#include using namespace std; using int64 = long long; //const int mod = 1e9 + 7; const int mod = 998244353; const int64 infll = (1LL << 62) - 1; const int inf = (1 << 30) - 1; struct IoSetup { IoSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); cerr << fixed << setprecision(10); } } iosetup; template< typename T1, typename T2 > ostream &operator<<(ostream &os, const pair< T1, T2 > &p) { os << p.first << " " << p.second; return os; } template< typename T1, typename T2 > istream &operator>>(istream &is, pair< T1, T2 > &p) { is >> p.first >> p.second; return is; } template< typename T > ostream &operator<<(ostream &os, const vector< T > &v) { for(int i = 0; i < (int) v.size(); i++) { os << v[i] << (i + 1 != v.size() ? " " : ""); } return os; } template< typename T > istream &operator>>(istream &is, vector< T > &v) { for(T &in : v) is >> in; return is; } template< typename T1, typename T2 > inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } template< typename T1, typename T2 > inline bool chmin(T1 &a, T2 b) { if(b < 0)b *= -1; return a > b && (a = b, true); } template< typename T = int64 > vector< T > make_v(size_t a) { return vector< T >(a); } template< typename T, typename... Ts > auto make_v(size_t a, Ts... ts) { return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...)); } template< typename T, typename V > typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) { t = v; } template< typename T, typename V > typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) { for(auto &e : t) fill_v(e, v); } template< typename F > struct FixPoint : F { FixPoint(F &&f) : F(forward< F >(f)) {} template< typename... Args > decltype(auto) operator()(Args &&... args) const { return F::operator()(*this, forward< Args >(args)...); } }; template< typename F > inline decltype(auto) MFP(F &&f) { return FixPoint< F >{forward< F >(f)}; } /** * @brief Formal-Power-Series(形式的冪級数) */ template< typename T > struct FormalPowerSeries : vector< T > { using vector< T >::vector; using P = FormalPowerSeries; using MULT = function< vector< T >(P, P) >; using FFT = function< void(P &) >; using SQRT = function< T(T) >; static MULT &get_mult() { static MULT mult = nullptr; return mult; } static void set_mult(MULT f) { get_mult() = f; } static FFT &get_fft() { static FFT fft = nullptr; return fft; } static FFT &get_ifft() { static FFT ifft = nullptr; return ifft; } static void set_fft(FFT f, FFT g) { get_fft() = f; get_ifft() = g; if(get_mult() == nullptr) { auto mult = [&](P a, P b) { int need = a.size() + b.size() - 1; int nbase = 1; while((1 << nbase) < need) nbase++; int sz = 1 << nbase; a.resize(sz, T(0)); b.resize(sz, T(0)); get_fft()(a); get_fft()(b); for(int i = 0; i < sz; i++) a[i] *= b[i]; get_ifft()(a); a.resize(need); return a; }; set_mult(mult); } } static SQRT &get_sqrt() { static SQRT sqr = nullptr; return sqr; } static void set_sqrt(SQRT sqr) { get_sqrt() = sqr; } void shrink() { while(this->size() && this->back() == T(0)) this->pop_back(); } P operator+(const P &r) const { return P(*this) += r; } P operator+(const T &v) const { return P(*this) += v; } P operator-(const P &r) const { return P(*this) -= r; } P operator-(const T &v) const { return P(*this) -= v; } P operator*(const P &r) const { return P(*this) *= r; } P operator*(const T &v) const { return P(*this) *= v; } P operator/(const P &r) const { return P(*this) /= r; } P operator%(const P &r) const { return P(*this) %= r; } P &operator+=(const P &r) { if(r.size() > this->size()) this->resize(r.size()); for(int i = 0; i < r.size(); i++) (*this)[i] += r[i]; return *this; } P &operator+=(const T &r) { if(this->empty()) this->resize(1); (*this)[0] += r; return *this; } P &operator-=(const P &r) { if(r.size() > this->size()) this->resize(r.size()); for(int i = 0; i < r.size(); i++) (*this)[i] -= r[i]; shrink(); return *this; } P &operator-=(const T &r) { if(this->empty()) this->resize(1); (*this)[0] -= r; shrink(); return *this; } P &operator*=(const T &v) { const int n = (int) this->size(); for(int k = 0; k < n; k++) (*this)[k] *= v; return *this; } P &operator*=(const P &r) { if(this->empty() || r.empty()) { this->clear(); return *this; } assert(get_mult() != nullptr); auto ret = get_mult()(*this, r); return *this = P(begin(ret), end(ret)); } P &operator%=(const P &r) { return *this -= *this / r * r; } P operator-() const { P ret(this->size()); for(int i = 0; i < this->size(); i++) ret[i] = -(*this)[i]; return ret; } P &operator/=(const P &r) { if(this->size() < r.size()) { this->clear(); return *this; } int n = this->size() - r.size() + 1; return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n); } P dot(P r) const { P ret(min(this->size(), r.size())); for(int i = 0; i < ret.size(); i++) ret[i] = (*this)[i] * r[i]; return ret; } P pre(int sz) const { return P(begin(*this), begin(*this) + min((int) this->size(), sz)); } P operator>>(int sz) const { if(this->size() <= sz) return {}; P ret(*this); ret.erase(ret.begin(), ret.begin() + sz); return ret; } P operator<<(int sz) const { P ret(*this); ret.insert(ret.begin(), sz, T(0)); return ret; } P rev(int deg = -1) const { P ret(*this); if(deg != -1) ret.resize(deg, T(0)); reverse(begin(ret), end(ret)); return ret; } T operator()(T x) const { T r = 0, w = 1; for(auto &v : *this) { r += w * v; w *= x; } return r; } P diff() const; P integral() const; // F(0) must not be 0 P inv_fast() const; P inv(int deg = -1) const; // F(0) must be 1 P log(int deg = -1) const; P sqrt(int deg = -1) const; // F(0) must be 0 P exp_fast(int deg = -1) const; P exp(int deg = -1) const; P pow(int64_t k, int deg = -1) const; P mod_pow(int64_t k, P g) const; P taylor_shift(T c) const; }; /** * @brief Diff ($f'(x)$) * @docs docs/diff.md */ template< typename T > typename FormalPowerSeries< T >::P FormalPowerSeries< T >::diff() const { const int n = (int) this->size(); P ret(max(0, n - 1)); for(int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i); return ret; } /** * @brief Exp ($e^{f(x)}$) * @docs docs/exp.md */ template< typename T > typename FormalPowerSeries< T >::P FormalPowerSeries< T >::exp_fast(int deg) const { if(deg == -1) deg = this->size(); assert((*this)[0] == T(0)); P inv; inv.reserve(deg + 1); inv.push_back(T(0)); inv.push_back(T(1)); auto inplace_integral = [&](P &F) -> void { const int n = (int) F.size(); auto mod = T::get_mod(); while((int) inv.size() <= n) { int i = inv.size(); inv.push_back((-inv[mod % i]) * (mod / i)); } F.insert(begin(F), T(0)); for(int i = 1; i <= n; i++) F[i] *= inv[i]; }; auto inplace_diff = [](P &F) -> void { if(F.empty()) return; F.erase(begin(F)); T coeff = 1, one = 1; for(int i = 0; i < (int) F.size(); i++) { F[i] *= coeff; coeff += one; } }; P 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); get_fft()(y); z1 = z2; P z(m); for(int i = 0; i < m; ++i) z[i] = y[i] * z1[i]; get_ifft()(z); fill(begin(z), begin(z) + m / 2, T(0)); get_fft()(z); for(int i = 0; i < m; ++i) z[i] *= -z1[i]; get_ifft()(z); c.insert(end(c), begin(z) + m / 2, end(z)); z2 = c; z2.resize(2 * m); get_fft()(z2); P x(begin(*this), begin(*this) + min< int >(this->size(), m)); inplace_diff(x); x.push_back(T(0)); get_fft()(x); for(int i = 0; i < m; ++i) x[i] *= y[i]; get_ifft()(x); x -= b.diff(); x.resize(2 * m); for(int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = T(0); get_fft()(x); for(int i = 0; i < 2 * m; ++i) x[i] *= z2[i]; get_ifft()(x); x.pop_back(); inplace_integral(x); for(int i = m; i < min< int >(this->size(), 2 * m); ++i) x[i] += (*this)[i]; fill(begin(x), begin(x) + m, T(0)); get_fft()(x); for(int i = 0; i < 2 * m; ++i) x[i] *= y[i]; get_ifft()(x); b.insert(end(b), begin(x) + m, end(x)); } return P{begin(b), begin(b) + deg}; } template< typename T > typename FormalPowerSeries< T >::P FormalPowerSeries< T >::exp(int deg) const { assert((*this)[0] == T(0)); const int n = (int) this->size(); if(deg == -1) deg = n; if(get_fft() != nullptr) { P ret(*this); ret.resize(deg, T(0)); return ret.exp_fast(deg); } P ret({T(1)}); for(int i = 1; i < deg; i <<= 1) { ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1); } return ret.pre(deg); } /** * @brief Integral ($\int f(x) dx$) * @docs docs/integral.md */ template< typename T > typename FormalPowerSeries< T >::P FormalPowerSeries< T >::integral() const { const int n = (int) this->size(); P ret(n + 1); ret[0] = T(0); for(int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1); return ret; } /** * @brief Inv ($\frac {1} {f(x)}$) */ template< typename T > typename FormalPowerSeries< T >::P FormalPowerSeries< T >::inv_fast() const { assert(((*this)[0]) != T(0)); const int n = (int) this->size(); P res{T(1) / (*this)[0]}; for(int d = 1; d < n; d <<= 1) { P f(2 * d), g(2 * d); for(int j = 0; j < min(n, 2 * d); j++) f[j] = (*this)[j]; for(int j = 0; j < d; j++) g[j] = res[j]; get_fft()(f); get_fft()(g); for(int j = 0; j < 2 * d; j++) f[j] *= g[j]; get_ifft()(f); for(int j = 0; j < d; j++) { f[j] = 0; f[j + d] = -f[j + d]; } get_fft()(f); for(int j = 0; j < 2 * d; j++) f[j] *= g[j]; get_ifft()(f); for(int j = 0; j < d; j++) f[j] = res[j]; res = f; } return res.pre(n); } template< typename T > typename FormalPowerSeries< T >::P FormalPowerSeries< T >::inv(int deg) const { assert(((*this)[0]) != T(0)); const int n = (int) this->size(); if(deg == -1) deg = n; if(get_fft() != nullptr) { P ret(*this); ret.resize(deg, T(0)); return ret.inv_fast(); } P ret({T(1) / (*this)[0]}); for(int i = 1; i < deg; i <<= 1) { ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1); } return ret.pre(deg); } /** * @brief Log ($\log {f(x)}$) * @docs docs/log.md */ template< typename T > typename FormalPowerSeries< T >::P FormalPowerSeries< T >::log(int deg) const { assert((*this)[0] == 1); const int n = (int) this->size(); if(deg == -1) deg = n; return (this->diff() * this->inv(deg)).pre(deg - 1).integral(); } /** * @brief Pow ($f(x)^k$) */ template< typename T > typename FormalPowerSeries< T >::P FormalPowerSeries< T >::pow(int64_t k, int deg) const { const int n = (int) this->size(); if(deg == -1) deg = n; for(int i = 0; i < n; i++) { if((*this)[i] != T(0)) { T rev = T(1) / (*this)[i]; P ret = (((*this * rev) >> i).log() * k).exp() * ((*this)[i].pow(k)); if(i * k > deg) return P(deg, T(0)); ret = (ret << (i * k)).pre(deg); if(ret.size() < deg) ret.resize(deg, T(0)); return ret; } } return *this; } template< int mod > struct ModInt { int x; ModInt() : x(0) {} ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} ModInt &operator+=(const ModInt &p) { if((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const ModInt &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt &operator*=(const ModInt &p) { x = (int) (1LL * x * p.x % mod); return *this; } ModInt &operator/=(const ModInt &p) { *this *= p.inverse(); return *this; } ModInt operator-() const { return ModInt(-x); } ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; } ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; } ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; } ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; } bool operator==(const ModInt &p) const { return x == p.x; } bool operator!