Problem:
Score : 600 points

Problem Statement

We have a sequence of k numbers: d_0,d_1,...,d_{k - 1}.

Process the following q queries in order:

The i-th query contains three integers n_i, x_i, and m_i.
Let a_0,a_1,...,a_{n_i - 1} be the following sequence of n_i numbers: \begin{eqnarray} a_j = \begin{cases} x_i & ( j = 0 ) \\ a_{j - 1} + d_{(j - 1)~\textrm{mod}~k} & ( 0 < j \leq n_i - 1 ) \end{cases}\end{eqnarray}
Print the number of j~(0 \leq j < n_i - 1) such that (a_j~\textrm{mod}~m_i) < (a_{j + 1}~\textrm{mod}~m_i).

Here (y~\textrm{mod}~z) denotes the remainder of y divided by z, for two integers y and z~(z > 0).

Constraints

All values in input are integers.

1 \leq k, q \leq 5000

0 \leq d_i \leq 10^9

2 \leq n_i \leq 10^9

0 \leq x_i \leq 10^9

2 \leq m_i \leq 10^9

Input

Input is given from Standard Input in the following format:

k q
d_0 d_1 ... d_{k - 1}
n_1 x_1 m_1
n_2 x_2 m_2
:
n_q x_q m_q

Output

Print q lines.

The i-th line should contain the response to the i-th query.

Sample Input 1

3 1
3 1 4
5 3 2

Sample Output 1

1

For the first query, the sequence {a_j} will be 3,6,7,11,14.

(a_0~\textrm{mod}~2) > (a_1~\textrm{mod}~2)

(a_1~\textrm{mod}~2) < (a_2~\textrm{mod}~2)

(a_2~\textrm{mod}~2) = (a_3~\textrm{mod}~2)

(a_3~\textrm{mod}~2) > (a_4~\textrm{mod}~2)

Thus, the response to this query should be 1.

Sample Input 2

7 3
27 18 28 18 28 46 1000000000
1000000000 1 7
1000000000 2 10
1000000000 3 12

Sample Output 2

224489796
214285714
559523809

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Time Limit Exceeded)

#-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))))

(defparameter *hash-memo* (make-hash-table :test #'equal))

(defmacro dp (&body func)
  `(let* ((f (quote func))
          (num (gethash f *hash-memo*)))
     (if num
       num
       (setf (gethash f *hash-memo*) ,func))))

(defun split (x str)
  (let ((pos (search x str))
        (size (length x)))
    (if pos
      (cons (subseq str 0 pos)
            (split x (subseq str (+ pos size))))
      (list str))))

(defun count-zeros (a m)
  (loop for i in a sum (if (zerop (car i)) (cdr i) 0)))

(defun culc-sum (a init)
  (+ init (loop for i in a sum (* (car i) (cdr i)))))
(labels ((count-zeros (a m)
                      (loop for i in a sum (if (zerop (car i)) (cdr i) 0)))
         (culc-sum (a init)
                   (+ init (loop for i in a sum (* (car i) (cdr i))))))

  (let* ((d (read))
         (querys (read))
         (a (loop repeat d collect (read))))
    (dotimes (query-cnt querys)
      (let* ((n (1- (read)))
             (x (read))
             (m (read))
             (ca (loop for i below d
                       for j in a
                       collect
                       (cons (mod j m) (floor (- (+ n d) i 1) d)))))
        (format t "~a~%" (- n (count-zeros ca m) (floor (culc-sum ca (mod x m)) m)))))))