#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];
map <int, vector <int> > off;
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];
}
}
vector < pair < pair <int, int>, ll > > a;
void solve(int T, vector <int> &qr) {
int add = T, last = 1;
a.clear();
for (int i = 1, j = 0; i <= n; j = i + 1, i = nxt[i]) {
int df = (d[i] + last - 1) / last;
if (!sz(a)) a.pb({{0, i - 1}, i - 1});
else a.pb({{j, i - 1}, {i - j}});
a.pb({{i, i}, 1 + last * (add % df)});
last *= df;
add /= df;
if (!add || nxt[i] > n) {
if (i < n) a.pb({{i + 1, n}, {n - i}});
break;
}
}
for (auto it : qr) {
int L = -1, R = -2;
if (T >= l[it]) { // it's for right
int ost = T - l[it];
if (sz(a)) {
R = min(ost, a[0].s);
}
}
int sum = 0;
rep(i, 0, sz(a) - 1) {
sum += a[i].s;
int val = T - sum;
if (val >= l[it]) {
R = a[i].f.s;
int ost = val - l[it];
if (i & 1 && i + 1 < sz(a)) {
R += min(ost, a[i + 1].s);
}
}
if (val <= r[it] && L == -1) {
L = a[i].f.s;
if (i % 2 == 0) {
L -= max(0ll, min(r[it] - val, a[i].s - 1));
}
}
}
if (L != -1 && L <= R) ans[it] += R - L + 1;
}
}
int32_t main() {
ios_base :: sync_with_stdio(0), cin.tie(0), cout.tie(0);
#ifdef IOI
freopen ("in.txt", "r", stdin);
freopen ("C.out", "w", stdout);
#endif
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();
for (auto it : off) {
solve(it.f, it.s);
}
rep(i, 1, q) {
cout << ans[i] << nl;
}
ioi
}
