(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
;;;
;;; Fast Number Theoretic Transform
;;; Reference: https://github.com/ei1333/library/blob/master/math/fft/number-theoretic-transform-friendly-mod-int.cpp
;;;

(defconstant +ntt-mod+ 998244353)
(defconstant +ntt-root+ 3)
(deftype ntt-int () '(unsigned-byte 31))
(deftype ntt-vector () '(simple-array ntt-int (*)))

(eval-when (:compile-toplevel :load-toplevel :execute)
  (assert (typep +ntt-mod+ 'ntt-int)))

(declaim (inline %tzcount))
(defun %tzcount (x)
  (- (integer-length (logand x (- x))) 1))

(declaim (inline %mod-power))
(defun %mod-power (base exp)
  (declare (ntt-int base)
           ((integer 0 #.most-positive-fixnum) exp))
  (let ((res 1))
    (declare (ntt-int res))
    (loop while (> exp 0)
          when (oddp exp)
          do (setq res (mod (* res base) +ntt-mod+))
          do (setq base (mod (* base base) +ntt-mod+)
                   exp (ash exp -1)))
    res))

(defun check-ntt-vector (vector)
  (declare (optimize (speed 3))
           (vector vector))
  (let ((len (length vector)))
    (assert (zerop (logand len (- len 1)))) ;; power of two
    (check-type len ntt-int)))

(defun make-ntt-base ()
  (labels ((mod-inverse (x) (%mod-power x (- +ntt-mod+ 2))))
    (let* ((base-size (%tzcount (- +ntt-mod+ 1)))
           (base (make-array base-size :element-type 'ntt-int))
           (inv-base (make-array base-size :element-type 'ntt-int)))
      (dotimes (i base-size)
        (setf (aref base i)
              (mod (- (%mod-power +ntt-root+ (ash (- +ntt-mod+ 1) (- (+ i 2)))))
                   +ntt-mod+)
              (aref inv-base i)
              (mod-inverse (aref base i))))
      (values base inv-base))))

(multiple-value-bind (base inv-base) (make-ntt-base)
  (defparameter *ntt-base* base)
  (defparameter *ntt-inv-base* inv-base))

;; FIXME: Here I resort to SBCL's behaviour. Actually ADJUST-ARRAY isn't
;; guaranteed to preserve the given VECTOR.
(declaim (ftype (function * (values ntt-vector &optional)) %adjust-array))
(defun %adjust-array (vector length)
  (declare (vector vector))
  (let ((vector (coerce vector 'ntt-vector)))
    (if (= (length vector) length)
        (copy-seq vector)
        (adjust-array vector length :initial-element 0))))

(declaim (ftype (function * (values ntt-vector &optional)) ntt!))
(defun ntt! (vector)
  (declare #.OPT
           (vector vector))
  (check-ntt-vector vector)
  (labels ((mod* (x y) (mod (* x y) +ntt-mod+))
           (mod+ (x y)
             (let ((res (+ x y)))
               (if (>= res +ntt-mod+)
                   (- res +ntt-mod+)
                   res)))
           (mod- (x y) (mod+ x (- +ntt-mod+ y))))
    (declare (inline mod* mod+ mod-))
    (let* ((vector (coerce vector 'ntt-vector))
           (len (length vector))
           (base *ntt-base*))
      (declare ((simple-array ntt-int (*)) vector base)
               (ntt-int len))
      (when (<= len 1)
        (return-from ntt! vector))
      (loop for m of-type ntt-int = (ash len -1) then (ash m -1)
            while (> m 0)
            for w of-type ntt-int = 1
            for k of-type ntt-int = 0
            do (loop for s of-type ntt-int from 0 below len by (* 2 m)
                     do (loop for i from s below (+ s m)
                              for j from (+ s m)
                              for x = (aref vector i)
                              for y = (mod* (aref vector j) w)
                              do (setf (aref vector i) (mod+ x y)
                                       (aref vector j) (mod- x y)))
                        (incf k)
                        (setq w (mod* w (aref base (%tzcount k))))))
      vector)))

(defun inverse-ntt! (vector &optional inverse)
  (declare #.OPT
           (vector vector))
  (check-ntt-vector vector)
  (labels ((mod* (x y)
             (declare (ntt-int x y))
             (mod (* x y) +ntt-mod+))
           (mod+ (x y)
             (declare (ntt-int x y))
             (let ((res (+ x y)))
               (if (>= res +ntt-mod+)
                   (- res +ntt-mod+)
                   res)))
           (mod- (x y)
             (declare (ntt-int x y))
             (mod+ x (- +ntt-mod+ y))))
    (declare (inline mod* mod+ mod-))
    (let* ((vector (coerce vector 'ntt-vector))
           (len (length vector))
           (base *ntt-inv-base*))
      (declare ((simple-array ntt-int (*)) vector base)
               (ntt-int len))
      (when (<= len 1)
        (return-from inverse-ntt! vector))
      (loop for m of-type ntt-int = 1 then (ash m 1)
            while (< m len)
            for w of-type ntt-int = 1
            for k of-type ntt-int = 0
            do (loop for s of-type ntt-int from 0 below len by (* 2 m)
                     do (loop for i from s below (+ s m)
                              for j from (+ s m)
                              for x = (aref vector i)
                              for y = (aref vector j)
                              do (setf (aref vector i) (mod+ x y)
                                       (aref vector j) (mod* (mod- x y) w)))
                        (incf k)
                        (setq w (mod* w (aref base (%tzcount k))))))
      (when inverse
        (let ((inv-len (%mod-power len (- +ntt-mod+ 2))))
          (dotimes (i len)
            (setf (aref vector i) (mod* inv-len (aref vector i))))))
      vector)))

