(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)
#-swank (disable-debugger) ; for CS Academy

;; BEGIN_INSERTED_CONTENTS
(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))))))))

;;;
;;; Some operations on symmetric group
;;;

;; NOTE: Here the underlying set is 0-based: {0, 1, 2, ..., N-1}

(declaim (inline decompose-to-cycles))
(defun decompose-to-cycles (permutation)
  "Returns the list of all the cyclic permutations in PERMUTATION and returns
the parity of it as the second value. (Actually the second value is the distance
to the identity permutation, (0, 1, ..., N-1), w.r.t. swapping.)"
  (declare (vector permutation))
  (let* ((n (length permutation))
         result
         (visited (make-array n :element-type 'bit :initial-element 0))
         (sign 0))
    (declare ((integer 0 #.most-positive-fixnum) sign))
    (dotimes (init n)
      (when (zerop (sbit visited init))
        (push (loop for x = init then (aref permutation x)
                    until (= (sbit visited x) 1)
                    collect x
                    do (setf (sbit visited x) 1)
                       (incf sign))
              result)
        (decf sign)))
    (values result sign)))

(declaim (inline perm*))
(defun perm* (perm1 perm2)
  "Composes two permutations."
  (let* ((n (length perm1))
         (result (make-array n :element-type 'fixnum)))
    (dotimes (i n)
      (setf (aref result i) (aref perm2 (aref perm1 i))))
    result))

(declaim (inline perm-inverse))
(defun perm-inverse (perm)
  (let* ((n (length perm))
         (result (make-array n :element-type 'fixnum)))
    (dotimes (i n)
      (setf (aref result (aref perm i)) i))
    result))

;;;
;;; Calculate a^n on any monoids in O(log(n)) time
;;;

(declaim (inline power))
(defun power (base exponent op identity)
  "OP := binary operation (comprising a monoid)
IDENTITY := identity element w.r.t. OP"
  (declare ((integer 0) exponent))
  (labels ((recur (x p)
             (declare ((integer 0 #.most-positive-fixnum) p))
             (cond ((zerop p) identity)
                   ((evenp p) (recur (funcall op x x) (ash p -1)))
                   (t (nth-value 0 (funcall op x (recur x (- p 1)))))))
           (recur-big (x p)
             (declare ((integer 0) p))
             (cond ((zerop p) identity)
                   ((evenp p) (recur-big (funcall op x x) (ash p -1)))
                   (t (nth-value 0 (funcall op x (recur-big x (- p 1))))))))
    (typecase exponent
      (fixnum (recur base exponent))
      (otherwise (recur-big base exponent)))))

(in-package :cl-user)

(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 main ()
  (let* ((n (read))
         (k (read))
         (as (make-array n :element-type 'uint31 :initial-element 0))
         (iden (make-array n :element-type 'uint31 :initial-element 0)))
    (dotimes (i n)
      (setf (aref as i) (- (read-fixnum) 1)
            (aref iden i) i))
    #>as
    (let ((res (power as k #'perm* iden)))
      #>res
      (println (+ 1 (aref res 0))))))

#-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 5
3 2 4 1
"
    "4
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "6 727202214173249351
6 5 2 5 3 2
"
    "2
")))


Measured memory_bytes: 119100