(in-package :cl-user)
(eval-when (:compile-toplevel :load-toplevel :execute)
  (defparameter *opt*
    #+swank '(optimize (speed 3) (safety 2))
    #-swank '(optimize (speed 3) (safety 0) (debug 0)))
  #+swank (ql:quickload '(:cl-debug-print :fiveam :cp/util) :silent t)
  #+swank (use-package :cp/util :cl-user)
  #-swank (set-dispatch-macro-character
           #\# #\> (lambda (s c p) (declare (ignore c p)) `(values ,(read s nil nil t))))
  #+sbcl (dolist (f '(:popcnt :sse4)) (pushnew f sb-c:*backend-subfeatures*))
  (setq *random-state* (make-random-state t)))
#-swank (eval-when (:compile-toplevel)
          (setq *break-on-signals* '(and warning (not style-warning))))
#+swank (set-dispatch-macro-character #\# #\> #'cl-debug-print:debug-print-reader)

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

(defconstant +mod+ 1000000007)

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

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

;; BEGIN_INSERTED_CONTENTS
(defpackage :cp/mod-operations
  (:use :cl)
  (:export #:define-mod-operations #:*modulus*)
  (:documentation "Provides modular arithmetic."))
(in-package :cp/mod-operations)

(eval-when (:compile-toplevel :load-toplevel :execute)
  (defvar *modulus* 0))
(declaim ((unsigned-byte 31) *modulus*)
         #+sbcl (sb-ext:always-bound *modulus*))

(defmacro define-mod-operations
    (divisor &optional (package #+sbcl (sb-int:sane-package) #-sbcl *package*))
  (let ((mod* (intern "MOD*" package))
        (mod+ (intern "MOD+" package))
        (mod- (intern "MOD-" package))
        (incfmod (intern "INCFMOD" package))
        (decfmod (intern "DECFMOD" package))
        (mulfmod (intern "MULFMOD" package)))
    `(progn
       (defun ,mod* (&rest args)
         (cond ((cdr args) (reduce (lambda (x y) (mod (* x y) ,divisor)) args))
               (args (mod (car args) ,divisor))
               (t (mod 1 ,divisor))))
       (defun ,mod+ (&rest args)
         (cond ((cdr args) (reduce (lambda (x y) (mod (+ x y) ,divisor)) args))
               (args (mod (car args) ,divisor))
               (t 0)))
       (defun ,mod- (&rest args)
         (if (cdr args)
             (reduce (lambda (x y) (mod (- x y) ,divisor)) args)
             (mod (- (car args)) ,divisor)))

       #+sbcl
       (eval-when (:compile-toplevel :load-toplevel :execute)
         (locally (declare (sb-ext:muffle-conditions warning))
           (sb-c:define-source-transform ,mod* (&rest args)
             (case (length args)
               (0 `(mod 1 ,',divisor))
               (1 `(mod ,(car args) ,',divisor))
               (otherwise (reduce (lambda (x y) `(mod (* ,x ,y) ,',divisor)) args))))
           (sb-c:define-source-transform ,mod+ (&rest args)
             (case (length args)
               (0 0)
               (1 `(mod ,(car args) ,',divisor))
               (otherwise (reduce (lambda (x y) `(mod (+ ,x ,y) ,',divisor)) args))))
           (sb-c:define-source-transform ,mod- (&rest args)
             (case (length args)
               (0 (values nil t))
               (1 `(mod (- ,(car args)) ,',divisor))
               (otherwise (reduce (lambda (x y) `(mod (- ,x ,y) ,',divisor)) args))))))

       (define-modify-macro ,incfmod (delta)
         (lambda (x y) (mod (+ x y) ,divisor)))
       (define-modify-macro ,decfmod (delta)
         (lambda (x y) (mod (- x y) ,divisor)))
       (define-modify-macro ,mulfmod (multiplier)
         (lambda (x y) (mod (* x y) ,divisor))))))

(define-mod-operations cl-user::+mod+ :cl-user)

(defpackage :cp/divisor-table
  (:use :cl)
  (:export #:make-divisors-table))
(in-package :cp/divisor-table)

(deftype uint () '(integer 0 #.most-positive-fixnum))

