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 Ruby (2.3.3) (judge verdict: Wrong Answer)

k, q = gets.chomp.split(' ').map{|i| i.to_i }
d = gets.chomp.split(' ').map{|i| i.to_i }

q.times{|i|
  n, x, m = gets.chomp.split(' ').map{|i| i.to_i }

  dans = 0
  danss = [0]

  dsummodms = [d[0] % m]
  (k - 1).times{|jj|
    j = jj + 1
    dsummodms[j] = (dsummodms[j - 1] + d[j]) % m
    dans += 1 if dsummodms[j - 1] < dsummodms[j]
    danss[j] = dans
  }
  danss[0] = 1 if dsummodms[k - 1] < dsummodms[0]

  nmodk = n % k
  sets = (n - nmodk) / k
  # p dsummodms
  # p danss
  # p [nmodk, sets]
  puts dans * sets + (sets - (nmodk == 0 ? 1 : 0)) * danss[0]
}