;; -*- 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
;;;
;;; Complement to the bitwise operations in CLHS
;;;

(eval-when (:compile-toplevel :load-toplevel :execute)
  (assert (= sb-vm:n-word-bits 64)))

;; KLUDGE: a variant of DPB that handles a 64-bit word efficiently
(defmacro u64-dpb (new spec int)
  (destructuring-bind (byte s p) spec
    (assert (eql 'byte byte))
    (let ((size (gensym)) (posn (gensym)) (mask (gensym)))
      `(let* ((,size ,s)
              (,posn ,p)
              (,mask (ldb (byte ,size 0) -1)))
         (logior (the (unsigned-byte 64) (ash (logand ,new ,mask) ,posn))
                 (the (unsigned-byte 64) (logand ,int (lognot (ash ,mask ,posn)))))))))

(defconstant +most-positive-word+ #.(- (ash 1 64) 1))

(defun bit-not! (sb-vector &optional (start 0) end)
  "Destructively flips the bits in the range [START, END)."
  (declare (optimize (speed 3))
           (simple-bit-vector sb-vector)
           ((integer 0 #.most-positive-fixnum) start)
           ((or null (integer 0 #.most-positive-fixnum)) end))
  (setq end (or end (length sb-vector)))
  (assert (<= start end (length sb-vector)))
  (multiple-value-bind (start/64 start%64) (floor start 64)
    (multiple-value-bind (end/64 end%64) (floor end 64)
      (declare (optimize (safety 0)))
      (if (= start/64 end/64)
          (setf (sb-kernel:%vector-raw-bits sb-vector start/64)
                (u64-dpb (ldb (byte (- end%64 start%64) start%64)
                              (logxor +most-positive-word+ (sb-kernel:%vector-raw-bits sb-vector start/64)))
                         (byte (- end%64 start%64) start%64)
                         (sb-kernel:%vector-raw-bits sb-vector start/64)))
          (progn
            (setf (sb-kernel:%vector-raw-bits sb-vector start/64)
                  (dpb (sb-kernel:%vector-raw-bits sb-vector start/64)
                       (byte start%64 0)
                       (logxor +most-positive-word+ (sb-kernel:%vector-raw-bits sb-vector start/64))))
            (loop for i from (+ 1 start/64) below end/64
                  do (setf (sb-kernel:%vector-raw-bits sb-vector i)
                           (logxor +most-positive-word+ (sb-kernel:%vector-raw-bits sb-vector i))))
            (unless (zerop end%64)
              (setf (sb-kernel:%vector-raw-bits sb-vector end/64)
                    (dpb (logxor +most-positive-word+ (sb-kernel:%vector-raw-bits sb-vector end/64))
                         (byte end%64 0)
                         (sb-kernel:%vector-raw-bits sb-vector end/64))))))))
  sb-vector)

;; (count 1 simple-bit-vector) is sufficiently fast on SBCL when handling whole
;; vector. If START or END are specified, however, it is slow as the transformer
;; for COUNT doesn't work. See
;; https://github.com/sbcl/sbcl/blob/cd7af0d5b15e98e21ace8ef164e0f39019e5ed4b/src/compiler/generic/vm-tran.lisp#L484-L527
(defun bit-count (sb-vector &optional (start 0) end)
  "Counts 1's in the range [START, END)."
  (declare (optimize (speed 3))
           (simple-bit-vector sb-vector)
           ((integer 0 #.most-positive-fixnum) start)
           ((or null (integer 0 #.most-positive-fixnum)) end))
  (setq end (or end (length sb-vector)))
  (assert (<= start end (length sb-vector)))
  (multiple-value-bind (start/64 start%64) (floor start 64)
    (multiple-value-bind (end/64 end%64) (floor end 64)
      (declare (optimize (safety 0)))
      (if (= start/64 end/64)
          (logcount (ldb (byte (- end%64 start%64) start%64)
                         (sb-kernel:%vector-raw-bits sb-vector start/64)))
          (let ((result 0))
            (declare ((integer 0 #.most-positive-fixnum) result))
            (incf result (logcount (ldb (byte (- 64 start%64) start%64)
                                        (sb-kernel:%vector-raw-bits sb-vector start/64))))
            (loop for i from (+ 1 start/64) below end/64
                  do (incf result (logcount (sb-kernel:%vector-raw-bits sb-vector i))))
            (unless (zerop end%64)
              (incf result (logcount (ldb (byte end%64 0)
                                          (sb-kernel:%vector-raw-bits sb-vector end/64)))))
            result)))))

;; unfinished
;; (defun bit-shift (bit-vector delta &optional result-vector)
;;   "Shifts BIT-VECTOR by DELTA bits and fills the new bits with zero. Positive
;; DELTA means left-shifting and negative DELTA means right-shifting.

