#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define rep(i, n) for (int i = 0; i < (n); i++) #define per(i, n) for (int i = (n)-1; i >= 0; i--) using ll = long long; #define vi vector #define vvi vector #define vl vector #define pii pair #define pll pair #define all(a) (a).begin(), (a).end() #define rall(a) (a).rbegin(), (a).rend() #define mod 998244353 using namespace std; struct mint { ll x; mint(ll x = 0) : x((x + mod) % mod) {} mint operator-() const { return mint(-x); } mint operator+=(const mint &a) { if ((x += a.x) >= mod) x -= mod; return *this; } mint &operator++() { if (++x == mod) x = 0; return *this; } mint operator++(int) { mint temp = *this; if (++x == mod) x = 0; return temp; } mint &operator-=(const mint &a) { if ((x -= a.x) < 0) x += mod; return *this; } mint &operator--() { if (--x < 0) x += mod; return *this; } mint operator--(int) { mint temp = *this; if (--x < 0) x += mod; return temp; } mint &operator*=(const mint &a) { (x *= a.x) %= mod; return *this; } mint operator+(const mint &a) const { return mint(*this) += a; } mint operator-(const mint &a) const { return mint(*this) -= a; } mint operator*(const mint &a) const { return mint(*this) *= a; } mint pow(ll t) const { if (!t) return 1; mint res = 1, v = *this; while (t) { if (t & 1) res *= v; v *= v; t >>= 1; } return res; } mint inv() const { return pow(mod - 2); } mint &operator/=(const mint &a) { return (*this) *= a.inv(); } mint operator/(const mint &a) const { return mint(*this) /= a; } bool operator==(const mint &a) const { return x == a.x; } bool operator!=(const mint &a) const { return x != a.x; } bool operator<(const mint &a) const { return x < a.x; } bool operator>(const mint &a) const { return x > a.x; } friend istream &operator>>(istream &is, mint &a) { return is >> a.x; } friend ostream &operator<<(ostream &os, const mint &a) { return os << a.x; } }; template struct FPS : vector { using vector::vector; FPS &operator+=(const FPS &r) { if (r.size() > this->size()) this->resize(r.size()); for (int i = 0; i < (int)r.size(); i++) (*this)[i] += r[i]; return *this; } FPS &operator+=(const mint &r) { if (this->empty()) this->resize(1); (*this)[0] += r; return *this; } FPS &operator-=(const FPS &r) { if (r.size() > this->size()) this->resize(r.size()); for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i]; return *this; } FPS &operator-=(const mint &r) { if (this->empty()) this->resize(1); (*this)[0] -= r; return *this; } FPS &operator*=(const mint &v) { for (int k = 0; k < (int)this->size(); k++) (*this)[k] *= v; return *this; } FPS &operator/=(const FPS &r) { if (this->size() < r.size()) { this->clear(); return *this; } const int n = this->size() - r.size() + 1; if ((int)r.size() <= 64) { FPS f(*this), g(r); g.shrink(); mint coeff = g.back().inv(); for (auto &x : g) x *= coeff; const int deg = (int)f.size() - (int)g.size() + 1; const int gs = g.size(); FPS quo(deg); for (int i = deg - 1; i >= 0; i--) { quo[i] = f[i + gs - 1]; for (int j = 0; j < gs; j++) f[i + j] -= quo[i] * g[j]; } *this = quo * coeff; this->resize(n, mint(0)); return *this; } return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev(); } FPS &operator%=(const FPS &r) { *this -= *this / r * r; shrink(); return *this; } FPS operator+(const FPS &r) const { return FPS(*this) += r; } FPS operator+(const mint &v) const { return FPS(*this) += v; } FPS operator-(const FPS &r) const { return FPS(*this) -= r; } FPS