;; -*- coding: utf-8 -*-
(eval-when (:compile-toplevel :load-toplevel :execute)
  (defparameter OPT
    #+swank '(optimize (speed 3) (safety 2))
    #-swank '(optimize (speed 3) (safety 0) (debug 0)))
  #+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
(declaim (ftype (function * (values (vector (integer 0 #.most-positive-fixnum)) &optional))
                enum-divisors))
(defun enum-divisors (x)
  "Enumerates all the divisors of X in O(sqrt(X)). Note that the resultant
vector is NOT sorted."
  (declare (optimize (speed 3))
           ((integer 0 #.most-positive-fixnum) x))
  (let* ((sqrt (isqrt x))
         (res (make-array (isqrt sqrt) ; FIXME: sets the initial size to x^1/4
                          :element-type '(integer 0 #.most-positive-fixnum)
                          :fill-pointer 0)))
    (loop for i from 1 to sqrt
          do (multiple-value-bind (quot rem) (floor x i)
               (when (zerop rem)
                 (vector-push-extend i res)
                 (unless (= i quot)
                   (vector-push-extend quot res)))))
    res))


(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 calc-distance (div sum as)
  (declare #.OPT
           ((simple-array uint32 (*)) as)
           (uint32 div sum)
           (inline sort))
  (let ((as (copy-seq as))
        (n (length as))
        (cumuls1 (make-array 501 :element-type 'uint62 :initial-element 0)))
    (declare (dynamic-extent cumuls1))
    (setf as (sort as (lambda (x y)
                        (declare (uint32 x y))
                        (< (mod x div) (mod y div)))))
    (dotimes (i n)
      (setf (aref cumuls1 (+ i 1))
            (+ (aref cumuls1 i) (* div (floor (aref as i) div)))))
    (loop for i from n downto 0
          for cumul2 of-type uint62 = 0 then (+ cumul2 (* div (ceiling (aref as i) div)))
          when (= sum (+ (aref cumuls1 i) cumul2))
          do (return (- (reduce #'+ as :end i) (aref cumuls1 i)))
          finally (error "Huh?"))))

(defun main ()
  (let* ((n (read))
         (k (read))
         (as (make-array n :element-type 'uint32))
         (sum 0))
    (dotimes (i n)
      (setf (aref as i) (read-fixnum))
      (incf sum (aref as i)))
    (let ((divs (enum-divisors sum)))
      (setf divs (sort divs #'>))
      (loop for d across divs
            when (<= (calc-distance d sum as) k)
            do (println d)
               (return-from main)))))

#-swank (main)


Measured memory_bytes: 29288