#-swank
(unless (member :child-sbcl *features*)
  (quit
   :unix-status
   (process-exit-code
    (run-program *runtime-pathname*
                 `("--control-stack-size" "128MB"
                   "--noinform" "--disable-ldb" "--lose-on-corruption" "--end-runtime-options"
                   "--eval" "(push :child-sbcl *features*)"
                   "--script" ,(namestring *load-pathname*))
                 :output t :error t :input t))))
(in-package :cl-user)
(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)

(defconstant +mod+ 1000000007)

(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))))

;; BEGIN_INSERTED_CONTENTS
;;;
;;; Minimum spanning tree (Boruvka's algorithm, O(ElogV))
;;;
;;; Reference:
;;; Ahuja, Magnanti, Orlin. Network Flows: Theory, Algorithms, and Applications.
;;;

(defpackage :cp/boruvka
  (:use :cl)
  (:export #:find-mst))
(in-package :cp/boruvka)

(defconstant +inf-cost+ most-positive-fixnum)

;; Here I express each connected component as a cycle with singly-linked list,
;; though Ahuja's book adopts doubly-linked list. I learned about this technique
;; in noshi91's article: http://noshi91.hatenablog.com/entry/2019/07/19/180606
;; (Japanese)

(declaim (inline find-mst)
         (ftype (function * (values (simple-array fixnum (*))
                                    (simple-array fixnum (*))
                                    (simple-array fixnum (*))
                                    &optional))
                find-mst))
(defun find-mst (graph &key (vertex-key #'car) (cost-key #'cdr) maximize)
  "Computes an MST by Boruvka's algorithm. Returns three values: a vector that
stores each cost of the edges, two vectors that store each end of the edges. If
GRAPH is not connected, this function computes MST for each connected component.

GRAPH := vector of adjacency lists
MAXIMIZE := if true, solve maximization problem instead"
  (declare (vector graph))
  (let* ((n (length graph))
         (roots (make-array n :element-type 'fixnum))
         ;; next node in a connected component
         (nexts (make-array n :element-type 'fixnum))
         (min-costs (make-array n :element-type 'fixnum))
         (min-srcs (make-array n :element-type 'fixnum))
         (min-dests (make-array n :element-type 'fixnum))
         (edge-count 0)
         (res-costs (make-array (max 0 (- n 1)) :element-type 'fixnum))
         (res-srcs (make-array (max 0 (- n 1)) :element-type 'fixnum))
         (res-dests (make-array (max 0 (- n 1)) :element-type 'fixnum)))
    (dotimes (i n)
      (setf (aref roots i) i
            (aref nexts i) i))
    (labels ((%add (src dest cost)
               "Adds a new edge to the (unfinished) MST."
               (declare (fixnum src dest cost))
               (when (> src dest) (rotatef src dest))
               (setf (aref res-srcs edge-count) src
                     (aref res-dests edge-count) dest
                     (aref res-costs edge-count) (if maximize (- cost) cost)
                     edge-count (+ edge-count 1)))
             (%merge (root1 root2)
               "Merges ROOT2 into ROOT1."
               (loop for v = (aref nexts root2) then (aref nexts v)
                     until (= v root2)
                     do (setf (aref roots v) root1)
                     finally (setf (aref roots v) root1))
               ;; meld two cycles
               (rotatef (aref nexts root1) (aref nexts root2))))
      (loop for updated = nil
            while (< edge-count (- n 1))
            do (fill min-costs +inf-cost+)
               ;; detect minimum cost edge starting from each connected component
               (dotimes (u n)
                 (let ((root (aref roots u)))
                   (dolist (edge (aref graph u))
                     (let ((v (funcall vertex-key edge))
                           (cost (funcall cost-key edge)))
                       (declare (fixnum v cost))
                       (when maximize (setq cost (- cost)))
                       (when (and (/= root (aref roots v))
                                  (<= cost (aref min-costs root)))
                         (setf (aref min-costs root) cost
                               (aref min-srcs root) u
                               (aref min-dests root) v))))))
               ;; merge all the pairs of connected components linked with above
               ;; enumerated edges
               (dotimes (v n)
                 (let* ((root (aref roots v))
                        (src (aref min-srcs root))
                        (dest (aref min-dests root))
                        (cost (aref min-costs root)))
                   (unless (= cost +inf-cost+) ; can be true if GRAPH is not connected
                     (loop for root2 = (aref roots dest)
                           until (= root root2)
                           do (setq updated t)
                              (%add src dest cost)
                              (%merge root root2)
                              (setq src (aref min-srcs root2)
                                    dest (aref min-dests root2)
                                    cost (aref min-costs root2))))))
            while updated)
      (values (adjust-array res-costs edge-count)
              (adjust-array res-srcs edge-count)
              (adjust-array res-dests edge-count)))))

