(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
;;;
;;; Queue with singly linked list
;;;

(defstruct (queue (:constructor make-queue
                      (&optional list &aux (tail (last list)))))
  (list nil :type list)
  (tail nil :type list))

(declaim (inline enqueue))
(defun enqueue (obj queue)
  "Pushes OBJ to the end of QUEUE."
  (symbol-macrolet ((list (queue-list queue))
                    (tail (queue-tail queue)))
    (if (null list)
        (setf tail (list obj)
              list tail)
        (setf (cdr tail) (list obj)
              tail (cdr tail))))
  queue)

(declaim (inline dequeue))
(defun dequeue (queue)
  "Removes and returns the element at the front of QUEUE. Returns NIL if QUEUE
is empty."
  (pop (queue-list queue)))

(declaim (inline queue-empty-p))
(defun queue-empty-p (queue)
  (null (queue-list queue)))

(declaim (inline queue-peek))
(defun queue-peek (queue)
  (car (queue-list queue)))

(declaim (inline enqueue-front))
(defun enqueue-front (obj queue)
  "Pushes OBJ to the front of QUEUE."
  (symbol-macrolet ((list (queue-list queue))
                    (tail (queue-tail queue)))
    (if (null list)
        (setf tail (list obj)
              list tail)
        (push obj list))
    queue))

(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))))))))

(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+ 1000000007)

;;;
;;; Body
;;;

(defun find-cycle (graph e1 e2)
  (let* ((n (length graph))
         (dists (make-array n :element-type 'uint32 :initial-element #xffffffff))
         (paths (make-array n :element-type 'list :initial-element nil))
         (que (make-queue)))
    ;; #>graph
    (dbg e1 e2)
    (enqueue e1 que)
    (setf (aref dists e1) 0)
    (push e1 (aref paths e1))
    (loop until (queue-empty-p que)
          for v = (dequeue que)
          do (dolist (next (aref graph v))
               (when (and (= #xffffffff (aref dists next))
                          (not (and (= e1 v) (= e2 next))))
                 (enqueue next que)
                 (setf (aref paths next)
                       (cons next (aref paths v)))
                 (setf (aref dists next)
                       (+ (aref dists v) 1)))))
    (cons e1 (aref paths e2))))

(defun main ()
  (let* ((n (read))
         (m (read))
         (graph (make-array n :element-type 'list :initial-element nil))
         (degs (make-array n :element-type 'uint31 :initial-element 0)))
    (labels ((no () (write-line "No") (return-from main)))
      (dotimes (i m)
        (let ((a (- (read-fixnum) 1))
              (b (- (read-fixnum) 1)))
          (push a (aref graph b))
          (push b (aref graph a))
          (incf (aref degs a))
          (incf (aref degs b))))
      (unless (loop for x across degs
                    always (evenp x))
        (no))
      (labels ((frob ()
                 (let ((e1 (position nil graph :test-not #'eq)))
                   #>e1
                   (unless e1 (no))
                   (let ((path (find-cycle graph e1 (car (aref graph e1))))
                         (table (make-hash-table :test #'equal)))
                     #>path
                     (loop for (u v) on path
                           while v
                           do (setf (gethash (cons u v) table) t
                                    (gethash (cons v u) table) t))
                     (dotimes (i n)
                       (setf (aref graph i)
                             (loop for j in (aref graph i)
                                   unless (gethash (cons i j) table)
                                   collect j)))
                     #>graph
                     ;; (dotimes (i n)
                     ;;   (dolist (j (aref graph i))
                     ;;     (when (< i j)
                     ;;       (format t "~D ~D~%" i j))))
                     (unless (find nil graph :test-not #'eq)
                       (no))))))
        (frob)
        (frob)
        (write-line "Yes")))))

#-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 "7 9
1 2
1 3
2 3
1 4
1 5
4 5
1 6
1 7
6 7
"
    "Yes
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "3 3
1 2
2 3
3 1
"
    "No
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "18 27
17 7
12 15
18 17
13 18
13 6
5 7
7 1
14 5
15 11
7 6
1 9
5 4
18 16
4 6
7 2
7 11
6 3
12 14
5 2
10 5
7 8
10 15
3 15
9 8
7 15
5 16
18 15
"
    "Yes
")))


Measured memory_bytes: 70244