#include<bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef vector<ll> vll;
typedef vector<vector<ll>> vvll;
typedef vector<vector<vector<ll>>> vvvll;
typedef vector<bool> vb;
typedef vector<vector<bool>> vvb;
typedef vector<vector<vector<bool>>> vvvb;
typedef pair<ll, ll> pll;
typedef vector<pll> vpll;
typedef vector<vpll> vvpll;
typedef vector<double> vd;
typedef vector<vd> vdd;

#define FOR(i,x,y) for(ll i=(ll)x; i<(ll)y; ++i)
#define REP(i,y) FOR(i, 0, y)
#define RFOR(i,x,y) for(ll i=(ll)x; i>=(ll)y; --i)
#define RREP(i,x) RFOR(i, x, 0)
#define ALL(a) a.begin(), a.end()
#define pb push_back
#define debug_print(x...) cerr << "line " << __LINE__ << " : "; debug_print_in(x);

template <typename First>
void debug_print_in(First first){
  cerr << first << endl;
  return;
}

template <typename First, typename... Rest>
void debug_print_in(First first, Rest... rest){
  cerr << first << " ";
  debug_print_in(rest...);
  return;
}

void IN(void){
  return;
}

template <typename First, typename... Rest>
void IN(First& first, Rest&... rest){
  cin >> first;
  IN(rest...);
  return;
}

template <typename First>
void OUT(First first){
  cout << first << endl;
  return;
}

template <typename First, typename... Rest>
void OUT(First first, Rest... rest){
  cout << first << " ";
  OUT(rest...);
  return;
}

template<class t, class u> void chmax(t&a,u b){if(a<b)a=b;};
template<class t, class u> void chmin(t&a,u b){if(a>b)a=b;};
int popcount(int t){return __builtin_popcount(t);} //GCC
int popcount(ll t){return __builtin_popcountll(t);} //GCC

template <typename T>
void vec_print(vector<T> VEC){
  REP(i, VEC.size()){
    cerr << VEC[i] << " ";
  }
  cerr << endl;
};

template <typename T>
void mat_print(vector<vector<T> > MAT){
  REP(i,MAT.size()){
    REP(j,MAT[i].size()){
      cerr << MAT[i][j] << " ";
    }
    cerr << endl;
  }
};

constexpr int INF = (1<<30);
constexpr ll INFLL = 1LL<<62;
constexpr long double EPS = 1e-12;
constexpr ll MOD = (ll)((1E+9)+7);

ll K, Q;
vll d;

int main(){
  cin.tie(0); // cut the cin and cout (default, std::flush is performed after std::cin)
  ios::sync_with_stdio(false); // cut the iostream and stdio (DON'T endl; BUT "\n";)

  IN(K,Q);
  d.resize(K);
  REP(k,K) IN(d[k]);

  REP(q,Q){
    ll n, x, m;
    IN(n,x,m);

    vll zero_count(K, 0);
    vll d_sum(K, 0);
    if(d[0]%m == 0) zero_count[0] = 1;
    FOR(k,1,K){
      zero_count[k] = zero_count[k-1];
      if(d[k]%m==0) zero_count[k]+=1;
    }
    d_sum[0] = d[0]%m;
    FOR(k,1,K){
      d_sum[k] += d_sum[k-1] + d[k]%m;
    }

    //vec_print(zero_count);

    ll num_of_zero = 0;
    num_of_zero += zero_count[K-1]*((n-2)/K);
    num_of_zero += zero_count[(n-2)%K];

    debug_print(num_of_zero);

    ll a_min = x;
    ll a_max = x + d_sum[K-1]*((n-2)/K);
    a_max += d_sum[(n-2)%K];

    debug_print(a_min, a_max);

    /*
    ll b_max = a_max/m;
    if(a_min%m==0) a_min++;
    ll b_min = a_min/m;
    //if(b_min>b_max) b_min=b_max;

    debug_print(b_min, b_max);

    ll m_count = b_max-b_min;
    */

    ll b_min = a_min/m;
    ll b_max = a_max/m;
    ll m_count = b_max - b_min;

    debug_print(m_count);

    OUT((n-1)-num_of_zero-m_count);
  }

  return 0;
}

Measured memory_bytes: 512