#include <bits/stdc++.h>
#define int ll
#define f first
#define s second
#define pb push_back
#define pp pop_back
#define all(x) x.begin(), x.end()
#define sz(x) (int)x.size()
#define rep(a, b, c) for (int a = (b); (a) <= (c); ++a)
#define per(a, b, c) for (int a = (b); (a) >= (c); --a)
#define nl '\n'
#define ioi exit(0);
using namespace std;
typedef long long ll;
const int MAX_N = (int)5e5 + 7;
int n, q;
int d[MAX_N], l[MAX_N], r[MAX_N], t[MAX_N], ans[MAX_N];
unordered_map <int, vector <int> > off;
struct fenwick {
pair <ll, int> f[MAX_N];
void upd(int p, ll df, int t) {
for (; p < MAX_N; p |= p + 1) {
f[p].f += df;
f[p].s += t;
}
}
pair <ll, int> get(int p) {
pair <ll, int> res = {0, 0};
for (; p >= 0; p = (p & (p + 1)) - 1) {
res.f += f[p].f;
res.s += f[p].s;
}
return res;
}
} F;
pair <int, int> inter(pair <int, int> x, pair <int, int> y) {
return {max(x.f, y.f), min(x.s, y.s)};
}
ll get_val(int p, int T) {
pair <ll, int> cur = F.get(p);
//cerr << cur.f << ' ' << T << nl;
int one = p - cur.s;
/* if (S != -1) {
pair <int, int> rng = inter({1, p}, {S, E});
if (rng.f <= rng.s) {
// cerr << cur.f << ' ' << one << nl;
one -= pref[rng.s].s - pref[rng.f - 1].s;
cur.f += pref[rng.s].f - pref[rng.f - 1].f;
}
}
*/
return T - (cur.f + one);
}
int nxt[MAX_N], lst[MAX_N];
void prep() {
int last = 1;
rep(i, 1, n) {
int df = (d[i] + last - 1) / last;
lst[i] = df * last;
last *= df;
}
per(i, n, 1) {
if (lst[i] != lst[i + 1] || i == n) nxt[i] = i + 1;
else nxt[i] = nxt[i + 1];
}
}
pair < pair <int, int>, ll> a[MAX_N];
void solve(int T, vector <int> &qr) {
int add = T;
// vector < pair < pair <int, int>, ll > > a;
int sz = 0;
int last = 1;
/* rep(i, 1, n) cerr << lst[i] << ' ';
cerr << nl; */
for (int i = 1, j = 0; i <= n; j = i + 1, i = nxt[i]) {
int df = (d[i] + last - 1) / last;
if (!sz) a[sz++] = {{0, i - 1}, i - 1};
else a[sz++] = {{j, i - 1}, {i - j}};
a[sz++] = {{i, i}, 1 + last * (add % df)};
//F.upd(i, 1 + last * (add % df), 1);
//cerr << 1 + last * (add % df) << ' ' << i << nl;
//sum += 1 + last * (add % df);
last *= df;
add /= df;
if (!add || nxt[i] > n) {
if (i < n) a[sz++] = {{i + 1, n}, {n - i}};
break;
}
}
/* last = 1;
cerr << nl;
add = T;
for (int i = 1; i <= n; i++) {
int df = (d[i] + last - 1) / last;
cerr << 1 + last * (add % df) << ' ' << i << ' ' << last * df << nl;
//sum += 1 + last * (add % df);
last *= df;
add /= df;
} */
/* for (auto it : a) {
cerr << it.f.f << ' ' << it.f.s << ' ' << it.s << nl;
} */
for (auto it : qr) {
int L = -1, R = -2;
if (T >= l[it]) { // it's for right
int ost = T - l[it];
if (sz) {
R = min(ost, a[0].s);
}
}
int sum = 0;
rep(i, 0, sz - 1) {
sum += a[i].s;
int val = T - sum;
// cerr << val << ' ' << a[i].f.f << ' ' << a[i].f.s << ' ' << r[it] << nl;
if (val >= l[it]) {
R = a[i].f.s;
int ost = val - l[it];
if (i & 1 && i + 1 < sz) {
R += min(ost, a[i + 1].s);
}
}
if (val <= r[it] && L == -1) {
L = a[i].f.s;
if (i % 2 == 0) {
// cerr << "DA";
// cerr << L << "<-\n";
L -= max(0ll, min(r[it] - val, a[i].s - 1));
// cerr << L << "<-\n";
}
}
}
/* cerr << nl;
cerr << L << ' ' << R << nl; */
/*
int lo = 1, hi = n;
while (lo <= hi) {
int mid = lo + hi >> 1;
if (get_val(mid, T) >= l[it]) L = mid, lo = mid + 1;
else hi = mid - 1;
}
lo = 1, hi = n;
while (lo <= hi) {
int mid = lo + hi >> 1;
if (get_val(mid, T) <= r[it]) R = mid, hi = mid - 1;
else lo = mid + 1;
}*/
//cerr << R << ' ' << L << nl;
if (L != -1 && L <= R) ans[it] += R - L + 1;
//if (l[it] <= T && T <= r[it]) ans[it]++;
// cerr << ans[it] << nl;
//ans[it] = upper_bound(all(a), r[it]) - lower_bound(all(a), l[it]);
}
// cout << ans[2] << nl;
/* for (auto it : del) {
F.upd(it.f, -it.s, -1);
} */
}
int32_t main() {
#ifdef IOI
freopen ("in.txt", "r", stdin);
freopen ("C.out", "w", stdout);
#endif
ios_base :: sync_with_stdio(0), cin.tie(0), cout.tie(0);
cin >> n >> q;
d[0] = 1;
rep(i, 1, n) {
cin >> d[i];
}
rep(i, 1, q) {
cin >> t[i] >> l[i] >> r[i];
off[t[i]].pb(i);
}
prep();
/* solve(4, off[4]);
ioi */
for (auto it : off) {
solve(it.f, it.s);
}
rep(i, 1, q) {
cout << ans[i] << nl;
}
ioi
}
