Problem:
Score : 600 points

Problem Statement

We have N colored balls arranged in a row from left to right; the color of the i-th ball from the left is c_i.

You are given Q queries. The i-th query is as follows: how many different colors do the l_i-th through r_i-th balls from the left have?

Constraints

1\leq N,Q \leq 5 \times 10^5

1\leq c_i \leq N

1\leq l_i \leq r_i \leq N

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N Q
c_1 c_2 \cdots c_N
l_1 r_1
l_2 r_2
:
l_Q r_Q

Output

Print Q lines. The i-th line should contain the response to the i-th query.

Sample Input 1

4 3
1 2 1 3
1 3
2 4
3 3

Sample Output 1

2
3
1

The 1-st, 2-nd, and 3-rd balls from the left have the colors 1, 2, and 1 - two different colors.

The 2-st, 3-rd, and 4-th balls from the left have the colors 2, 1, and 3 - three different colors.

The 3-rd ball from the left has the color 1 - just one color.

Sample Input 2

10 10
2 5 6 5 2 1 7 9 7 2
5 5
2 4
6 7
2 2
7 8
7 9
1 8
6 9
8 10
6 8

Sample Output 2

1
2
2
1
2
2
6
3
3
3

Solution in Common Lisp (SBCL 2.0.3) (judge verdict: Accepted)

(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)

(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)

;; BEGIN_INSERTED_CONTENTS
;;;
;;; 1-dimensional binary indexed tree on arbitrary commutative monoid
;;;

(defmacro define-bitree (name &key (operator '#'+) (identity 0) sum-type (order '#'<))
  "OPERATOR := binary operator (comprising a commutative monoid)
IDENTITY := object (identity element of the monoid)
ORDER := nil | strict comparison operator on the monoid
SUM-TYPE := nil | type specifier

Defines no structure; BIT is just a vector. This macro defines the three
functions: <NAME>-UPDATE!, point-update function, <NAME>-FOLD, query function for
prefix sum, and COERCE-TO-<NAME>!, constructor. If ORDER is specified, this
macro in addition defines <NAME>-BISECT-LEFT and <NAME>-BISECT-RIGHT, the
bisection functions for prefix sums. (Note that these functions work only when
the sequence of prefix sums (VECTOR[0], VECTOR[0]+VECTOR[1], ...) is monotone.)

SUM-TYPE is used only for the type declaration: each sum
VECTOR[i]+VECTOR[i+1]...+VECTOR[i+k] is declared to be this type. When SUM-TYPE
is NIL, type declaration is omitted. (The array-element-type of vector itself
doesn't need to be identical to SUM-TYPE.)"
  (let* ((name (string name))
         (fname-update (intern (format nil "~A-UPDATE!" name)))
         (fname-fold (intern (format nil "~A-FOLD" name)))
         (fname-coerce (intern (format nil "COERCE-TO-~A!" name)))
         (fname-bisect-left (intern (format nil "~A-BISECT-LEFT" name)))
         (fname-bisect-right (intern (format nil "~A-BISECT-RIGHT" name))))
    `(progn
       (declaim (inline ,fname-update))
       (defun ,fname-update (bitree index delta)
         "Destructively increments the vector: vector[INDEX] = vector[INDEX] +
DELTA"
         (let ((len (length bitree)))
           (do ((i index (logior i (+ i 1))))
               ((>= i len) bitree)
             (declare ((integer 0 #.most-positive-fixnum) i))
             (setf (aref bitree i)
                   (funcall ,operator (aref bitree i) delta)))))

       (declaim (inline ,fname-fold))
       (defun ,fname-fold (bitree end)
         "Returns the sum of the prefix: vector[0] + ... + vector[END-1]."
         (declare ((integer 0 #.most-positive-fixnum) end))
         (let ((res ,identity))
           ,@(when sum-type `((declare (type ,sum-type res))))
           (do ((i (- end 1) (- (logand i (+ i 1)) 1)))
               ((< i 0) res)
             (declare ((integer -1 #.most-positive-fixnum) i))
             (setf res (funcall ,operator res (aref bitree i))))))

       (declaim (inline ,fname-coerce))
       (defun ,fname-coerce (vector)
         "Destructively constructs BIT from VECTOR. (You doesn't need to call
this constructor if what you need is a `zero-filled' BIT, because a vector
filled with the identity element is a valid BIT as it is.)"
         (loop with len = (length vector)
               for i below len
               for dest-i = (logior i (+ i 1))
               when (< dest-i len)
               do (setf (aref vector dest-i)
                        (funcall ,operator (aref vector dest-i) (aref vector i)))
               finally (return vector)))

