#include <iostream>
#include <iomanip>
#include <string>
#include <cmath>
#include <algorithm>
#include <vector>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <list>
#include <stack>
#include <queue>
#include <bitset>
#include <numeric>
#include <cassert>
#include <array>
#include <memory>
#include <random>
#include <complex>
#ifdef DEBUG
#include "./Lib/debug.hpp"
#include "./Lib/Timer.hpp"
#include "./Lib/sample.hpp"
#else
#define dump(...)
#endif

/* (=＾o＾=) */
//#define int ll

/* macro */
#define FOR(i, b, e) for(ll i = (ll)(b); i < (ll)(e); ++i)
#define RFOR(i, b, e) for(ll i = (ll)(e-1); i >= (ll)(b); --i)
#define REP(i, n) FOR(i, 0, n)
#define RREP(i, n) RFOR(i, 0, n)
#define REPC(x,c) for(const auto& x:(c))
#define REPI2(it,b,e) for(auto it = (b); it != (e); ++it)
#define REPI(it,c) REPI2(it, (c).begin(), (c).end())
#define RREPI(it,c) REPI2(it, (c).rbegin(), (c).rend())
#define REPI_ERACE2(it, b, e) for(auto it = (b); it != (e);)
#define REPI_ERACE(it, c) REPI_ERACE2(it, (c).begin(), (c).end())
#define ALL(x) (x).begin(),(x).end()
#define cauto const auto&
/* macro func */
template<class T>
inline void sort(T& t) { std::sort(ALL(t)); }
template<class T>
inline void rsort(T& t) { std::sort((t).rbegin(), (t).rend()); }
template<class T>
inline void unique(T& t) { (t).erase(unique((t).begin(), (t).end()), (t).end()); }
template<class T, class S>
inline bool chmax(T& t, const S& s) { if (s > t) { t = s; return true; } return false; }
template<class T, class S>
inline bool chmaxE(T& t, const S& s) { if (s >= t) { t = s; return true; } return false; }
template<class T, class S>
inline bool chmin(T& t, const S& s) { if (s < t) { t = s; return true; } return false; }
inline void BR() { std::cout << "\n"; }

/* type define */
using ll = long long;
using PAIR = std::pair<ll, ll>;
using VS = std::vector<std::string>;
using VL = std::vector<long long>;
using VVL = std::vector<VL>;
using VVVL = std::vector<VVL>;
using VD = std::vector<double>;
template<class T>
using V = std::vector<T>;

/* using std */
using std::cout;
constexpr char endl = '\n';
using std::cin;
using std::pair;
using std::string;
using std::stack;
using std::queue;
using std::vector;
using std::list;
using std::map;
using std::unordered_map;
using std::multimap;
using std::unordered_multimap;
using std::set;
using std::unordered_set;
using std::unordered_multiset;
using std::multiset;
using std::bitset;
using std::priority_queue;
using std::tuple;

/* constant value */
constexpr ll MOD = 1000000007;
//constexpr ll MOD = 998244353;

/* Initial processing  */
struct Preprocessing { Preprocessing() { std::cin.tie(0); std::ios::sync_with_stdio(0); }; }_Preprocessing;

/* Remove the source of the bug */
inline signed pow(signed, signed) { assert(false); return -1; }

/* define hash */
namespace std {
template <>	class hash<std::pair<ll, ll>> { public:	size_t operator()(const std::pair<ll, ll>& x) const { return hash<ll>()(1000000000 * x.first + x.second); } };
}

/* input */
template<class T> std::istream& operator >> (std::istream& is, vector<T>& vec) { for (T& x : vec) is >> x; return is; }

//=============================================================================================

class CumulativeSum {
	const ll size;
	std::vector<ll> sumList;
public:

	CumulativeSum() = delete;
	CumulativeSum(const std::vector<ll>& v) :size(v.size()), sumList(size + 1) {
		for (ll i = 0; i < size; ++i) {
			sumList[i + 1] = sumList[i] + v[i];
		}
	}
	ll get(ll n) {
		return sumList[n + 1];
	}
	ll get(ll l, ll r) {
		if (r < l) { return 0LL; }
		l = std::max(l, 0LL); r = std::min(r, size - 1);
		return sumList[r + 1] - sumList[l];
	}
};


auto solve(ll k, VL d, ll n, ll x, ll m) {
	// mod m
	for (auto&& x : d) { x %= m; }

	// 0累積
	VL v0; v0.reserve(k);
	REPC(x, d) { v0.emplace_back((x == 0) ? 1 : 0); }
	auto sum0 = CumulativeSum(v0);

	// 累積
	auto sum = CumulativeSum(d);

	ll p = 0;
	{// 足す奴
		ll all = (x % m);
		all += ((n - 1) / k) * sum.get(0, k);
		//dump(all);
		all += sum.get(0, (n - 1) % k - 1);
		p += all / m;
	}
	{// 0のやつ
		ll all = 0;
		all += ((n - 1) / k) * sum0.get(0, k);
		all += sum0.get(0, (n - 1) % k - 1);
		//dump(all);
		p += all;
	}
	//dump(p);
	ll ans = n - 1 - p;
	return ans;
}


auto solve_c(ll k, VL d, ll n, ll x, ll m) {
	VL v; v.reserve(n);
	v.emplace_back(x);
	REP(i, n - 1) {
		ll r = v.back();
		v.emplace_back(r + d[i % k]);
	}
	ll ans = 0;
	REP(i, n - 1)if ((v[i] % m) < (v[i + 1]) % m) {
		++ans;
	}
	//dump(v);
	for (auto&& x : v) { x %= m; }
	//dump(v);
	return ans;
}

signed main() {
	/**/
	ll k, q;
	cin >> k >> q;

	VL d(k);
	cin >> d;
	REP(_, q) {
		ll n, x, m;
		cin >> n >> x >> m;
		auto ans = solve(k, d, n, x, m);
		cout << ans << endl;

		//auto ans_c = solve_c(k, d, n, x, m);
		//dump(ans_c);
	}
	/*/
	auto gen = Sample::SampleGenerator();
	REP(_, 100) {
		auto [k] = gen.generate(PAIR{2,4});
		auto [d] = gen.generate(V<PAIR>(k, PAIR{1,3}));
		auto [n, x, m] = gen.generate(PAIR{k,7}, PAIR{1,4}, PAIR{3,5});

		auto ans = solve(k, d, n, x, m);
		auto ans_c = solve_c(k, d, n, x, m);
		if (ans != ans_c) {
			cout << k << " " << 1 << endl;
			REPC(x, d) { cout << x << " "; }BR();
			cout << n << " " << x << " " << m << endl;
			dump(ans, ans_c);
			return 0;
		}
	}
	/**/
}


Measured memory_bytes: 576