;; -*- 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) :silent t)
  #-swank (set-dispatch-macro-character
           ;; enclose the form with VALUES to avoid being captured by LOOP macro
           #\# #\> (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
(declaim (ftype (function * (values fixnum &optional)) read-fixnum))
(defun read-fixnum (&optional (in *standard-input*))
  (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))))))))

(macrolet ((def (name fname)
             `(define-modify-macro ,name (new-value) ,fname)))
  (def minf min)
  (def maxf max)
  (def mulf *)
  (def divf /)
  (def iorf logior)
  (def xorf logxor)
  (def andf logand))

;;;
;;; Diameter of tree
;;;

(defun find-diameter (graph)
  "Finds a diameter of a tree. Returns three values: the length of the diameter
and its two ends."
  (declare ((array list (*)) graph))
  (let ((end 0)
        (max-depth 0))
    (assert (> (length graph) 0))
    (labels ((traverse (v parent depth)
               (declare ((integer 0 #.array-total-size-limit) v parent depth))
               (when (> depth max-depth)
                 (setq max-depth depth
                       end v))
               (dolist (child (aref graph v))
                 (declare ((integer 0 #.most-positive-fixnum) child))
                 (unless (= child parent)
                   (traverse child v (+ depth 1))))))
      (traverse 0 array-total-size-limit 0)
      (let ((end1 end))
        (setq max-depth 0)
        (traverse end1 array-total-size-limit 0)
        (values max-depth end1 end)))))

(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
;;;

(defconstant +inf+ #xffffffff)
(defun main ()
  (declare (inline sort))
  (let* ((n (read))
         (k (read))
         (graph (make-array n :element-type 'list :initial-element nil))
         edges
         (res #xffffffff))
    (declare (uint32 n k res))
    (dotimes (i (- n 1))
      (let ((a (- (read-fixnum) 1))
            (b (- (read-fixnum) 1)))
        (push a (aref graph b))
        (push b (aref graph a))
        (push (cons a b) edges)))
    (when (<= (find-diameter graph) k)
      (println 0)
      (return-from main))
    (let ((k/2 (floor k 2))
          (dists (make-array n :element-type 'uint32)))
      (declare (uint32 k/2))
      (labels ((fill-dists! (v parent depth)
                 (declare (int32 v parent depth))
                 (setf (aref dists v) depth)
                 (dolist (child (aref graph v))
                   (declare (uint32 child))
                   (unless (= child parent)
                     (fill-dists! child v (+ depth 1)))))
               (get-max-depth (v parent)
                 (let ((res (aref dists v)))
                   (declare (uint32 res))
                   (dolist (child (aref graph v))
                     (declare (uint32 child))
                     (unless (= child parent)
                       (maxf res (get-max-depth child v))))
                   res)))
        (if (evenp k)
            (dotimes (root n)
              (when (cdr (aref graph root)) ;; exclude one branch case
                (fill dists +inf+)
                (fill-dists! root -1 0)
                (let ((branch-depths (loop for child in (aref graph root)
                                           collect (get-max-depth child root))))
                  (setq branch-depths (sort branch-depths
                                            (lambda (x y)
                                              (declare (uint32 x y))
                                              (> x y))))
                  (when (>= (second branch-depths) k/2)
                    (minf res (count-if (lambda (x) (> (the uint32 x) k/2)) dists))))))
            (loop
              for (root1 . root2) in edges
              when (and (car (aref graph root1))
                        (car (aref graph root2)))
              do (fill dists +inf+)
                 (fill-dists! root1 root2 0)
                 (fill-dists! root2 root1 0)
                 (let ((branch-depths1 (loop for child in (aref graph root1)
                                             collect (get-max-depth child root1)))
                       (branch-depths2 (loop for child in (aref graph root2)
                                             collect (get-max-depth child root2))))
                   (when (and (>= (reduce #'max branch-depths1) k/2)
                              (>= (reduce #'max branch-depths2) k/2))
                     (minf res (count-if (lambda (x) (> (the uint32 x) k/2)) dists))))))
        (println res)))))

#-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 "C:/Windows/System32/WindowsPowerShell/v1.0/powershell.exe" '("get-clipboard") :output out)))

#+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 "2
1 3 1 2
"
    "3
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "5
100 1 2 3 14 15 58 58 58 29
"
    "135
")))


Measured memory_bytes: 62180