       ,@(when order
           `((declaim (inline ,fname-bisect-left))
             (defun ,fname-bisect-left (bitree value)
               "Returns the smallest index that satisfies VECTOR[0]+ ... +
VECTOR[index] >= VALUE. Returns the length of VECTOR if VECTOR[0]+
... +VECTOR[length-1] < VALUE. Note that this function deals with a **closed**
interval."
               (declare (vector bitree))
               (if (not (funcall ,order ,identity value))
                   0
                   (let ((len (length bitree))
                         (index+1 0)
                         (cumul ,identity))
                     (declare ((integer 0 #.most-positive-fixnum) index+1)
                              ,@(when sum-type
                                  `((type ,sum-type cumul))))
                     (do ((delta (ash 1 (- (integer-length len) 1))
                                 (ash delta -1)))
                         ((zerop delta) index+1)
                       (declare ((integer 0 #.most-positive-fixnum) delta))
                       (let ((next-index (+ index+1 delta -1)))
                         (when (< next-index len)
                           (let ((next-cumul (funcall ,operator cumul (aref bitree next-index))))
                             ,@(when sum-type
                                 `((declare (type ,sum-type next-cumul))))
                             (when (funcall ,order next-cumul value)
                               (setf cumul next-cumul)
                               (incf index+1 delta)))))))))
             (declaim (inline ,fname-bisect-right))
             (defun ,fname-bisect-right (bitree value)
               "Returns the smallest index that satisfies VECTOR[0]+ ... +
VECTOR[index] > VALUE. Returns the length of VECTOR if VECTOR[0]+
... +VECTOR[length-1] <= VALUE. Note that this function deals with a **closed**
interval."
               (declare (vector bitree))
               (if (funcall ,order value ,identity)
                   0
                   (let ((len (length bitree))
                         (index+1 0)
                         (cumul ,identity))
                     (declare ((integer 0 #.most-positive-fixnum) index+1)
                              ,@(when sum-type
                                  `((type ,sum-type cumul))))
                     (do ((delta (ash 1 (- (integer-length len) 1))
                                 (ash delta -1)))
                         ((zerop delta) index+1)
                       (declare ((integer 0 #.most-positive-fixnum) delta))
                       (let ((next-index (+ index+1 delta -1)))
                         (when (< next-index len)
                           (let ((next-cumul (funcall ,operator cumul (aref bitree next-index))))
                             ,@(when sum-type
                                 `((declare (type ,sum-type next-cumul))))
                             (unless (funcall ,order value next-cumul)
                               (setf cumul next-cumul)
                               (incf index+1 delta))))))))))))))

(define-bitree bitree
  :operator #'+
  :identity 0
  :sum-type fixnum
  :order #'<)

(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))))))))

(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)))

(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 +nan+ #x7fffffff)
(defun main ()
  (declare #.opt
           (inline sort))
  (let* ((n (read))
         (q (read))
         (cs (make-array n :element-type 'uint31 :initial-element 0))
         (ls (make-array q :element-type 'uint31 :initial-element 0))
         (rs (make-array q :element-type 'uint31 :initial-element 0))
         (ords (make-array q :element-type 'uint31 :initial-element 0)))
    (dotimes (i n)
      (setf (aref cs i) (read-fixnum)))
    (dotimes (i q)
      (setf (aref ords i) i))
    (dotimes (i q)
      (setf (aref ls i) (- (read-fixnum) 1)
            (aref rs i) (read-fixnum)))
    (setq ords (sort ords #'< :key (lambda (i) (aref rs i))))
    (let ((appeared (make-array (+ n 1) :element-type 'uint31 :initial-element +nan+))
          (bitree (make-array n :element-type 'uint31 :initial-element 0))
          (res (make-array q :element-type 'uint31 :initial-element 0))
          (pos 0))
      (loop for i across ords
            for l = (aref ls i)
            for r = (aref rs i)
            do (loop while (< pos r)
                     for c = (aref cs pos)
                     do (bitree-update! bitree pos 1)
                        (unless (= +nan+ (aref appeared c))
                          (bitree-update! bitree (aref appeared c) -1))
                        (setf (aref appeared c) pos)
                        (incf pos))
               (setf (aref res i)
                     (- (bitree-fold bitree r)
                        (bitree-fold bitree l))))
      (write-string
       (with-output-to-string (*standard-output* nil :element-type 'base-char)
         (map () #'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)
    #+os-windows (run-program "powershell.exe" '("-Command" "Get-Clipboard") :output out :search t)
    #+os-unix (run-program "xsel" '("-b" "-o") :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 "4 3
1 2 1 3
1 3
2 4
3 3
"
    "2
3
1
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "10 10
2 5 6 5 2 1 7 9 7 2
5 5
2 4
6 7
2 2
7 8
7 9
1 8
6 9
8 10
6 8
"
    "1
2
2
1
2
2
6
3
3
3
")))