;; -*- 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 (progn (ql:quickload '(:cl-debug-print :fiveam))
                 (shadow :run)
                 (use-package :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)

;; BEGIN_INSERTED_CONTENTS
(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
;; TODO: use DEFTRANSFORM to optimize these functions when they are passed to a
;; inlined function
(defmacro define-mod-operations (&optional (divisor 1000000007))
  `(progn
     (defun mod* (&rest args)
        (reduce (lambda (x y) (mod (* x y) ,divisor)) args))

     (define-compiler-macro mod* (&rest args)
        (if (null args)
            1
            (reduce (lambda (x y) `(mod (* ,x ,y) ,',divisor)) args)))

     (defun mod+ (&rest args)
        (reduce (lambda (x y) (mod (+ x y) ,divisor)) args))

     (define-compiler-macro mod+ (&rest args)
       (format t "Called!: ~A~%" args)
        (if (null args)
            0
            (reduce (lambda (x y) `(mod (+ ,x ,y) ,',divisor)) args)))

     (define-modify-macro incfmod (delta divisor)
        (lambda (x y divisor) (mod (+ x y) divisor)))

     (define-modify-macro decfmod (delta divisor)
        (lambda (x y divisor) (mod (- x y) divisor)))))

(define-mod-operations)

(defun main ()
  (declare #.OPT
           (inline sort))
  (let* ((n (read))
         (x (read))
         (ss (make-array n :element-type 'uint31))
         (dp0 (make-array 100001 :element-type 'uint31))
         (dp1 (make-array 100001 :element-type 'uint31)))
    (declare (uint8 n))
    (dotimes (i n) (setf (aref ss i) (read-fixnum)))
    (setf ss (sort ss #'>))
    (setf (aref dp0 x) 1)
    (dotimes (i n)
      (let ((new-dp (if (evenp i) dp1 dp0))
            (dp (if (evenp i) dp0 dp1)))
        (dotimes (y 100001)
          (setf (aref new-dp y)
                (mod* (the uint8 (- n i 1)) (aref dp y))))
        (dotimes (y 100001)
          (incfmod (aref new-dp (mod y (aref ss i)))
                   (aref dp y)
                   +mod+))))
    (let ((dp (if (evenp n) dp0 dp1))
          (res 0))
      (declare (uint31 res))
      (dotimes (y 100001)
        (incfmod res (mod* y (aref dp y)) +mod+))
      (println res))))

#-swank(main)


Measured memory_bytes: 27240