(defpackage :cp/mod-power
  (:use :cl)
  (:export #:mod-power))
(in-package :cp/mod-power)

(declaim (inline mod-power))
(defun mod-power (base power modulus)
  "Returns BASE^POWER mod MODULUS. Note: 0^0 = 1.

BASE := integer
POWER, MODULUS := non-negative fixnum"
  (declare ((integer 0 #.most-positive-fixnum) modulus power)
           (integer base))
  (let ((base (mod base modulus))
        (res (mod 1 modulus)))
    (declare ((integer 0 #.most-positive-fixnum) base res))
    (loop while (> power 0)
          when (oddp power)
          do (setq res (mod (* res base) modulus))
          do (setq base (mod (* base base) modulus)
                   power (ash power -1)))
    res))


;;;
;;; Arithmetic operations with static modulus
;;;

(defpackage :cp/mod-operations
  (:use :cl)
  (:export #:define-mod-operations))
(in-package :cp/mod-operations)

;; NOTE: Currently MOD* and MOD+ doesn't apply MOD when the number of
;; parameters is one. For simplicity I won't fix it for now.
(defmacro define-mod-operations (divisor)
  (let ((mod* (intern "MOD*"))
        (mod+ (intern "MOD+"))
        (incfmod (intern "INCFMOD"))
        (decfmod (intern "DECFMOD"))
        (mulfmod (intern "MULFMOD")))
    `(progn
       (defun ,mod* (&rest args)
         (reduce (lambda (x y) (mod (* x y) ,divisor)) args))

       (defun ,mod+ (&rest args)
         (reduce (lambda (x y) (mod (+ x y) ,divisor)) args))

       #+sbcl
       (eval-when (:compile-toplevel :load-toplevel :execute)
         (locally (declare (sb-ext:muffle-conditions warning))
           (sb-c:define-source-transform ,mod* (&rest args)
             (if (null args)
                 1
                 (reduce (lambda (x y) `(mod (* ,x ,y) ,',divisor)) args)))
           (sb-c:define-source-transform ,mod+ (&rest args)
             (if (null args)
                 0
                 (reduce (lambda (x y) `(mod (+ ,x ,y) ,',divisor)) args)))))

       (define-modify-macro ,incfmod (delta)
         (lambda (x y) (mod (+ x y) ,divisor)))

       (define-modify-macro ,decfmod (delta)
         (lambda (x y) (mod (- x y) ,divisor)))

       (define-modify-macro ,mulfmod (multiplier)
         (lambda (x y) (mod (* x y) ,divisor))))))

(defpackage :cp/read-fixnum
  (:use :cl)
  (:export #:read-fixnum))
(in-package :cp/read-fixnum)

(declaim (ftype (function * (values fixnum &optional)) read-fixnum))
(defun read-fixnum (&optional (in *standard-input*))
  "NOTE: cannot read -2^62"
  (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))))))))

;;;
;;; Disjoint set (union by size & path compression)
;;;

(defpackage :cp/disjoint-set
  (:use :cl)
  (:export #:disjoint-set #:make-disjoint-set #:ds-data
           #:ds-root #:ds-unite! #:ds-connected-p #:ds-size))
(in-package :cp/disjoint-set)

