(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
(macrolet ((def (name fname)
             `(define-modify-macro ,name (new-value) ,fname)))
  (def minf min)
  (def maxf max)
  (def mulf *)
  (def divf /)
  (def iorf logior)
  (def xorf logxor)
  (def andf logand))

(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))))))))

(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
;;;

(defun %sort (list)
  (declare (list list)
           (inline sort sb-impl::stable-sort-list))
  (sort list #'< :key (lambda (x) (the fixnum (car x)))))

(defun main ()
  (let* ((n (read))
         (m (read))
         (as (make-array n :element-type 'uint31))
         (a-deltas (make-array (- n 1) :element-type 'uint31))
         ;; time . index
         add-queries
         del-queries)
    (dotimes (i n)
      (setf (aref as i) (- (read-fixnum) 1)))
    (dotimes (i (- n 1))
      (let ((a1 (aref as i))
            (a2 (aref as (+ i 1))))
        (when (> a1 a2)
          (incf a2 m))
        (setf (aref a-deltas i) (- a2 a1))
        (let ((a1+1 (mod (+ a1 1) m))
              (a2+1 (mod (+ a2 1) m)))
          (assert (/= a1+1 a2+1))
          (when (> a1+1 a2+1)
            (incf a2+1 m))
          (push (cons a1+1 i) add-queries)
          (push (cons a2+1 i) del-queries)
          (push (cons (+ m a1+1) i) add-queries)
          (push (cons (+ m a2+1) i) del-queries))))
    #>a-deltas
    (setq add-queries (%sort add-queries))
    (setq del-queries (%sort del-queries))
    #>add-queries
    #>del-queries
    (let* ((base (reduce #'+ a-deltas))
           (res base)
           (shortcut-size 0)
           (shortcut-sum 0))
      (dotimes (x (* 2 m))
        (dbg x base res shortcut-size shortcut-sum)
        ;; process del-queries
        (loop (unless del-queries (return))
              (destructuring-bind (time . idx) (car del-queries)
                (assert (>= time x))
                (unless (= time x) (return))
                (decf shortcut-size)
                (decf shortcut-sum)
                (incf base (aref a-deltas idx)))
              (pop del-queries))
        ;; process remaining nodes
        (decf shortcut-sum shortcut-size)
        ;; process add-queries
        (loop (unless add-queries (return))
              (destructuring-bind (time . idx) (car add-queries)
                (assert (>= time x))
                (unless (= time x) (return))
                (incf shortcut-size)
                (incf shortcut-sum (aref a-deltas idx))
                (decf base (aref a-deltas idx)))
              (pop add-queries))
        (minf res (+ base shortcut-sum)))
      (println res))))

#-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 "powershell.exe" '("-Command" "Get-Clipboard") :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* 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 "4 6
1 5 1 4
"
    "5
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "10 10
10 9 8 7 6 5 4 3 2 1
"
    "45
")))


Measured memory_bytes: 53600