#-swank
(unless (member :child-sbcl *features*)
  (quit
   :unix-status
   (process-exit-code
    (run-program *runtime-pathname*
                 `("--control-stack-size" "128MB"
                   "--noinform" "--disable-ldb" "--lose-on-corruption" "--end-runtime-options"
                   "--eval" "(push :child-sbcl *features*)"
                   "--script" ,(namestring *load-pathname*))
                 :output t :error t :input t))))
(in-package :cl-user)
(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
           #\# #\> (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)

(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)

(defconstant +mod+ 1000000007)

(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)))

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

;; BEGIN_INSERTED_CONTENTS
(defpackage :cp/println-matrix
  (:use :cl)
  (:export #:println-matrix))
(in-package :cp/println-matrix)

(declaim (inline println-matrix))
(defun println-matrix (array &key (separator #\ ) (key #'identity) (writer #'write) (row-start 0) row-end (col-start 0) col-end)
  "Prints a 2-dimensional array."
  (declare ((array * (* *)) array)
           ((integer 0 #.most-positive-fixnum) row-start col-start))
  (let ((row-end (or row-end (array-dimension array 0)))
        (col-end (or col-end (array-dimension array 1))))
    (declare ((integer 0 #.most-positive-fixnum) row-end col-end))
    (loop for i from row-start below row-end
          do (loop for j from col-start below col-end
                   unless (= j col-start)
                   do (princ separator)
                   do (funcall writer (funcall key (aref array i j))))
             (terpri))))

(defpackage :cp/read-fixnum
  (:use :cl)
  (:export #:read-fixnum))
(in-package :cp/read-fixnum)

(declaim (ftype (function * (values fixnum &optional)) read-fixnum))
(defun read-fixnum (&optional (in *standard-input*))
  "NOTE: cannot read -2^62"
  (macrolet ((%read-byte ()
               `(the (unsigned-byte 8)
                     #+swank (char-code (read-char in nil #\Nul))
                     #-swank (sb-impl::ansi-stream-read-byte in nil #.(char-code #\Nul) nil))))
    (let* ((minus nil)
           (result (loop (let ((byte (%read-byte)))
                           (cond ((<= 48 byte 57)
                                  (return (- byte 48)))
                                 ((zerop byte) ; #\Nul
                                  (error "Read EOF or #\Nul."))
                                 ((= byte #.(char-code #\-))
                                  (setq minus t)))))))
      (declare ((integer 0 #.most-positive-fixnum) result))
      (loop
        (let* ((byte (%read-byte)))
          (if (<= 48 byte 57)
              (setq result (+ (- byte 48)
                              (* 10 (the (integer 0 #.(floor most-positive-fixnum 10))
                                         result))))
              (return (if minus (- result) result))))))))

;; BEGIN_USE_PACKAGE
(eval-when (:compile-toplevel :load-toplevel :execute)
  (use-package :cp/read-fixnum :cl-user))
(eval-when (:compile-toplevel :load-toplevel :execute)
  (use-package :cp/println-matrix :cl-user))
(in-package :cl-user)

;;;
;;; Body
;;;

(defun test (n m &rest as)
  (let ((matrix (make-array (list n 7) :element-type 'base-char :initial-element #\.)))
    (dotimes (i (* n 7))
      (when (member (mod i m) as)
        (setf (row-major-aref matrix i) #\#)))
    (println-matrix matrix :separator "" :writer #'write-char)))

(defun solve (n m as)
  (declare #.cl-user::opt
           ((integer 0 #.(expt 10 12)) n m)
           ((simple-array uint31 (*)) as))
  (let ((plan (make-array (list n 7) :element-type 'bit :initial-element 0))
        (res 0))
    (declare (uint62 res))
    (loop for a across as
          do (loop for i from a below (* n 7) by m
                   do (setf (row-major-aref plan i) 1)))
    (dotimes (i n)
      (dotimes (j 7)
        (when (zerop (aref plan i j))
          (sb-int:named-let dfs ((i i) (j j))
            (labels ((visit (y x)
                       (when (and (<= 0 y (- n 1))
                                  (<= 0 x 6))
                         (dfs y x))))
              (when (zerop (aref plan i j))
                (setf (aref plan i j) 1)
                (visit (- i 1) j)
                (visit (+ i 1) j)
                (visit i (- j 1))
                (visit i (+ j 1)))))
          (incf res))))
    res))

(defun main ()
  (let* ((n (read))
         (m (read))
         (q (read))
         (as (make-array q :element-type 'uint31 :initial-element 0)))
    (dotimes (i q)
      (setf (aref as i) (read-fixnum)))
    (println
     (let* ((period m)
            (term1 (solve period m as))
            (term2 (solve (* 2 period) m as))
            (coef (- term2 term1))
            (intercept (- term1 coef)))
       (multiple-value-bind (quot rem) (floor n period)
         (+ intercept
            (* quot coef)
            (- (solve (+ period rem) m as) term1)))))
    ;; (println
    ;;  (cond
    ;;    ((zerop (mod m 7))
    ;;     (let* ((period (floor m 7))
    ;;            (term1 (solve period m as))
    ;;            (term2 (solve (* 2 period) m as))
    ;;            (coef (- term2 term1))
    ;;            (intercept (- term1 coef)))
    ;;       (multiple-value-bind (quot rem) (floor n period)
    ;;         (+ intercept (* quot coef)
    ;;            (- (solve (+ period rem) m as) term1)))))
    ;;    ((<= n 100000)
    ;;     (solve n m as))
    ;;    (t (let* ((period m)
    ;;              (term1 (solve period m as))
    ;;              (term2 (solve (* 2 period) m as))
    ;;              (coef (- term2 term1))
    ;;              (intercept (- term1 coef)))
    ;;         (multiple-value-bind (quot rem) (floor n period)
    ;;           (+ intercept
    ;;              (* quot coef)
    ;;              (- (solve (+ period rem) m as) term1)))))))
    ))

#-swank (main)

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

#+swank
(defun get-clipbrd ()
  (with-output-to-string (out)
    #+os-windows (run-program "powershell.exe" '("-Command" "Get-Clipboard") :output out :search t)
    #+os-unix (run-program "xsel" '("-b" "-o") :output out :search t)))

#+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* (or out (make-string-output-stream)))
         (res (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))))))
    (if out res (get-output-stream-string *standard-output*))))

#+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
   (equal "4
"
          (run "7 7 3
1 3 5
" nil)))
  (it.bese.fiveam:is
   (equal "10
"
          (run "10 14 8
5 6 7 8 9 10 11 12
" nil))))


Measured memory_bytes: 64384