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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

#!/usr/bin/env python3

import sys

debug = False

def solve(ds, n, x, m):
    ds = [d % m for d in ds]

    nr_loop = (n - 1) // len(ds)
    lastloop_remaining = (n - 1) % len(ds)
    a_n = x
    cnt_zero = 0
    for i in range(0, len(ds)):
        dmod = ds[i] % m
        a_n += (dmod) * nr_loop
        if dmod == 0:
            cnt_zero += nr_loop
        if i < lastloop_remaining:
            a_n += dmod
            if dmod == 0:
                cnt_zero += 1
    cnt_decrease = a_n // m - x // m
    return n - 1 - cnt_decrease - cnt_zero


def read_int_list(sep = " "):
    return [int(s) for s in sys.stdin.readline().split(sep)]


def dprint(*args, **kwargs):
    if debug:
        print(*args, **kwargs)
    return


def main():
    k, q = read_int_list()
    d = read_int_list()
    for _ in range(0, q):
        n, x, m = read_int_list()
        print(str(solve(d, n, x, m)))
    

if __name__ == "__main__":
    main()