#define LOCAL #include using namespace std; #pragma region Macros typedef long long ll; typedef __int128_t i128; typedef unsigned int uint; typedef unsigned long long ull; #define ALL(x) (x).begin(), (x).end() template istream& operator>>(istream& is, vector& v) { for (T& x : v) is >> x; return is; } template ostream& operator<<(ostream& os, const vector& v) { for (int i = 0; i < (int)v.size(); i++) { os << v[i] << (i + 1 == (int)v.size() ? "" : " "); } return os; } template ostream& operator<<(ostream& os, const pair& p) { os << '(' << p.first << ',' << p.second << ')'; return os; } template ostream& operator<<(ostream& os, const tuple& t) { os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ')'; return os; } template ostream& operator<<(ostream& os, const tuple& t) { os << '(' << get<0>(t) << ',' << get<1>(t) << ',' << get<2>(t) << ',' << get<3>(t) << ')'; return os; } template ostream& operator<<(ostream& os, const map& m) { os << '{'; for (auto itr = m.begin(); itr != m.end();) { os << '(' << itr->first << ',' << itr->second << ')'; if (++itr != m.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const unordered_map& m) { os << '{'; for (auto itr = m.begin(); itr != m.end();) { os << '(' << itr->first << ',' << itr->second << ')'; if (++itr != m.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const set& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const multiset& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const unordered_set& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const deque& v) { for (int i = 0; i < (int)v.size(); i++) { os << v[i] << (i + 1 == (int)v.size() ? "" : " "); } return os; } void debug_out() { cerr << '\n'; } template void debug_out(Head&& head, Tail&&... tail) { cerr << head; if (sizeof...(Tail) > 0) cerr << ", "; debug_out(move(tail)...); } #ifdef LOCAL #define debug(...) \ cerr << " "; \ cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \ cerr << " "; \ debug_out(__VA_ARGS__) #else #define debug(...) 42 #endif template T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; } template T lcm(T x, T y) { return x / gcd(x, y) * y; } template inline bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; } #pragma endregion /** * @brief modint * @docs docs/modulo/modint.md */ template class modint { using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; public: u32 v; constexpr modint(const i64 x = 0) noexcept : v(x < 0 ? mod - 1 - (-(x + 1) % mod) : x % mod) {} constexpr u32& value() noexcept { return v; } constexpr const u32& value() const noexcept { return v; } constexpr modint operator+(const modint& rhs) const noexcept { return modint(*this) += rhs; } constexpr modint operator-(const modint& rhs) const noexcept { return modint(*this) -= rhs; } constexpr modint operator*(const modint& rhs) const noexcept { return modint(*this) *= rhs; } constexpr modint operator/(const modint& rhs) const noexcept { return modint(*this) /= rhs; } constexpr modint& operator+=(const modint& rhs) noexcept { v += rhs.v; if (v >= mod) v -= mod; return *this; } constexpr modint& operator-=(const modint& rhs) noexcept { if (v < rhs.v) v += mod; v -= rhs.v; return *this; } constexpr modint& operator*=(const modint& rhs) noexcept { v = (u64)v * rhs.v % mod; return *this; } constexpr modint& operator/=(const modint& rhs) noexcept { return *this *= rhs.pow(mod - 2); } constexpr modint pow(u64 exp) const noexcept { modint self(*this), res(1); while (exp > 0) { if (exp & 1) res *= self; self *= self; exp >>= 1; } return res; } constexpr modint& operator++() noexcept { if (++v == mod) v = 0; return *this; } constexpr modint& operator--() noexcept { if (v == 0) v = mod; return --v, *this; } constexpr modint operator++(int) noexcept { modint t = *this; return ++*this, t; } constexpr modint operator--(int) noexcept { modint t = *this; return --*this, t; } constexpr modint operator-() const noexcept { return modint(mod - v); } template friend constexpr modint operator+(T x, modint y) noexcept { return modint(x) + y; } template friend constexpr modint operator-(T x, modint y) noexcept { return modint(x) - y; } template friend constexpr modint operator*(T x, modint y) noexcept { return modint(x) * y; } template friend constexpr modint operator/(T x, modint y) noexcept { return modint(x) / y; } constexpr bool operator==(const modint& rhs) const noexcept { return v == rhs.v; } constexpr bool operator!