;; -*- 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
;;;
;;; Modular arithmetic
;;;

;; Blankinship algorithm
;; Reference: https://topcoder.g.hatena.ne.jp/spaghetti_source/20130126/1359171466 (Japanese)
(declaim (ftype (function * (values fixnum fixnum &optional)) %ext-gcd))
(defun %ext-gcd (a b)
  (declare (optimize (speed 3) (safety 0))
           (fixnum a b))
  (let ((y 1)
        (x 0)
        (u 1)
        (v 0))
    (declare (fixnum y x u v))
    (loop (when (zerop a)
            (return (values x y)))
          (let ((q (floor b a)))
            (decf x (the fixnum (* q u)))
            (rotatef x u)
            (decf y (the fixnum (* q v)))
            (rotatef y v)
            (decf b (the fixnum (* q a)))
            (rotatef b a)))))

;; recursive version
;; (defun %ext-gcd (a b)
;;   (declare (optimize (speed 3) (safety 0))
;;            (fixnum a b))
;;   (if (zerop b)
;;       (values 1 0)
;;       (multiple-value-bind (p q) (floor a b) ; a = pb + q
;;         (multiple-value-bind (v u) (%ext-gcd b q)
;;           (declare (fixnum u v))
;;           (values u (the fixnum (- v (the fixnum (* p u)))))))))

;; TODO: deal with bignums
(declaim (inline ext-gcd))
(defun ext-gcd (a b)
  "Returns two integers X and Y which satisfy AX + BY = gcd(A, B)."
  (declare ((integer #.(- most-positive-fixnum) #.most-positive-fixnum) a b))
  (if (>= a 0)
      (if (>= b 0)
          (%ext-gcd a b)
          (multiple-value-bind (x y) (%ext-gcd a (- b))
            (declare (fixnum x y))
            (values x (- y))))
      (if (>= b 0)
          (multiple-value-bind (x y) (%ext-gcd (- a) b)
            (declare (fixnum x y))
            (values (- x) y))
          (multiple-value-bind (x y) (%ext-gcd (- a) (- b))
            (declare (fixnum x y))
            (values (- x) (- y))))))

(declaim (inline mod-inverse)
         (ftype (function * (values (mod #.most-positive-fixnum) &optional)) mod-inverse))
;; (defun mod-inverse (a modulus)
;;   "Solves ax ≡ 1 mod m. A and M must be coprime."
;;   (declare (integer a)
;;            ((integer 1 #.most-positive-fixnum) modulus))
;;   (mod (%ext-gcd (mod a modulus) modulus) modulus))

(defun mod-inverse (a modulus)
  (declare ((integer 1 #.most-positive-fixnum) modulus))
  (let ((a (mod a modulus))
        (b modulus)
        (u 1)
        (v 0))
    (declare (fixnum a b u v))
    (loop until (zerop b)
          for quot = (floor a b)
          do (decf a (the fixnum (* quot b)))
             (rotatef a b)
             (decf u (the fixnum (* quot v)))
             (rotatef u v))
    (setq u (mod u modulus))
    (if (< u 0)
        (+ u modulus)
        u)))

(declaim (inline %calc-min-factor))
(defun %calc-min-factor (x alpha)
  "Returns k, so that x+k*alpha is the smallest non-negative number."
  (if (plusp alpha)
      (ceiling (- x) alpha)
      (floor (- x) alpha)))

(declaim (inline %calc-max-factor))
(defun %calc-max-factor (x alpha)
  "Returns k, so that x+k*alpha is the largest non-positive number."
  (if (plusp alpha)
      (floor (- x) alpha)
      (ceiling (- x) alpha)))

(defun solve-bezout (a b c &optional min max)
  "Returns an integer solution of a*x+b*y = c if it exists, otherwise
returns (VALUES NIL NIL).

If MIN is specified and MAX is null, the returned x is the smallest integer
equal or larger than MIN. If MAX is specified and MIN is null, x is the largest
integer equal or smaller than MAX. If the both are specified, x is an integer in
[MIN, MAX]. This function returns NIL when no x that satisfies the given
condition exists."
  (declare (fixnum a b c)
           ((or null fixnum) min max))
  (let ((gcd-ab (gcd a b)))
    (if (zerop (mod c gcd-ab))
        (multiple-value-bind (init-x init-y) (ext-gcd a b)
          (let* ((factor (floor c gcd-ab))
                 ;; m*x0 + n*y0 = d
                 (x0 (* init-x factor))
                 (y0 (* init-y factor)))
            (if (and (null min) (null max))
                (values x0 y0)
                (let (;; general solution: x = x0 + kΔx, y = y0 - kΔy
                      (deltax (floor b gcd-ab))
                      (deltay (floor a gcd-ab)))
                  (if min
                      (let* ((k-min (%calc-min-factor (- x0 min) deltax))
                             (x (+ x0 (* k-min deltax)))
                             (y (- y0 (* k-min deltay))))
                        (if (and max (> x max))
                            (values nil nil)
                            (values x y)))
                      (let* ((k-max (%calc-max-factor (- x0 max) deltax))
                             (x (+ x0 (* k-max deltax)))
                             (y (- y0 (* k-max deltay))))
                        (if (<= x max)
                            (values x y)
                            (values nil nil))))))))
        (values nil nil))))

(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* ((a (read))
         (b (read))
         (c (read))
         (d (read))
         (e (read))
         (f (read))
         (gcd-ab (gcd a b))
         (gcd-cd (gcd c d))
         (max 0)
         (arg-total 0)
         (arg-sugar 0)
         water-set
         sugar-set)
    (declare (uint16 a b c d e f))
    (loop for x from 1 to (ceiling f 100)
          do (multiple-value-bind (_ v) (solve-bezout a b x 0)
               (when (and v (>= v 0))
                 (push x water-set))))
    (loop for x from 1 to f
          do (multiple-value-bind (_ v) (solve-bezout c d x 0)
               (when (and v (>= v 0))
                 (push x sugar-set))))
    (dbg water-set sugar-set)
    (dolist (water water-set)
      (dolist (sugar sugar-set)
        (declare (uint31 water sugar))
        (let* ((total (+ sugar (* 100 water)))
               (strength (/ sugar total)))
          (when (and (<= total f)
                     (<= sugar (* e water))
                     (> strength max))
            (setq max strength
                  arg-total total
                  arg-sugar sugar)))))
    (if (zerop max)
        (format t "~D 0~%" (* 100 a))
        (format t "~D ~D~%" arg-total arg-sugar))))

#-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)
    (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 "1 2 10 20 15 200
"
    "110 10
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "1 2 1 2 100 1000
"
    "200 100
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "17 19 22 26 55 2802
"
    "2634 934
")))


Measured memory_bytes: 29028