(declaim (ftype (function * (values (simple-array t (*)) &optional))
                %make-divisors-table))
(defun %make-divisors-list-table (max)
  "Returns a vector of length MAX+1 whose each cell, vector[X], is a list
containing all the divisors of X in ascending order. Time and space complexity
is O(Nlog(N)). Note that vector[0] = NIL."
  (declare (optimize (speed 3))
           (uint max)
           #+sbcl (sb-ext:muffle-conditions style-warning))
  (let ((result (make-array (+ 1 max) :element-type 'list))
        (tails (make-array (+ 1 max) :element-type 'list))) ; stores the last cons cell
    (declare (optimize (speed 3) (safety 0)))
    (loop for i from 1 to max
          for cell = (list 1)
          do (setf (aref result i) cell
                   (aref tails i) cell))
    (setf (aref result 0) nil)
    (loop for divisor from 2 to max
          do (loop for number from divisor to max by divisor
                   do (setf (cdr (aref tails number)) (list divisor)
                            (aref tails number) (cdr (aref tails number)))))
    result))

(declaim (ftype (function * (values (simple-array t (*)) &optional))
                %make-divisors-vector-table))
(defun %make-divisors-vector-table (max)
  "Returns a vector of length MAX+1 whose each cell, vector[X], is a vector
containing all the divisors of X in ascending order. Time and space complexity
is O(Nlog(N)). Note that vector[0] = #()."
  (declare (optimize (speed 3))
           (uint max))
  (let ((counter (make-array (+ max 1) :element-type 'uint :initial-element 1))
        (res (make-array (+ max 1) :element-type t)))
    (loop for d from 2 to max
          do (loop for x from d to max by d
                   do (incf (aref counter x))))
    (setf (aref res 0) (make-array 0 :element-type 'uint))
    (loop for i from 1 to max
          for vector = (make-array (aref counter i) :element-type 'uint)
          do (setf (aref vector 0) 1
                   (aref res i) vector
                   (aref counter i) 1))
    (loop for d from 2 to max
          do (loop for x from d to max by d
                   for end = (aref counter x)
                   for vector of-type (simple-array uint (*)) = (aref res x)
                   do (setf (aref counter x) (+ end 1)
                            (aref vector end) d)))
    res))

(declaim (ftype (function * (values (simple-array t (*)) &optional))
                make-divisors-table))
(defun make-divisors-table (max sequence-type)
  "Returns a vector of length MAX+1 whose each cell, vector[X], is a vector or
list containing all the divisors of X in ascending order. Time complexity is
O(Nlog(N)). Note that vector[0] is an empty sequence."
  (declare ((member list vector) sequence-type))
  (ecase sequence-type
    (list (%make-divisors-list-table max))
    (vector (%make-divisors-vector-table max))))

;; BEGIN_USE_PACKAGE
(eval-when (:compile-toplevel :load-toplevel :execute)
  (use-package :cp/divisor-table :cl-user))
(eval-when (:compile-toplevel :load-toplevel :execute)
  (use-package :cp/mod-operations :cl-user))
(in-package :cl-user)

;;;
;;; Body
;;;

(defun main ()
  (declare (optimize (speed 3)))
  (let* ((m (read))
         (dp (make-array (+ m 1) :element-type 'uint31 :initial-element 0))
         (divs (make-divisors-table m 'list)))
    (declare (uint31 m))
    (setf (aref dp m) 1)
    (loop for x from m downto 1
          for val = (aref dp x)
          do (dolist (div (aref divs x))
               (declare (uint31 div))
               (incfmod (aref dp (- div 1)) val)))
    (println (aref dp 0))))

#-swank (main)

;;;
;;; Test
;;;

#+swank
(progn
  (defparameter *lisp-file-pathname* (uiop:current-lisp-file-pathname))
  (setq *default-pathname-defaults* (uiop:pathname-directory-pathname *lisp-file-pathname*))
  (uiop:chdir *default-pathname-defaults*)
  (defparameter *dat-pathname* (uiop:merge-pathnames* "test.dat" *lisp-file-pathname*))
  (defparameter *problem-url* "https://yukicoder.me/problems/no/1581"))

#+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)))

#+(and sbcl (not swank))
(eval-when (:compile-toplevel)
  (when sb-c::*undefined-warnings*
    (error "undefined warnings: ~{~A~^ ~}" sb-c::*undefined-warnings*)))

;; To run: (5am:run! :sample)
#+swank
(5am:test :sample
  (5am:is
   (equal "10
"
          (run "6
" nil)))
  (5am:is
   (equal "1
"
          (run "1
" nil)))
  (5am:is
   (equal "917384154
"
          (run "82931
" nil))))