=(const modint& rhs) const noexcept { return v != rhs.v; } constexpr bool operator!() const noexcept { return !v; } friend istream& operator>>(istream& s, modint& rhs) noexcept { i64 v; rhs = modint{(s >> v, v)}; return s; } friend ostream& operator<<(ostream& s, const modint& rhs) noexcept { return s << rhs.v; } }; /** * @brief Number Theoretic Transform * @docs docs/convolution/NumberTheoreticTransform.md */ template struct NumberTheoreticTransform { using Mint = modint; vector roots; vector rev; int base, max_base; Mint root; NumberTheoreticTransform() : base(1), rev{0, 1}, roots{Mint(0), Mint(1)} { int tmp = mod - 1; for (max_base = 0; tmp % 2 == 0; max_base++) tmp >>= 1; root = 2; while (root.pow((mod - 1) >> 1) == 1) root++; root = root.pow((mod - 1) >> max_base); } void ensure_base(int nbase) { if (nbase <= base) return; rev.resize(1 << nbase); for (int i = 0; i < (1 << nbase); i++) { rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (nbase - 1)); } roots.resize(1 << nbase); for (; base < nbase; base++) { Mint z = root.pow(1 << (max_base - 1 - base)); for (int i = 1 << (base - 1); i < (1 << base); i++) { roots[i << 1] = roots[i]; roots[i << 1 | 1] = roots[i] * z; } } } void ntt(vector& a) { const int n = a.size(); int zeros = __builtin_ctz(n); ensure_base(zeros); int shift = base - zeros; for (int i = 0; i < n; i++) { if (i < (rev[i] >> shift)) { swap(a[i], a[rev[i] >> shift]); } } for (int k = 1; k < n; k <<= 1) { for (int i = 0; i < n; i += (k << 1)) { for (int j = 0; j < k; j++) { Mint z = a[i + j + k] * roots[j + k]; a[i + j + k] = a[i + j] - z; a[i + j] = a[i + j] + z; } } } } vector multiply(vector a, vector b) { int need = a.size() + b.size() - 1; int nbase = 1; while ((1 << nbase) < need) nbase++; ensure_base(nbase); int sz = 1 << nbase; a.resize(sz, Mint(0)); b.resize(sz, Mint(0)); ntt(a); ntt(b); Mint inv_sz = 1 / Mint(sz); for (int i = 0; i < sz; i++) a[i] *= b[i] * inv_sz; reverse(a.begin() + 1, a.end()); ntt(a); a.resize(need); return a; } vector multiply(vector a, vector b) { vector A(a.size()), B(b.size()); for (int i = 0; i < a.size(); i++) A[i] = Mint(a[i]); for (int i = 0; i < b.size(); i++) B[i] = Mint(b[i]); vector C = multiply(A, B); vector res(C.size()); for (int i = 0; i < C.size(); i++) res[i] = C[i].v; return res; } }; /** * @brief Formal Power Series * @docs docs/polynomial/FormalPowerSeries.md */ template struct FormalPowerSeries : vector { using vector::vector; using Poly = FormalPowerSeries; using MUL = function; static MUL& get_mul() { static MUL mul = nullptr; return mul; } static void set_mul(MUL f) { get_mul() = f; } void shrink() { while (this->size() && this->back() == M(0)) this->pop_back(); } Poly pre(int deg) const { return Poly(this->begin(), this->begin() + min((int)this->size(), deg)); } Poly operator+(const M& v) const { return Poly(*this) += v; } Poly operator+(const Poly& p) const { return Poly(*this) += p; } Poly operator-(const M& v) const { return Poly(*this) -= v; } Poly operator-(const Poly& p) const { return Poly(*this) -= p; } Poly operator*(const M& v) const { return Poly(*this) *= v; } Poly operator*(const Poly& p) const { return Poly(*this) *= p; } Poly operator/(const Poly& p) const { return Poly(*this) /= p; } Poly operator%(const Poly& p) const { return Poly(*this) %= p; } Poly& operator+=(const M& v) { if (this->empty()) this->resize(1); (*this)[0] += v; return *this; } Poly& operator+=(const Poly& p) { if (p.size() > this->size()) this->resize(p.size()); for (int i = 0; i < (int)p.size(); i++) (*this)[i] += p[i]; return *this; } Poly& operator-=(const M& v) { if (this->empty()) this->resize(1); (*this)[0] -= v; return *this; } Poly& operator-=(const Poly& p) { if (p.size() > this->size()) this->resize(p.size()); for (int i = 0; i < (int)p.size(); i++) (*this)[i] -= p[i]; return *this; } Poly& operator*=(const M& v) { for (int i = 0; i < (int)this->size(); i++) (*this)[i] *= v; return *this; } Poly& operator*=(const Poly& p) { if (this->empty() || p.empty()) { this->clear(); return *this; } assert(get_mul() != nullptr); return *this = get_mul()(*this, p); } Poly& operator/=(const Poly& p) { if (this->size() < p.size()) { this->clear(); return *this; } int n = this->size() - p.size() - 1; debug(n); Poly a = rev().pre(n); debug(p.size()); return *this = (rev().pre(n) * p.rev().inv(n)).pre(n).rev(n); } Poly& operator%=(const Poly& p) { return *this -= *this / p * p; } Poly operator<<(const int deg) { Poly res(*this); res.insert(res.begin(), deg, M(0)); return res; } Poly operator>>(const int deg) { if (this->size() <= deg) return {}; Poly res(*this); res.erase(res.begin(), res.begin() + deg); return res; } Poly operator-() const { Poly res(this->size()); for (int i = 0; i < (int)this->size(); i++) res[i] = -(*this)[i]; return res; } Poly rev(int deg = -1) const { Poly res(*this); if (~deg) res.resize(deg, M(0)); reverse(res.begin(), res.end()); return res; } Poly diff() const { Poly res(max(0, (int)this->size() - 1)); for (int i = 1; i < (int)this->size(); i++) res[i - 1] = (*this)[i] * M(i); return res; } Poly integral() const { Poly res(this->size() + 1); res[0] = M(0); for (int i = 0; i < (int)this->size(); i++) res[i + 1] = (*this)[i] / M(i + 1); return res; } Poly inv(int deg = -1) const { assert((*this)[0] != M(0)); if (deg < 0) deg = this->size(); Poly res({M(1) / (*this)[0]}); for (int i = 1; i < deg; i <<= 1) { res = (res + res - res * res * pre(i << 1)).pre(i << 1); } return res.pre(deg); } Poly log(int deg = -1) const { assert((*this)[0] == M(1)); if (deg < 0) deg = this->size(); return (this->diff() * this->inv(deg)).pre(deg - 1).integral(); } Poly sqrt(int deg = -1) const { assert((*this)[0] == M(1)); if (deg == -1) deg = this->size(); Poly res({M(1)}); M inv2 = M(1) / M(2); for (int i = 1; i < deg; i <<= 1) { res = (res + pre(i << 1) * res.inv(i << 1)) * inv2; } return res.pre(deg); } Poly exp(int deg = -1) { assert((*this)[0] == M(0)); if (deg < 0) deg = this->size(); Poly res({M(1)}); for (int i = 1; i < deg; i <<= 1) { res = (res * (pre(i << 1) + M(1) - res.log(i << 1))).pre(i << 1); } return res.pre(deg); } Poly pow(long long k, int deg = -1) const { if (deg < 0) deg = this->size(); for (int i = 0; i < (int)this->size(); i++) { if ((*this)[i] == M(0)) continue; if (k * i > deg) return Poly(deg, M(0)); M inv = M(1) / (*this)[i]; Poly res = (((*this * inv) >> i).log() * k).exp() * (*this)[i].pow(k); res = (res << (i * k)).pre(deg); if ((int)res.size() < deg) res.resize(deg, M(0)); return res; } return *this; } Poly pow_mod(long long k, const Poly& mod) const { Poly x(*this), res = {M(1)}; while (k > 0) { if (k & 1) res = res * x % mod; x = x * x % mod; k >>= 1; } return res; } Poly linear_mul(const M& a, const M& b) { Poly res(this->size() + 1); for (int i = 0; i < this->size() + 1; i++) { res[i] = (i - 1 >= 0 ? (*this)[i - 1] * a : M(0)) + (i < (int)this->size() ? (*this)[i] * b : M(0)); } return res; } Poly linear_div(const M& a, const M& b) { Poly res(this->size() - 1); M inv_b = M(1) / b; for (int i = 0; i + 1 < (int)this->size(); i++) { res[i] = ((*this)[i] - (i - 1 >= 0 ? res[i - 1] * a : M(0))) * inv_b; } return res; } Poly sparse_mul(const M& c, const M& d) { Poly res(*this); res.resize(this->size() + d, M(0)); for (int i = 0; i < (int)this->size(); i++) { res[i + d] += (*this)[i] * c; } return res; } Poly sparse_div(const M& c, const M& d) { Poly res(*this); for (int i = 0; i < res.size() - d; i++) { res[i + d] -= res[i] * c; } return res; } M operator()(const M& x) const { M res = 0, power = 1; for (int i = 0; i < (int)this->size(); i++, power *= x) { res += (*this)[i] * power; } return res; } }; /** * @brief compress */ template map compress(vector& v) { sort(v.begin(), v.end()); v.erase(unique(v.begin(), v.end()), v.end()); map res; for (int i = 0; i < v.size(); i++) res[v[i]] = i; return res; } /** * @brief Segment Tree * @docs docs/datastructure/SegmentTree.md */ template struct SegmentTree { typedef function F; int n; F f; Monoid id; vector dat; SegmentTree(int n_, F f, Monoid id) : f(f), id(id) { init(n_); } void init(int n_) { n = 1; while (n < n_) n <<= 1; dat.assign(n << 1, id); } void build(const vector& v) { for (int i = 0; i < (int)v.size(); i++) dat[i + n] = v[i]; for (int i = n - 1; i; i--) dat[i] = f(dat[i << 1 | 0], dat[i << 1 | 1]); } void update(int k, Monoid x) { dat[k += n] = x; while (k >>= 1) dat[k] = f(dat[k << 1 | 0], dat[k << 1 | 1]); } Monoid query(int a, int b) { if (a >= b) return id; Monoid vl = id, vr = id; for (int l = a + n, r = b + n; l < r; l >>= 1, r >>= 1) { if (l & 1) vl = f(vl, dat[l++]); if (r & 1) vr = f(dat[--r], vr); } return f(vl, vr); } template int find_subtree(int k, const C& check, Monoid& M, bool type) { while (k < n) { Monoid nxt = type ? f(dat[k << 1 | type], M) : f(M, dat[k << 1 | type]); if (check(nxt)) k = k << 1 | type; else M = nxt, k = k << 1 | (type ^ 1); } return k - n; } // min i s.t. f(seg[a],seg[a+1],...,seg[i]) satisfy "check" template int find_first(int a, const C& check) { Monoid L = id; if (a <= 0) { if (check(f(L, dat[1]))) return find_subtree(1, check, L, false); return -1; } int b = n; for (int l = a + n, r = b + n; l < r; l >>= 1, r >>= 1) { if (l & 1) { Monoid nxt = f(L, dat[l]); if (check(nxt)) return find_subtree(l, check, L, false); L = nxt; l++; } } return -1; } // max i s.t. f(seg[i],...,seg[b-2],seg[b-1]) satisfy "check" template int find_last(int b, const C& check) { Monoid R = id; if (b >= n) { if (check(f(dat[1], R))) return find_subtree(1, check, R, true); return -1; } int a = n; for (int l = a, r = b + n; l < r; l >>= 1, r >>= 1) { if (r & 1) { Monoid nxt = f(dat[--r], R); if (check(nxt)) return find_subtree(r, check, R, true); R = nxt; } } return -1; } Monoid operator[](int i) { return dat[i + n]; } }; const int INF = 1e9; const long long IINF = 1e18; const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; const char dir[4] = {'D', 'R', 'U', 'L'}; // const long long MOD = 1000000007; const long long MOD = 998244353; using mint = modint; using FPS = FormalPowerSeries; const int MAX_N = 3010; int main() { cin.tie(0); ios::sync_with_stdio(false); NumberTheoreticTransform NTT; auto mul = [&](const FPS::Poly& a, const FPS::Poly& b) { auto res = NTT.multiply(a, b); return FPS::Poly(res.begin(), res.begin() + min((int)res.size(), MAX_N)); }; FPS::set_mul(mul); ll N; int Q; cin >> N >> Q; vector K(Q); vector 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], --K[i]; vector comp = K; map mp = compress(comp); for (ll& x : K) x = mp[x]; int sz = mp.size(); vector> comb(sz + 1, vector(MAX_N)); // 和 j を N - i 要素に分割 for (int i = 0; i <= sz; i++) { ll cur = N - i - 1; if (i == N) { comb[i][0] = 1; continue; } comb[i][0] = 1; for (int j = 1; j < MAX_N; j++) comb[i][j] = comb[i][j - 1] * (++cur) / j; } vector a(sz, FPS(MAX_N, 1)); FPS id(1, 1); auto f = [](FPS a, FPS b) -> FPS { auto c = a * b; return c; }; SegmentTree seg(sz, f, id); seg.build(a); FPS other(MAX_N, 0); for (int i = 0; i < MAX_N; i++) other[i] = comb[sz][i]; // for (int j = 0; j < 10; j++) cerr << other[j] << (j + 1 == 10 ? '\n' : ' '); for (int i = 0; i < Q; i++) { for (int j = A[i]; j <= B[i]; j++) a[K[i]][j] = 0; seg.update(K[i], a[K[i]]); auto res = seg.query(0, sz); // for (int j = 0; j < 10; j++) cerr << res[j] << (j + 1 == 10 ? '\n' : ' '); res *= other; // for (int j = 0; j < 10; j++) cerr << res[j] << (j + 1 == 10 ? '\n' : ' '); mint ans = 0; for (int j = S[i]; j <= min((int)res.size() - 1, T[i]); j++) ans += res[j]; cout << ans << '\n'; } return 0; }