;; -*- coding: utf-8 -*-
(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))
  #-swank (set-dispatch-macro-character #\# #\> (lambda (s c p) (declare (ignore c p)) (read s nil (values) t))))
#+swank (cl-syntax:use-syntax cl-debug-print:debug-print-syntax)
#-swank (disable-debugger) ; for CS Academy

;; BEGIN_INSERTED_CONTENTS
;;;
;;; Complement to the bitwise operations in CLHS
;;;

(eval-when (:compile-toplevel :load-toplevel :execute)
  (assert (= sb-vm:n-word-bits 64)))

;; KLUDGE: a variant of DPB that handles a 64-bit word efficiently
(defmacro u64-dpb (new spec int)
  (destructuring-bind (byte s p) spec
    (assert (eql 'byte byte))
    (let ((size (gensym)) (posn (gensym)) (mask (gensym)))
      `(let* ((,size ,s)
              (,posn ,p)
              (,mask (ldb (byte ,size 0) -1)))
         (logior (the (unsigned-byte 64) (ash (logand ,new ,mask) ,posn))
                 (the (unsigned-byte 64) (logand ,int (lognot (ash ,mask ,posn)))))))))

(defconstant +most-positive-word+ #.(- (ash 1 64) 1))

(defun bit-lshift (bit-vector delta &optional result-vector end)
  "Left-shifts BIT-VECTOR by DELTA bits and fills the new bits with zero.
The behaviour is the same as the bit-wise operations in CLHS: The result is
copied to RESULT-VECTOR; if it is T, BIT-VECTOR is destructively modified; if it
is NIL, a new bit-vector of the same length is created. If END is specified,
this function shifts only the range [0, END) of BIT-VECTOR and copies it to the
range [0, END+DELTA) of RESULT-VECTOR."
  (declare (optimize (speed 3))
           (simple-bit-vector bit-vector)
           ((or null (eql t) simple-bit-vector) result-vector)
           ((integer 0 #.most-positive-fixnum) delta)
           ((or null (integer 0 #.most-positive-fixnum)) end))
  (setq result-vector
        (etypecase result-vector
          (null (make-array (length bit-vector) :element-type 'bit :initial-element 0))
          ((eql t) bit-vector)
          (simple-bit-vector result-vector)))
  (setq end (or end (length bit-vector)))
  (assert (<= end (length bit-vector)))
  (setq end (min end (max 0 (- (length result-vector) delta))))
  (multiple-value-bind (d/64 d%64) (floor delta 64)
    (declare (optimize (safety 0))
             (simple-bit-vector result-vector))
    (multiple-value-bind (end/64 end%64) (floor end 64)
      ;; process the last word separately
      (unless (zerop end%64)
        (let ((word (sb-kernel:%vector-raw-bits bit-vector end/64)))
          (setf (sb-kernel:%vector-raw-bits result-vector (+ end/64 d/64))
                (u64-dpb (ldb (byte (min end%64 (- 64 d%64)) 0) word)
                         (byte (min end%64 (- 64 d%64)) d%64)
                         (sb-kernel:%vector-raw-bits result-vector (+ end/64 d/64))))
          (when (> end%64 (- 64 d%64))
            (setf (ldb (byte (- end%64 (- 64 d%64)) 0)
                       (sb-kernel:%vector-raw-bits result-vector (+ 1 end/64 d/64)))
                  (ldb (byte (- end%64 (- 64 d%64)) (- 64 d%64)) word)))))
      (let* ((mask0 (ldb (byte 64 0) (lognot (ldb (byte d%64 0) -1))))
             (mask1-lo (ldb (byte (- 64 d%64) 0) -1))
             (mask1-hi (ldb (byte 64 0) (lognot (ash mask1-lo d%64)))))
        (declare ((unsigned-byte 64) mask0 mask1-lo mask1-hi))
        (do ((i (- end/64 1) (- i 1)))
            ((< i 0))
          (let ((word (sb-kernel:%vector-raw-bits bit-vector i))
                (i+d/64 (+ i d/64)))
            (declare ((unsigned-byte 64) word))
            (setf (sb-kernel:%vector-raw-bits result-vector i+d/64)
                  (logior (the (unsigned-byte 64)
                               (ash (logand word mask1-lo) d%64))
                          (logand (sb-kernel:%vector-raw-bits result-vector i+d/64)
                                  mask1-hi)))
            (setf (sb-kernel:%vector-raw-bits result-vector (+ 1 i+d/64))
                  (logior (ash word (- d%64 64))
                          (logand (sb-kernel:%vector-raw-bits result-vector (+ 1 i+d/64))
                                  mask0))))))
      ;; zero padding
      (when (< d/64 (ceiling (length result-vector) 64))
        (setf (ldb (byte d%64 0) (sb-kernel:%vector-raw-bits result-vector d/64)) 0))
      ;; REVIEW: May we set the last word of a bit vector to zero beyond the
      ;; actual bound?
      (dotimes (i (min d/64 (ceiling (length result-vector) 64)))
        (setf (sb-kernel:%vector-raw-bits result-vector i) 0))
      result-vector)))

;; (defun test-lshift (size sample)
;;   (let ((exemplar (make-array size :element-type 'bit :initial-element 0))
;;         (vec1 (make-array size :element-type 'bit))
;;         (vec2 (make-array size :element-type 'bit)))
;;     (dotimes (i size)
;;       (setf (aref exemplar i) (random 2)))
;;     (dotimes (_ sample)
;;       (fill vec2 0)
;;       (let ((delta (random 150)))
;;         (dotimes (i (max 0 (- size delta)))
;;           (setf (aref vec2 (+ i delta)) (aref exemplar i)))
;;         (assert (equal vec2 (bit-lshift exemplar delta vec1)))))))

(declaim (ftype (function * (values fixnum &optional)) read-fixnum))
(defun read-fixnum (&optional (in *standard-input*))
  (declare #.OPT)
  (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 #\-))
                                  (setf 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 required-p (as k pivot dp1 dp2)
  (declare #.OPT
           (uint32 k pivot)
           ((simple-array bit (5000)) dp1 dp2)
           ((simple-array uint32 (*)) as))
  (let* ((inf (max 0 (- k (aref as pivot))))
         (n (length as)))
    (declare (uint31 inf n))
    (fill dp1 0)
    (setf (aref dp1 0) 1)
    (loop for i from 1 below n
          for prev-dp = (if (oddp i) dp1 dp2)
          for new-dp = (if (oddp i) dp2 dp1)
          for a = (if (> i pivot)
                      (aref as i)
                      (aref as (- i 1)))
          do (bit-lshift prev-dp a new-dp)
             (bit-ior new-dp prev-dp new-dp))
    (loop with dp = (if (oddp (- n 1)) dp2 dp1)
          for j from inf below k
          thereis (= 1 (aref dp j)))))

(defun main ()
  (declare #.OPT)
  (let* ((n (read))
         (k (read))
         (as (make-array n :element-type 'uint32))
         (dp1 (make-array '(5000) :element-type 'bit :initial-element 0))
         (dp2 (make-array '(5000) :element-type 'bit :initial-element 0)))
    (declare (uint16 n k))
    (dotimes (i n) (setf (aref as i) (read-fixnum)))
    (setf as (sort as #'<))
    (sb-int:named-let bisect ((ng -1) (ok n))
      (declare (int32 ng ok))
      (if (<= (- ok ng) 1)
          (println ok)
          (let ((mid (ash (+ ng ok) -1)))
            (if (required-p as k mid dp1 dp2)
                (bisect ng mid)
                (bisect mid ok)))))))

#-swank (main)


Measured memory_bytes: 33380