;; The behaviour is the same as the bit-wise operations in CLHS: The result is
;; copied to RESULT-VECTOR; if it is T, BIT-VECTOR is destructively modified; if it
;; is NIL, a new bit-vector of the same length is created."
;;   (declare (simple-bit-vector bit-vector)
;;            ((or null (eql t) simple-bit-vector) result-vector)
;;            (fixnum delta))
;;   (setq result-vector
;;         (etypecase result-vector
;;           (null (make-array (length bit-vector) :element-type 'bit :initial-element 0))
;;           ((eql t) bit-vector)
;;           (simple-bit-vector result-vector)))
;;   (when (>= delta 0)
;;     (return-from bit-shift (bit-lshift bit-vector delta result-vector)))
;;   (let* ((delta (- delta))
;;          (end (length bit-vector)))
;;     (unless (zerop end)
;;       (multiple-value-bind (d/64 d%64) (floor delta 64)
;;         (multiple-value-bind (end/64 end%64) (floor end 64)
;;           ;; process the initial word separately
;;           (when (and (> d%64 0) (< d/64 (ceiling end 64)))
;;             (setf (ldb (byte (- 64 d%64) 0)
;;                        (sb-kernel:%vector-raw-bits result-vector 0))
;;                   (ldb (byte (- 64 d%64) d%64)
;;                        (sb-kernel:%vector-raw-bits bit-vector d/64))))
;;           (do ((i (ceiling delta 64) (+ i 1)))
;;               ((>= i end/64))
;;             (setf (ldb (byte d%64 (- 64 d%64))
;;                        (sb-kernel:%vector-raw-bits result-vector (- i d/64 1)))
;;                   (ldb (byte d%64 0)
;;                        (sb-kernel:%vector-raw-bits bit-vector i)))
;;             (setf (ldb (byte (- 64 d%64) 0)
;;                        (sb-kernel:%vector-raw-bits result-vector (- i d/64)))
;;                   (ldb (byte (- 64 d%64) d%64)
;;                        (sb-kernel:%vector-raw-bits bit-vector i))))
;;           ;; process the last word separately
;;           (unless (zerop end%64)
;;             (setf (ldb (byte d%64 (- 64 d%64))
;;                        (sb-kernel:%vector-raw-bits result-vector (- end/64 d/64 1)))
;;                   (ldb (byte (min d%64 end%64) 0)
;;                        (sb-kernel:%vector-raw-bits bit-vector end/64)))
;;             (setf (ldb (byte (- 64 d%64) 0)
;;                        (sb-kernel:%vector-raw-bits result-vector (- end/64 d/64)))
;;                   (ldb (byte (max 0 (- end%64 d%64)) d%64)
;;                        (sb-kernel:%vector-raw-bits bit-vector end/64)))))))
;;     result-vector))

;; TODO: right shift
(defun bit-lshift (bit-vector delta &optional result-vector end)
  "Left-shifts BIT-VECTOR by DELTA bits and fills the new bits with zero.
The behaviour is the same as the bit-wise operations in CLHS: The result is
copied to RESULT-VECTOR; if it is T, BIT-VECTOR is destructively modified; if it
is NIL, a new bit-vector of the same length is created. If END is specified,
this function shifts only the range [0, END) of BIT-VECTOR and copies it to the
range [0, END+DELTA) of RESULT-VECTOR.