operator-(const mint &v) const { return FPS(*this) -= v; } FPS operator*(const FPS &r) const { return FPS(*this) *= r; } FPS operator*(const mint &v) const { return FPS(*this) *= v; } FPS operator/(const FPS &r) const { return FPS(*this) /= r; } FPS operator%(const FPS &r) const { return FPS(*this) %= r; } FPS operator-() const { FPS ret(this->size()); for (int i = 0; i < (int)this->size(); i++) ret[i] = -(*this)[i]; return ret; } void shrink() { while (this->size() && this->back() == mint(0)) this->pop_back(); } FPS rev() const { FPS ret(*this); reverse(begin(ret), end(ret)); return ret; } FPS dot(FPS r) const { FPS ret(min(this->size(), r.size())); for (int i = 0; i < (int)ret.size(); i++) ret[i] = (*this)[i] * r[i]; return ret; } FPS pre(int sz) const { return FPS(begin(*this), begin(*this) + min((int)this->size(), sz)); } FPS operator>>(int sz) const { if ((int)this->size() <= sz) return {}; FPS ret(*this); ret.erase(ret.begin(), ret.begin() + sz); return ret; } FPS operator<<(int sz) const { FPS ret(*this); ret.insert(ret.begin(), sz, mint(0)); return ret; } FPS diff() const { const int n = (int)this->size(); FPS ret(max(0, n - 1)); const mint one(1); mint coeff(1); for (int i = 1; i < n; i++) { ret[i - 1] = (*this)[i] * coeff; coeff += one; } return ret; } FPS integral() const { const int n = (int)this->size(); FPS ret(n + 1); ret[0] = mint(0); if (n > 0) ret[1] = mint(1); for (int i = 2; i <= n; i++) ret[i] = (-ret[mod % i]) * (mod / i); for (int i = 0; i < n; i++) ret[i + 1] *= (*this)[i]; return ret; } mint eval(mint x) const { mint r = 0, w = 1; for (auto &v : *this) r += w * v, w *= x; return r; } FPS log(int deg = -1) const { assert((*this)[0] == mint(1)); if (deg == -1) deg = (int)this->size(); return (this->diff() * this->inv(deg)).pre(deg - 1).integral(); } FPS pow(int64_t k, int deg = -1) const { const int n = (int)this->size(); if (deg == -1) deg = n; if (k == 0) { FPS ret(deg); if (deg) ret[0] = 1; return ret; } for (int i = 0; i < n; i++) { if ((*this)[i] != mint(0)) { const mint rev = mint(1) / (*this)[i]; FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg); ret *= (*this)[i].pow(k); ret = (ret << (i * k)).pre(deg); if ((int)ret.size() < deg) ret.resize(deg, mint(0)); return ret; } if (__int128_t(i + 1) * k >= deg) return FPS(deg, mint(0)); } return FPS(deg, mint(0)); } static void *ntt_ptr; static void set_fft(); FPS &operator*=(const FPS &r); void ntt(); void intt(); void ntt_doubling(); static int ntt_pr(); FPS inv(int deg = -1) const; FPS exp(int deg = -1) const; }; template void *FPS::ntt_ptr = nullptr; template struct NTT { static constexpr uint32_t pr = 3; static_assert(mod == 998244353); static constexpr int level = __builtin_ctzll(mod - 1); mint dw[level], dy[level]; void setwy(const int k) { mint w[level], y[level]; w[k - 1] = mint(pr).pow((mod - 1) / (1 << k)); y[k - 1] = w[k - 1].inv(); for (int i = k - 2; i > 0; i--) w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1]; dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2]; for (int i = 3; i < k; ++i) { dw[i] = dw[i - 1] * y[i - 2] * w[i]; dy[i] = dy[i - 1] * w[i - 2] * y[i]; } } NTT() { setwy(level); } void fft4(vector &a, const int k) { if ((int)a.size() <= 1) return; if (k == 1) { mint a1 = a[1]; a[1] = a[0] - a[1]; a[0] = a[0] + a1; return; } if (k & 1) { const int v = 1 << (k - 1); for (int j = 0; j < v; j++) { mint ajv = a[j + v]; a[j + v] = a[j] - ajv; a[j] += ajv; } } int