bin/cat.exe" '("/dev/clipboard") :output out)))

#+swank (defparameter *this-pathname* (uiop:current-lisp-file-pathname))
#+swank (defparameter *dat-pathname* (uiop:merge-pathnames* "test.dat" *this-pathname*))

#+swank
(defun run (&optional thing (out *standard-output*))
  "THING := null | string | symbol | pathname

null: run #'MAIN using the text on clipboard as input.
string: run #'MAIN using the string as input.
symbol: alias of FIVEAM:RUN!.
pathname: run #'MAIN using the text file as input."
  (let ((*standard-output* out))
    (etypecase thing
      (null
       (with-input-from-string (*standard-input* (delete #\Return (get-clipbrd)))
         (main)))
      (string
       (with-input-from-string (*standard-input* (delete #\Return thing))
         (main)))
      (symbol (5am:run! thing))
      (pathname
       (with-open-file (*standard-input* thing)
         (main))))))

#+swank
(defun gen-dat ()
  (uiop:with-output-file (out *dat-pathname* :if-exists :supersede)
    (format out "")))

#+swank
(defun bench (&optional (out (make-broadcast-stream)))
  (time (run *dat-pathname* out)))

;; To run: (5am:run! :sample)
#+swank
(it.bese.fiveam:test :sample
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "10
"
    "1
2
3
4
5
6
7
8
9
19
")))