#include <bits/stdc++.h>
#ifdef LOCAL_DEBUG
#define DEBUG 1
#define CERR if(DEBUG) cerr
#define MACRO(_1,_2,_3,_4,_5,_6,_7,_8,_9,_10,NAME,...) NAME
#define pr(...) CERR<<MACRO(__VA_ARGS__,pr10,pr9,pr8,pr7,pr6,pr5,pr4,pr3,pr2,pr1)(__VA_ARGS__)<<endl
#define pr1(a) (#a)<<"="<<(a)<<" "
#define pr2(a,b) pr1(a)<<pr1(b)
#define pr3(a,b,c) pr1(a)<<pr2(b,c)
#define pr4(a,b,c,d) pr1(a)<<pr3(b,c,d)
#define pr5(a,b,c,d,e) pr1(a)<<pr4(b,c,d,e)
#define pr6(a,b,c,d,e,f) pr1(a)<<pr5(b,c,d,e,f)
#define pr7(a,b,c,d,e,f,g) pr1(a)<<pr6(b,c,d,e,f,g)
#define pr8(a,b,c,d,e,f,g,h) pr1(a)<<pr7(b,c,d,e,f,g,h)
#define pr9(a,b,c,d,e,f,g,h,i) pr1(a)<<pr8(b,c,d,e,f,g,h,i)
#define pr10(a,b,c,d,e,f,g,h,i,j) pr1(a)<<pr9(b,c,d,e,f,g,h,i,j)
#define prArr(a){CERR<<(#a)<<"={";int i=0;for(auto t:(a))CERR<<(i++?", ":"")<<t;CERR<<"}"<<endl;}
#else
#define DEBUG 0
#define pr(...)
#define prArr(a)
#endif
using namespace std;
using Int = long long;
using _int = int;
using ll = long long;
using Double = long double;
const Int INF = (1LL<<60)+1e9; // ~ 1.15 * 1e18
const Int mod = (1e9)+7;
const Double EPS = 1e-8;
const Double PI = 6.0 * asin((Double)0.5);
using P = pair<Int,Int>;
template<class T> T Max(T &a,T b){return a=max(a,b);}
template<class T> T Min(T &a,T b){return a=min(a,b);}
template<class T1, class T2> ostream& operator<<(ostream& o,pair<T1,T2> p){return o<<"("<<p.first<<","<<p.second<<")";}
template<class T1, class T2, class T3> ostream& operator<<(ostream& o,tuple<T1,T2,T3> t){return o<<"("<<get<0>(t)<<","<<get<1>(t)<<","<<get<2>(t)<<")";}
template<class T1, class T2> istream& operator>>(istream& i,pair<T1,T2> &p){return i>>p.first>>p.second;}
template<class T> ostream& operator<<(ostream& o,vector<T> a){Int i=0;for(T t:a)o<<(i++?" ":"")<<t;return o;}
template<class T> istream& operator>>(istream& i,vector<T> &a){for(T &t:a)i>>t;return i;}
//INSERT ABOVE HERE

Int solve_(vector<Int> d, Int n, Int x, Int m){
  x %= m;
  for(Int &a:d) a %= m;
  Int N = d.size();
  vector<Int> A;
  Int res = 0;
  for(Int i=0;i<n;i++){
    if(i == 0) A.push_back(x % m);
    else {
      A.push_back((A[i - 1] + d[(i - 1) % N]));
      res += A[i-1] % m < A[i] % m;
    }
  }
  //pr(A);
  for(Int &a:A) a %= m;
  //pr(A);
  return res;
}

Int solve(vector<Int> D, Int n, Int x, Int m){
  x %= m;
  for(Int &d:D) d %= m;
  Int k = D.size();
  Int sum = 0;
  for(Int d:D) sum += d;
  Int zero = 0;
  for(Int &d:D) zero += (d == 0);
  Int a = zero * ((n - 1) / k);
  for(Int i=0;i<(n - 1) % k;i++) a += D[i] == 0;

  Int s = x;
  Int t = x + sum * ((n - 1) / k);
  for(Int i=0;i<(n - 1) % k;i++) t += D[i];
  Int b = t / m - s / m;
  //pr(D, n, a, b, s, t);
  Int res = n - 1 - a - b;
  return res;
}

void test(){
  while(1){
    Int N = rand()%100 + 1;
    vector<Int> d(N);
    for(Int i=0;i<N;i++) d[i] = rand()%10;
    Int n = rand()%100 + 2;
    Int x = rand()%100;
    Int m = rand()%100 + 2;
    Int a = solve_(d, n, x, m);
    Int b = solve(d, n, x, m);
    //pr(d, n, x, m, a, b);
    assert(a == b);
  }
}

signed main(){
  srand((unsigned)time(NULL));
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  cout << fixed << setprecision(12);
  //test();
  Int k, q;
  cin>>k>>q;
  vector<Int> d(k);
  cin>>d;
  while(q--){
    Int n, x, m;
    cin>>n>>x>>m;
    Int ans = solve(d, n, x, m);
    cout<<ans<<endl;
  }

  return 0;
}


Measured memory_bytes: 384