Note that here `left' means the direction from a smaller index to a larger one,
i.e. (bit-lshift #*1011000 2) |-> #*0010110"
  (declare (optimize (speed 3))
           (simple-bit-vector bit-vector)
           ((or null (eql t) simple-bit-vector) result-vector)
           ((integer 0 #.most-positive-fixnum) delta)
           ((or null (integer 0 #.most-positive-fixnum)) end))
  (setq result-vector
        (etypecase result-vector
          (null (make-array (length bit-vector) :element-type 'bit :initial-element 0))
          ((eql t) bit-vector)
          (simple-bit-vector result-vector)))
  (setq end (or end (length bit-vector)))
  (assert (<= end (length bit-vector)))
  (setq end (min end (max 0 (- (length result-vector) delta))))
  (multiple-value-bind (d/64 d%64) (floor delta 64)
    (declare (optimize (safety 0))
             (simple-bit-vector result-vector))
    (multiple-value-bind (end/64 end%64) (floor end 64)
      ;; process the last word separately
      (unless (zerop end%64)
        (let ((word (sb-kernel:%vector-raw-bits bit-vector end/64)))
          (setf (sb-kernel:%vector-raw-bits result-vector (+ end/64 d/64))
                (u64-dpb word
                         (byte (min end%64 (- 64 d%64)) d%64)
                         (sb-kernel:%vector-raw-bits result-vector (+ end/64 d/64))))
          (when (> end%64 (- 64 d%64))
            (setf (ldb (byte (- end%64 (- 64 d%64)) 0)
                       (sb-kernel:%vector-raw-bits result-vector (+ 1 end/64 d/64)))
                  (ldb (byte (- end%64 (- 64 d%64)) (- 64 d%64)) word)))))
      ;; Body. We avoid LDB and DPB here for efficiency, though this seems to
      ;; be somewhat incomprehensible...
      (let* ((mask0 (ldb (byte 64 0) (lognot (ldb (byte d%64 0) -1))))
             (mask1-lo (ldb (byte (- 64 d%64) 0) -1))
             (mask1-hi (ldb (byte 64 0) (lognot (ash mask1-lo d%64)))))
        (declare ((unsigned-byte 64) mask0 mask1-lo mask1-hi))
        (do ((i (- end/64 1) (- i 1)))
            ((< i 0))
          (let ((word (sb-kernel:%vector-raw-bits bit-vector i))
                (i+d/64 (+ i d/64)))
            (declare ((unsigned-byte 64) word)
                     ((mod #.most-positive-fixnum) i+d/64))
            (setf (sb-kernel:%vector-raw-bits result-vector i+d/64)
                  (logior (the (unsigned-byte 64)
                               (ash (logand word mask1-lo) d%64))
                          (logand (sb-kernel:%vector-raw-bits result-vector i+d/64)
                                  mask1-hi)))
            (setf (sb-kernel:%vector-raw-bits result-vector (+ 1 i+d/64))
                  (logior (ash word (- d%64 64))
                          (logand (sb-kernel:%vector-raw-bits result-vector (+ 1 i+d/64))
                                  mask0))))))
      ;; zero padding
      (when (< d/64 (ceiling (length result-vector) 64))
        (setf (ldb (byte d%64 0) (sb-kernel:%vector-raw-bits result-vector d/64)) 0))
      ;; REVIEW: May we set the last word of a bit vector to zero beyond the
      ;; actual bound?
      (dotimes (i (min d/64 (ceiling (length result-vector) 64)))
        (setf (sb-kernel:%vector-raw-bits result-vector i) 0))
      result-vector)))

;; We must implement the right shift beforehand.
;; (defun bit-rotate (bit-vector delta &optional result-vector)
;;   (declare (optimize (speed 3))
;;            ((integer 0 #.most-positive-fixnum) delta)
;;            (simple-bit-vector bit-vector)
;;            ((or null simple-bit-vector) result-vector))
;;   (assert (not (eql bit-vector result-vector)))
;;   (let* ((end (length bit-vector))
;;          (result-vector (or result-vector (make-array end :element-type 'bit)))
;;          (delta (mod delta end)))
;;     :unfinished))

(defun bench (size sample)
  (declare ((unsigned-byte 32) size sample))
  (let ((seq (make-array size :element-type 'bit))
        (state (sb-ext:seed-random-state 0)))
    (gc :full t)
    (time (loop repeat sample
                sum (aref (bit-lshift seq (random 128 state)) 0) of-type bit))))

(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 solve (a b c)
  (when (= c 1)
    (return-from solve -1))
  (sb-int:named-let recur ((a a) (res 0))
    (if (zerop a)
        res
        (if (<= a (- c 1))
            (+ res b)
            (if (<= a (* 2 (- c 1)))
                (+ res b b)
                (multiple-value-bind (quot rem) (floor a c)
                  (if (zerop rem)
                      (recur quot (+ res b))
                      (recur (- a rem) (+ res b)))))))))

(define-modify-macro minf (new-value) min)
(defun test (a c)
  (let ((dp (make-array 200 :element-type 'uint32 :initial-element #xffffffff)))
    (dotimes (i c)
      (setf (aref dp i) 1))
    (loop repeat 200
          do (loop for i from 1 below (length dp)
                   do (unless (zerop (aref dp i))
                        (loop for j from 1 below c
                              while (< (+ i j) (length dp))
                              do (minf (aref dp (+ i j))
                                       (+ 1 (aref dp i))))
                        (when (< (* i c) (length dp))
                          (minf (aref dp (* i c))
                                (+ 1 (aref dp i)))))))
    (let ((dp2 (make-array 200)))
      (setf (aref dp2 0) 1)
      (loop for i from 1 below (length dp)
            do (setf (aref dp2 i) (solve i 1 c)))
      (values dp dp2)
      (equalp dp dp2))))

(defun main ()
  (let ((q (read)))
    (dotimes (_ q)
      (let* ((a (read))
             (b (read))
             (c (read)))
        ;; (dbg a b c)
        (println (solve a b c))))))

#-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)))