(declaim (ftype (function * (values ntt-vector &optional)) ntt-convolute!))
(defun ntt-convolute! (vector1 vector2)
  (declare (ntt-vector vector1 vector2))
  (let* ((len1 (length vector1))
         (len2 (length vector2))
         (mul-len (- (+ len1 len2) 1))
         (required-len (sb-int:power-of-two-ceiling mul-len))
         (vector1 (ntt! (adjust-array vector1 required-len)))
         (vector2 (ntt! (adjust-array vector2 required-len))))
    (dotimes (i required-len)
      (setf (aref vector1 i)
            (mod (* (aref vector1 i) (aref vector2 i)) +ntt-mod+)))
    (inverse-ntt! vector1 t)))

;; NOTE: buggy
(declaim (ftype (function * (values ntt-vector &optional)) ntt-convolute))
(defun ntt-convolute (vector1 vector2 &optional fixed)
  (declare (optimize (speed 3))
           (vector vector1 vector2))
  (let ((len1 (length vector1))
        (len2 (length vector1)))
    (when fixed
      (assert (= len1 len2)))
    (let* ((mul-len (max 0 (- (+ len1 len2) 1)))
           ;; power of two ceiling
           (required-len (if fixed
                             len1
                             (ash 1 (integer-length (max 0 (- mul-len 1))))))
           (vector1 (ntt! (%adjust-array vector1 required-len)))
           (vector2 (ntt! (%adjust-array vector2 required-len))))
      
      (dotimes (i required-len)
        (setf (aref vector1 i)
              (mod (* (aref vector1 i) (aref vector2 i)) +ntt-mod+)))
      (inverse-ntt! vector1))))

(declaim (ftype (function * (values fixnum &optional)) read-fixnum))
(defun read-fixnum (&optional (in *standard-input*))
  "NOTE: cannot read -2^62"
  (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 #\-))
                                  (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))))))))

;;;
;;; Arithmetic operations with static modulus
;;;

;; FIXME: Currently MOD* and MOD+ doesn't apply MOD when the number of
;; parameters is one.
(defmacro define-mod-operations (divisor)
  `(progn
     (defun mod* (&rest args)
       (reduce (lambda (x y) (mod (* x y) ,divisor)) args))

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

     #+sbcl
     (eval-when (:compile-toplevel :load-toplevel :execute)
       (locally (declare (muffle-conditions warning))
         (sb-c:define-source-transform mod* (&rest args)
           (if (null args)
               1
               (reduce (lambda (x y) `(mod (* ,x ,y) ,',divisor)) args)))
         (sb-c:define-source-transform mod+ (&rest args)
           (if (null args)
               0
               (reduce (lambda (x y) `(mod (+ ,x ,y) ,',divisor)) args)))))

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

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

     (define-modify-macro mulfmod (multiplier)
       (lambda (x y) (mod (* x y) ,divisor)))))


(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+ 998244353)

;;;
;;; Body
;;;

(define-mod-operations +mod+)
(defun main ()
  (declare #.OPT)
  (let* ((n (read))
         (n2 (sb-int:power-of-two-ceiling n))
         (q (read))
         (polys (make-array n2 :element-type 'ntt-vector)))
    (declare (uint31 n q))
    (dotimes (i n2)
      (if (< i n)
          (let ((a (read-fixnum))
                (poly (make-array 2 :element-type 'uint31)))
            (setf (aref poly 1) (mod (- a 1) +mod+)
                  (aref poly 0) 1)
            (setf (aref polys i) poly))
          (let ((poly (make-array 2 :element-type 'uint31)))
            (setf (aref poly 1) 0
                  (aref poly 0) 1)
            (setf (aref polys i) poly))))
    (loop for width = 1 then (ash width 1)
          while (< width n2)
          do (loop for i from 0 below n2 by (* width 2)
                   do (setf (aref polys i)
                            (ntt-convolute!
                             (aref polys i)
                             (aref polys (+ i width))))))
    (let ((poly (aref polys 0)))
      (declare (ntt-vector poly))
      (write-string
       (with-output-to-string (*standard-output* nil :element-type 'base-char)
         (dotimes (i q)
           (let ((b (read-fixnum)))
             (println (aref poly (- n b))))))))))

#-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 "3 4
3 4 5
0 1 2 3
"
    "24
26
9
1
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "4 3
1 3 3 3
3 1 4
"
    "6
8
1
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "3 2
5 7 5
1 3
"
    "64
1
")))