u = 1 << (2 + (k & 1)); int v = 1 << (k - 2 - (k & 1)); const mint one = mint(1); const mint imag = dw[1]; while (v) { // jh = 0 { int j0 = 0; int j1 = v; int j2 = j1 + v; int j3 = j2 + v; for (; j0 < v; j0++, j1++, j2++, j3++) { const mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3]; const mint t0p2 = t0 + t2, t1p3 = t1 + t3; const mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag; a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3; a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3; } } // jh >= 1 mint ww = one, xx = one * dw[2], wx = one; for (int jh = 4; jh < u;) { ww = xx * xx, wx = ww * xx; int j0 = jh * v; const int je = j0 + v; int j2 = je + v; for (; j0 < je; j0++, j2++) { const mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww, t3 = a[j2 + v] * wx; const mint t0p2 = t0 + t2, t1p3 = t1 + t3; const mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag; a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3; a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3; } xx *= dw[__builtin_ctzll((jh += 4))]; } u <<= 2; v >>= 2; } } void ifft4(vector &a, const int k) { if ((int)a.size() <= 1) return; if (k == 1) { mint a1 = a[1]; a[1] = a[0] - a[1]; a[0] = a[0] + a1; return; } int u = 1 << (k - 2); int v = 1; const mint one = mint(1); const mint imag = dy[1]; while (u) { // jh = 0 { int j0 = 0; int j1 = v; int j2 = v + v; int j3 = j2 + v; for (; j0 < v; j0++, j1++, j2++, j3++) { const mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3]; const mint t0p1 = t0 + t1, t2p3 = t2 + t3; const mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag; a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3; a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3; } } // jh >= 1 mint ww = one, xx = one * dy[2], yy = one; u <<= 2; for (int jh = 4; jh < u;) { ww = xx * xx, yy = xx * imag; int j0 = jh * v; const int je = j0 + v; int j2 = je + v; for (; j0 < je; j0++, j2++) { const mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v]; const mint t0p1 = t0 + t1, t2p3 = t2 + t3; const mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy; a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww; a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww; } xx *= dy[__builtin_ctzll(jh += 4)]; } u >>= 4; v <<= 2; } if (k & 1) { u = 1 << (k - 1); for (int j = 0; j < u; j++) { mint ajv = a[j] - a[j + u]; a[j] += a[j + u]; a[j + u] = ajv; } } } void ntt(vector &a) { if ((int)a.size() <= 1) return; fft4(a, __builtin_ctz(a.size())); } void intt(vector &a) { if ((int)a.size() <= 1) return; ifft4(a, __builtin_ctz(a.size())); const mint iv = mint(a.size()).inv(); for (auto &x : a) x *= iv; } vector multiply(const vector &a, const vector &b) { const int l = a.size() + b.size() - 1; if (min(a.size(), b.size()) <= 40) { vector s(l); for (int i = 0; i < (int)a.size(); i++) for (int j = 0; j < (int)b.size(); j++) s[i + j] += a[i] * b[j]; return s; } int k = 2, M = 4; while (M < l) M <<= 1, k++; setwy(k); vector s(M), t(M); for (int i = 0; i < (int)a.size(); i++) s[i] = a[i]; for (int i = 0; i < (int)b.size(); i++) t[i] = b[i]; fft4(s, k); fft4(t, k); for (int i = 0; i < M; i++) s[i] *= t[i]; ifft4(s, k); s.resize(l); const mint invm = mint(M).inv(); for (int i = 0; i < l; i++) s[i] *= invm; return s; } void ntt_doubling(vector &a) { const int M = (int)a.size(); auto b = a; intt(b); mint r = 1, zeta = mint(pr).pow((mod - 1) / (M << 1)); for (int i = 0; i < M; i++) b[i] *= r, r *= zeta; ntt(b); copy(begin(b), end(b), back_inserter(a)); } }; template void FPS::set_fft() { if (!ntt_ptr) ntt_ptr = new NTT; } template FPS &FPS::operator*=(const FPS &r) { if (this->empty() || r.empty()) { this->clear(); return *this; } set_fft(); const auto ret = static_cast *>(ntt_ptr)->multiply(*this, r); return *this = FPS(ret.begin(), ret.end()); } template void FPS::ntt() { set_fft(); static_cast *>(ntt_ptr)->ntt(*this); } template void FPS::intt() { set_fft(); static_cast *>(ntt_ptr)->intt(*this); } template void FPS::ntt_doubling() { set_fft(); static_cast *>(ntt_ptr)->ntt_doubling(*this); } template int FPS::ntt_pr() { set_fft(); return static_cast *>(ntt_ptr)->pr; } template FPS FPS::inv(int deg) const { assert((*this)[0] != mint(0)); if (deg == -1) deg = (int)this->size(); FPS res(deg); res[0] = {mint(1) / (*this)[0]}; for (int d = 1; d < deg; d <<= 1) { FPS f(2 * d), g(2 * d); for (int j = 0; j < min((int)this->size(), 2 * d); j++) f[j] = (*this)[j]; for (int j = 0; j < d; j++) g[j] = res[j]; f.ntt(); g.ntt(); for (int j = 0; j < 2 * d; j++) f[j] *= g[j]; f.intt(); for (int j = 0; j < d; j++) f[j] = 0; f.ntt(); for (int j = 0; j < 2 * d; j++) f[j] *= g[j]; f.intt(); for (int j = d; j < min(2 * d, deg); j++) res[j] = -f[j]; } return res.pre(deg); } template FPS FPS::exp(int deg) const { using fps = FPS; assert((*this).size() == 0 || (*this)[0] == mint(0)); if (deg == -1) deg = this->size(); fps inv; inv.reserve(deg + 1); inv.push_back(mint(0)); inv.push_back(mint(1)); auto inplace_integral = [&](fps &F) -> void { const int n = (int)F.size(); while ((int)inv.size() <= n) { const int i = inv.size(); inv.push_back((-inv[mod % i]) * (mod / i)); } F.insert(begin(F), mint(0)); for (int i = 1; i <= n; i++) F[i] *= inv[i]; }; auto inplace_diff = [](fps &F) -> void { if (F.empty()) return; F.erase(begin(F)); mint coeff = 1, one = 1; for (int i = 0; i < (int)F.size(); i++) { F[i] *= coeff; coeff += one; } }; fps b{1, 1 < (int)this->size() ? (*this)[1] : 0}, c{1}, z1, z2{1, 1}; for (int m = 2; m < deg; m *= 2) { auto y = b; y.resize(2 * m); y.ntt(); z1 = z2; fps z(m); for (int i = 0; i < m; i++) z[i] = y[i] * z1[i]; z.intt(); fill(begin(z), begin(z) + m / 2, mint(0)); z.ntt(); for (int i = 0; i < m; i++) z[i] *= -z1[i]; z.intt(); c.insert(end(c), begin(z) + m / 2, end(z)); z2 = c; z2.resize(2 * m); z2.ntt(); fps x(begin(*this), begin(*this) + min(this->size(), m)); x.resize(m); inplace_diff(x); x.push_back(mint(0)); x.ntt(); for (int i = 0; i < m; i++) x[i] *= y[i]; x.intt(); x -= b.diff(); x.resize(2 * m); for (int i = 0; i < m - 1; i++) x[m + i] = x[i], x[i] = mint(0); x.ntt(); for (int i = 0; i < 2 * m; i++) x[i] *= z2[i]; x.intt(); x.pop_back(); inplace_integral(x); for (int i = m; i < min(this->size(), 2 * m); i++) x[i] += (*this)[i]; fill(begin(x), begin(x) + m, mint(0)); x.ntt(); for (int i = 0; i < 2 * m; i++) x[i] *= y[i]; x.intt(); b.insert(end(b), begin(x) + m, end(x)); } return fps{begin(b), begin(b) + deg}; } void solve() { int n; cin >> n; vector> dp(1, FPS(1)); dp[0][0] = 1; rep(j, n) { auto addition = dp[j]; addition.push_back(0); int x; cin >> x; rep(i, j + 1) addition[i + 1] += x * dp[j][i].x; dp.push_back(addition); } int query; cin >> query; rep(loop, query) { int l, r, k; cin >> l >> r >> k; l--; auto x = dp[r] / dp[l]; cout << x[k].x << '\n'; } } int main() { cin.tie(nullptr); ios::sync_with_stdio(false); solve(); return 0; }