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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Control.Monad
import qualified Data.Vector as V

main = do
  [k, q] <- map read.words <$> getLine
  d <- V.fromList.map read.words <$> getLine
  nxm <- replicateM q $ map read.words <$> getLine
  mapM_ (print.solve k d) nxm

count :: Eq a => a -> V.Vector a -> Int
count a v = V.length $ V.elemIndices a v

solve :: Int -> V.Vector Int -> [Int] -> Int
solve k d' [n, x, m] = n - 1 - eqs - gts where
  d = V.map (`rem` m) d'
  eqs = count 0 d * quot (n-1) k + count 0 (V.take (rem (n-1) k) d)
  gts = quot alast m - quot x m
  alast = V.foldl (+) x dcnt
  (nq, nr) = quotRem (n-1) k
  cnt i | i < nr = nq + 1
        | otherwise = nq
  dcnt = V.map f $ V.indexed d
  f (i, d) = cnt i * d