(defun prime-table (&optional (m 1000000000)) (let* ((thre (ceiling (sqrt m))) (flg (make-array (1+ thre) :initial-element nil)) (i 2) (res '())) (loop while (<= (* i i) thre) do (unless (aref flg i) (loop for j from (* i i) to thre by i do (setf (aref flg j) t))) (incf i)) (loop for i from 2 to thre do (unless (aref flg i) (push i res))) (nreverse res))) (defvar *prime-table* (prime-table)) (defun totient (n_) (let ((n n_) (res n_)) (dolist (p *prime-table*) (when (> (* p p) n) (return)) (when (zerop (mod n p)) (setq res (* (floor res p) (1- p))) (loop while (zerop (mod n p)) do (setf n (floor n p))))) (when (/= n 1) (setf res (* (floor res n) (1- n)))) res)) (defun mpow (a_ p_ m_) (let ((a a_) (p p_) (m m_) (flg t) (res (mod 1 m_))) (loop unless (zerop p) do (when (oddp p) (setf res (* res a)) (when (>= res m) (setf flg nil res (mod res m)))) (when (= p 1) (return)) (setf a (* a a)) (when (>= a m) (setf flg nil a (mod a m))) (setf p (ash p -1))) (cons flg res))) (defun tetration (a b m) (labels ((rec (aa bb mm) (cond ((= 0 aa) (cons t (logxor (logand bb 1) 1))) ((= 1 aa) (cons t 1)) ((= 1 mm) (cons nil 0)) ((= 0 bb) (cons t 1)) ((= 1 bb) (cons (< aa mm) (mod aa mm))) (t (let* ((phi-m (totient mm)) (flg1pre (rec aa (1- bb) phi-m)) (flg1 (car flg1pre)) (pre (cdr flg1pre)) (flg t) (res 0)) (if flg1 (let ((flgres (mpow (mod aa mm) pre mm))) (setf flg (car flgres) res (cdr flgres)) (cons (and flg flg1) res)) (let ((flgres (mpow (mod aa mm) (+ pre phi-m) mm))) (setf flg (car flgres) res (cdr flgres)) (cons (and flg flg1) res)))))))) (mod (cdr (rec a b m)) m))) (defun main (&rest argv) (declare (ignorable argv)) (let* ((query (read))) (dotimes (_ query) (let* ((a (read)) (n (read)) (m (read))) (format t "~d~%" (tetration a n m)))))) (main)