(defstruct (disjoint-set
            (:constructor make-disjoint-set
                (size &aux (data (make-array size :element-type 'fixnum :initial-element -1))))
            (:conc-name ds-)
            (:predicate nil)
            (:copier nil))
  (data nil :type (simple-array fixnum (*))))

(declaim (inline ds-root))
(defun ds-root (disjoint-set x)
  "Returns the root of X."
  (declare ((mod #.array-total-size-limit) x))
  (let ((data (ds-data disjoint-set)))
    (labels ((recur (x)
               (if (< (aref data x) 0)
                   x
                   (setf (aref data x)
                         (recur (aref data x))))))
      (recur x))))

(declaim (inline ds-unite!))
(defun ds-unite! (disjoint-set x1 x2)
  "Destructively unites X1 and X2 and returns true iff X1 and X2 become
connected for the first time."
  (let ((root1 (ds-root disjoint-set x1))
        (root2 (ds-root disjoint-set x2)))
    (unless (= root1 root2)
      (let ((data (ds-data disjoint-set)))
        ;; NOTE: If you want X1 to always be root, just delete this form. (Time
        ;; complexity becomes worse, however.)
        (when (> (aref data root1) (aref data root2))
          (rotatef root1 root2))
        (incf (aref data root1) (aref data root2))
        (setf (aref data root2) root1)))))

(declaim (inline ds-connected-p))
(defun ds-connected-p (disjoint-set x1 x2)
  "Returns true iff X1 and X2 have the same root."
  (= (ds-root disjoint-set x1) (ds-root disjoint-set x2)))

(declaim (inline ds-size))
(defun ds-size (disjoint-set x)
  "Returns the size of the connected component to which X belongs."
  (- (aref (ds-data disjoint-set)
           (ds-root disjoint-set x))))

;;;
;;; Sort multiple vectors
;;;

(defpackage :cp/parallel-sort
  (:use :cl)
  (:export #:parallel-sort!))
(in-package :cp/parallel-sort)

;; TODO: throw an error if there are two ore more identical vectors in the given
;; vectors

(declaim (inline %median3))
(defun %median3 (x y z order)
  (if (funcall order x y)
      (if (funcall order y z)
          y
          (if (funcall order z x)
              x
              z))
      (if (funcall order z y)
          y
          (if (funcall order x z)
              x
              z))))

(defun parallel-sort! (vector order &rest vectors)
  "Destructively sorts VECTOR w.r.t. ORDER and applies the same permutation to
all the vectors in VECTORS.

Note: not randomized; shuffle the inputs if necessary"
  (declare (vector vector))
  (labels
      ((recur (left right)
         (when (< left right)
           (let* ((l left)
                  (r right)
                  (pivot (%median3 (aref vector l)
                                   (aref vector (ash (+ l r) -1))
                                   (aref vector r)
                                   order)))
             (declare ((integer 0 #.most-positive-fixnum) l r))
             (loop (loop while (funcall order (aref vector l) pivot)
                         do (incf l 1))
                   (loop while (funcall order pivot (aref vector r))
                         do (decf r 1))
                   (when (>= l r)
                     (return))
                   (rotatef (aref vector l) (aref vector r))
                   (dolist (v vectors)
                     (rotatef (aref v l) (aref v r)))
                   (incf l 1)
                   (decf r 1))
             (recur left (- l 1))
             (recur (+ r 1) right)))))
    (recur 0 (- (length vector) 1))
    vector))

