Problem:
Score : 700 points

Problem Statement

There is a circle with a circumference of L.
Each point on the circumference has a coordinate value, which represents the arc length from a certain reference point clockwise to the point.
On this circumference, there are N ants.
These ants are numbered 1 through N in order of increasing coordinate, and ant i is at coordinate X_i.

The N ants have just started walking.
For each ant i, you are given the initial direction W_i. Ant i is initially walking clockwise if W_i is 1; counterclockwise if W_i is 2.
Every ant walks at a constant speed of 1 per second.
Sometimes, two ants bump into each other.
Each of these two ants will then turn around and start walking in the opposite direction.

For each ant, find its position after T seconds.

Constraints

All input values are integers.

1 \leq N \leq 10^5

1 \leq L \leq 10^9

1 \leq T \leq 10^9

0 \leq X_1 < X_2 < ... < X_N \leq L - 1

1 \leq W_i \leq 2

Input

The input is given from Standard Input in the following format:

N L T
X_1 W_1
X_2 W_2
:
X_N W_N

Output

Print N lines.
The i-th line should contain the coordinate of ant i after T seconds. Here, each coordinate must be between 0 and L-1, inclusive.

Sample Input 1

3 8 3
0 1
3 2
6 1

Sample Output 1

1
3
0

1.5 seconds after the ants start walking, ant 1 and 2 bump into each other at coordinate 1.5.
1 second after that, ant 1 and 3 bump into each other at coordinate 0.5.
0.5 seconds after that, that is, 3 seconds after the ants start walking, ants 1, 2 and 3 are at coordinates 1, 3 and 0, respectively.

Sample Input 2

4 20 9
7 2
9 1
12 1
18 1

Sample Output 2

7
18
18
1

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

;; -*- 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 (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
                                  ;; (return-from read-fixnum 0)
                                  (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

(declaim (inline count-collision))
(defun count-collision (anticlock clock l time)
  (if (< (* 2 time) (mod (- anticlock clock) l))
      0
      (let ((remain (- (* 2 time) (mod (- anticlock clock) l))))
        (+ 1 (floor remain l)))))

(defun main ()
  (declare #.OPT (inline sort))
  (let* ((n (read))
         (l (read))
         (time (read))
         (inits (make-array n :element-type 'uint32))
         (dirs (make-array n :element-type 'bit)))
    (declare (uint32 n l time))
    (dotimes (i n) (setf (aref inits i) (read-fixnum)
                         (aref dirs i) (mod (read-fixnum) 2)))
    (let* ((count0 (loop for i below n
                         unless (= (aref dirs 0) (aref dirs i))
                         sum (if (zerop (aref dirs 0))
                                 (count-collision (aref inits 0) (aref inits i) l time)
                                 (count-collision (aref inits i) (aref inits 0) l time))
                         of-type uint32))
           (end-index (mod (if (zerop (aref dirs 0))
                               (- count0)
                               count0)
                           n))
           (ends (make-array n :element-type 'uint32))
           (end0 (mod (+ (aref inits 0)
                         (if (zerop (aref dirs 0))
                             (- time)
                             time))
                      l)))
      (dotimes (i n)
        (setf (aref ends i)
              (mod (+ (aref inits i)
                      (if (zerop (aref dirs i))
                          (- time)
                          time))
                   l)))
      (setf ends (sort ends #'<))
      (let ((end0-pos (position end0 ends))
            (res (make-array n :element-type 'uint32)))
        (cond ((and (= (aref ends end0-pos) (aref ends (mod (+ end0-pos 1) n)))
                    (= 1 (aref dirs 0)))
               (setf end0-pos (mod (+ end0-pos 1) n)))
              ((and (= (aref ends end0-pos) (aref ends (mod (- end0-pos 1) n)))
                    (= 0 (aref dirs 0)))
               (setf end0-pos (mod (- end0-pos 1) n))))
        (let ((actual-index (mod (- end0-pos end-index) n)))
          (loop for i below n
                do (setf (aref res i)
                         (aref ends (mod (+ actual-index i) n))))
          (map () #'println res))))))

#-swank(main)