=(const ModInt &p) const { return x != p.x; } ModInt inverse() const { int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); } ModInt pow(int64_t n) const { ModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt< mod >(t); return (is); } static int get_mod() { return mod; } }; using modint = ModInt< mod >; template< typename Mint > struct NumberTheoreticTransformFriendlyModInt { vector< Mint > dw, idw; int max_base; Mint root; NumberTheoreticTransformFriendlyModInt() { const unsigned mod = Mint::get_mod(); assert(mod >= 3 && mod % 2 == 1); auto tmp = mod - 1; max_base = 0; while(tmp % 2 == 0) tmp >>= 1, max_base++; root = 2; while(root.pow((mod - 1) >> 1) == 1) root += 1; assert(root.pow(mod - 1) == 1); dw.resize(max_base); idw.resize(max_base); for(int i = 0; i < max_base; i++) { dw[i] = -root.pow((mod - 1) >> (i + 2)); idw[i] = Mint(1) / dw[i]; } } void ntt(vector< Mint > &a) { const int n = (int) a.size(); assert((n & (n - 1)) == 0); assert(__builtin_ctz(n) <= max_base); for(int m = n; m >>= 1;) { Mint w = 1; for(int s = 0, k = 0; s < n; s += 2 * m) { for(int i = s, j = s + m; i < s + m; ++i, ++j) { auto x = a[i], y = a[j] * w; a[i] = x + y, a[j] = x - y; } w *= dw[__builtin_ctz(++k)]; } } } void intt(vector< Mint > &a, bool f = true) { const int n = (int) a.size(); assert((n & (n - 1)) == 0); assert(__builtin_ctz(n) <= max_base); for(int m = 1; m < n; m *= 2) { Mint w = 1; for(int s = 0, k = 0; s < n; s += 2 * m) { for(int i = s, j = s + m; i < s + m; ++i, ++j) { auto x = a[i], y = a[j]; a[i] = x + y, a[j] = (x - y) * w; } w *= idw[__builtin_ctz(++k)]; } } if(f) { Mint inv_sz = Mint(1) / n; for(int i = 0; i < n; i++) a[i] *= inv_sz; } } vector< Mint > multiply(vector< Mint > a, vector< Mint > b) { int need = a.size() + b.size() - 1; int nbase = 1; while((1 << nbase) < need) nbase++; int sz = 1 << nbase; a.resize(sz, 0); b.resize(sz, 0); ntt(a); ntt(b); Mint inv_sz = Mint(1) / sz; for(int i = 0; i < sz; i++) a[i] *= b[i] * inv_sz; intt(a, false); a.resize(need); return a; } }; int main() { int64 N; cin >> N; int Q; cin >> Q; vector< int64 > K(Q); vector< int > A(Q), B(Q), S(Q), T(Q); for(int i = 0; i < Q; i++) { cin >> K[i] >> A[i] >> B[i] >> S[i] >> T[i]; } auto ks{K}; sort(begin(ks), end(ks)); ks.erase(unique(begin(ks), end(ks)), end(ks)); for(int i = 0; i < Q; i++) { K[i] = lower_bound(begin(ks), end(ks), K[i]) - begin(ks); } NumberTheoreticTransformFriendlyModInt< modint > ntt; using FPS = FormalPowerSeries< modint >; FPS::set_fft([&](FPS &a) { ntt.ntt(a); }, [&](FPS &a) { ntt.intt(a); }); FPS fps(3001, 1); vector< FPS > mark(ks.size(), fps); fps = fps.pow(N, 3001); auto can = make_v< int >(ks.size(), 3001); for(int i = 0; i < Q; i++) { fps *= mark[K[i]].inv(3001); fps.resize(3001); for(int j = A[i]; j <= B[i]; j++) { can[K[i]][j] = 1; } mark[K[i]].assign(3001, modint(0)); for(int j = 0; j < 3001; j++) { if(can[K[i]][j] == 0) mark[K[i]][j] = 1; } fps *= mark[K[i]]; fps.resize(3001); modint sum = 0; for(int j = S[i]; j <= T[i]; j++) { sum += fps[j]; } cout << sum << "\n"; } }