;; -*- 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
           #\# #\> (lambda (s c p) (declare (ignore c p)) (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
;;;
;;; Bignum arithmetic by Chinese remainder theorem
;;;

;; Extended Euclidean algorithm (Blankinship algorithm)
(declaim (ftype (function * (values integer integer &optional)) %ext-gcd/bignum))
(defun %ext-gcd/bignum (a b)
  (declare (optimize (speed 3) (safety 0))
           (unsigned-byte a b))
  (let ((y 1)
        (x 0)
        (u 1)
        (v 0))
    (declare (integer y x u v))
    (loop (when (zerop a)
            (return (values x y)))
          (let ((q (floor b a)))
            (decf x (* q u))
            (rotatef x u)
            (decf y (* q v))
            (rotatef y v)
            (decf b (* q a))
            (rotatef b a)))))

;; Reference: https://qiita.com/drken/items/ae02240cd1f8edfc86fd (Japanese)
(declaim (inline chinese-rem))
(defun chinese-rem (b1 mod1 b2 mod2)
  "Solves x ≡ b1 mod m1, x ≡ b2 mod m2. The returned integer is in [0, LCM(m1,
m2)). Returns LCM(m1, m2) as the second value.

This function returns (VALUES NIL NIL) when the system is infeasible."
  (declare (integer b1 b2)
           ((integer 1) mod1 mod2))
  (multiple-value-bind (p q) (%ext-gcd/bignum mod1 mod2)
    (let ((gcd (+ (* p mod1) (* q mod2))))
      (declare (unsigned-byte gcd))
      (unless (zerop (mod (- b2 b1) gcd))
        ;; b1 ≡ b2 mod gcd(m1, m2) must holds
        (return-from chinese-rem (values nil nil)))
      (let* ((lcm/mod1 (floor mod2 gcd))
             (tmp (mod (* (floor (- b2 b1) gcd) p) lcm/mod1))
             (lcm (* mod1 lcm/mod1)))
        (values (mod (+ b1 (* mod1 tmp)) lcm) lcm)))))

(defun chinese-rem* (rems moduli)
  "Solves x_i ≡ b_i mod m_i, i in {1, 2, ..., k}. The returned integers are in
[0, LCM(m_1, m_2, ..., m_k)). Returns LCM(m_1, m_2, ..., m_k} as the second
value.

This function returns (VALUES NIL NIL) when the system is infeasible.

REMS := vector of integers
MODULI := vector of positive integers"
  (declare (vector rems moduli))
  (let ((result 0)
        (modulus 1))
    (declare (unsigned-byte result modulus))
    (dotimes (i (length rems))
      ;; Iteratively solves the system of two equations: x1 ≡ b1 mod m1 and x2
      ;; ≡ b2 mod m2, where RESULT = b1, MODULUS = m1, (AREF REMS I) = b2, and
      ;; (AREF MODULI I) = m2.
      (let ((b2 (aref rems i))
            (m2 (aref moduli i)))
        (declare (integer b2)
                 ((integer 1) m2))
        (multiple-value-bind (p q) (%ext-gcd/bignum modulus m2)
          (let ((gcd (+ (* p modulus) (* q m2))))
            (declare (unsigned-byte gcd))
            (unless (zerop (mod (- b2 result) gcd))
              ;; b1 ≡ b2 mod gcd(m1, m2) must holds
              (return-from chinese-rem* (values nil nil)))
            (let* ((lcm/m1 (floor m2 gcd))
                   (tmp (mod (* (floor (- b2 result) gcd) p) lcm/m1)))
              (declare (unsigned-byte lcm/m1 tmp))
              (setq result (+ result (* modulus tmp)))
              (setq modulus (* modulus lcm/m1)))))))
    (values result modulus)))

(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 main ()
  (let ((res 0)
        (modulus 1))
    (dotimes (i 3)
      (let ((x (read))
            (y (read)))
        (multiple-value-setq (res modulus)
          (chinese-rem res modulus x y))
        (unless res
          (println -1)
          (return-from main))))
    (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:/msys64/usr/bin/cat.exe" '("/dev/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)))