(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/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))
(in-package :cl-user)

;;;
;;; Body
;;;

(defconstant +max-depth+ 17)

(defun feasible-p (n k cumuls threshold)
  (declare #.cl-user::opt
           (uint31 n k)
           ((simple-array uint62 (*)) cumuls)
           (uint62 threshold))
  (let ((dp (make-array (list +max-depth+ n) :element-type 'uint62 :initial-element 0))
        (dest 0))
    (dotimes (src n)
      (loop while (< (- (aref cumuls dest) (aref cumuls src)) threshold)
            do (incf dest))
      (setf (aref dp 0 src) (- dest src)))
    (loop for depth from 1 below +max-depth+
          do (dotimes (i n)
               (let ((prev-delta (aref dp (- depth 1) i)))
                 (setf (aref dp depth i)
                       (+ prev-delta
                          (+ (aref dp (- depth 1) (mod (+ i prev-delta) n))))))))
    (dotimes (init n)
      (let ((count 0)
            (stride 0))
        (declare (uint62 count stride))
        (loop for depth from (- +max-depth+ 1) downto 0
              for delta = (ash 1 depth)
              when (<= (+ count delta) k)
              do (incf stride (aref dp depth (mod (+ init stride) n)))
                 (incf count delta)
              while (<= stride n))
        (when (<= stride n)
          (return-from feasible-p t))))
    nil))

(defun main ()
  (let* ((n (read))
         (k (read))
         (as (make-array n :element-type 'uint31 :initial-element 0))
         (cumuls (make-array (+ 1 (* 2 n)) :element-type 'uint62 :initial-element 0)))
    (dotimes (i n)
      (let ((a (read-fixnum)))
        (setf (aref as i) a
              (aref cumuls (+ i 1)) a
              (aref cumuls (+ i n 1)) a)))
    (dotimes (i (* 2 n))
      (incf (aref cumuls (+ i 1)) (aref cumuls i)))
    (sb-int:named-let bisect ((ok 0) (ng (+ 1 (aref cumuls n))))
      (if (<= (- ng ok) 1)
          (println ok)
          (let ((mid (ash (+ ok ng) -1)))
            #>mid
            (if (feasible-p n k cumuls mid)
                (bisect mid ng)
                (bisect ok mid)))))))

#-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 "6 4
8 6 9 1 2 1
" nil)))
  (it.bese.fiveam:is
   (equal "15
"
          (run "15 7
12 9 11 15 15 11 9 7 2 3 1 14 15 6 11
" nil))))