#+sbcl
(eval-when (:compile-toplevel :load-toplevel :execute)
  (locally (declare (sb-ext:muffle-conditions warning))
    (sb-c:define-source-transform parallel-sort! (vector order &rest vectors)
      (let ((vec (gensym))
            (vecs (loop for _ in vectors collect (gensym))))
        `(let ((,vec ,vector)
               ,@(loop for v in vectors
                       for sym in vecs
                       collect `(,sym ,v)))
           (labels
               ((recur (left right)
                  (when (< left right)
                    (let* ((l left)
                           (r right)
                           (pivot (%median3 (aref ,vec l)
                                            (aref ,vec (ash (+ l r) -1))
                                            (aref ,vec r)
                                            ,order)))
                      (declare ((integer 0 #.most-positive-fixnum) l r))
                      (loop (loop while (funcall ,order (aref ,vec l) pivot)
                                  do (incf l 1))
                            (loop while (funcall ,order pivot (aref ,vec r))
                                  do (decf r 1))
                            (when (>= l r)
                              (return))
                            (rotatef (aref ,vec l) (aref ,vec r))
                            ,@(loop for sym in vecs
                                    collect `(rotatef (aref ,sym l) (aref ,sym r)))
                            (incf l 1)
                            (decf r 1))
                      (recur left (- l 1))
                      (recur (+ r 1) right)))))
             (recur 0 (- (length ,vec) 1))
             ,vec))))))

;; BEGIN_USE_PACKAGE
(eval-when (:compile-toplevel :load-toplevel :execute)
  (use-package :cp/parallel-sort :cl-user))
(eval-when (:compile-toplevel :load-toplevel :execute)
  (use-package :cp/disjoint-set :cl-user))
(eval-when (:compile-toplevel :load-toplevel :execute)
  (use-package :cp/read-fixnum :cl-user))
(eval-when (:compile-toplevel :load-toplevel :execute)
  (use-package :cp/mod-operations :cl-user))
(eval-when (:compile-toplevel :load-toplevel :execute)
  (use-package :cp/mod-power :cl-user))
(eval-when (:compile-toplevel :load-toplevel :execute)
  (use-package :cp/boruvka :cl-user))
(in-package :cl-user)

;;;
;;; Body
;;;

(define-mod-operations +mod+)
(defun main ()
  (let* ((n (read))
         (m (read))
         (x (read))
         (us (make-array m :element-type 'uint31 :initial-element 0))
         (vs (make-array m :element-type 'uint31 :initial-element 0))
         (zs (make-array m :element-type 'uint31 :initial-element 0))
         (res 0))
    (declare (uint31 n m x res))
    (dotimes (i m)
      (let ((x (- (read-fixnum) 1))
            (y (- (read-fixnum) 1))
            (z (read-fixnum)))
        (setf (aref us i) x
              (aref vs i) y
              (aref zs i) z)))
    (parallel-sort! zs #'< us vs)
    (let ((dset (make-disjoint-set n))
          (graph (make-array n :element-type 'list :initial-element nil))
          (sizes (make-array n :element-type 'uint31 :initial-element 0)))
      (loop for u across us
            for v across vs
            for z across zs
            for cost = (mod-power x z +mod+)
            when (ds-unite! dset u v)
            do (push (cons u cost) (aref graph v))
               (push (cons v cost) (aref graph u)))
      (sb-int:named-let dfs ((v 0) (parent -1))
        (let ((value 1))
          (loop for (child . cost) in (aref graph v)
                unless (= child parent)
                do (dfs child v)
                   (incf value (aref sizes child)))
          (setf (aref sizes v) value)))
      #>sizes
      (sb-int:named-let dfs ((v 0) (parent -1))
        (loop for (child . cost) of-type (uint31 . uint31) in (aref graph v)
              for size1 = (aref sizes child)
              for size2 of-type uint31 = (- n size1)
              unless (= child parent)
              do (incfmod res (mod* cost size1 size2))
                 (dfs child v))))
    (println res)))

#-swank (main)

;;;
;;; Test and benchmark
;;;

#+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* (or out (make-string-output-stream)))
         (res (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))))))
    (if out res (get-output-stream-string *standard-output*))))

#+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
   (equal "8
"
          (run "3 2 3
1 2 0
2 3 1
" nil)))
  (it.bese.fiveam:is
   (equal "2660500
"
          (run "5 5 5
1 4 3
2 4 4
3 5 7
2 3 8
2 3 10
" nil)))
  (it.bese.fiveam:is
   (equal "524978526
"
          (run "6 8 1000000
2 6 10
3 5 11
4 6 23
1 3 26
1 6 30
5 6 48
3 5 88
3 6 100
" nil))))