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#define PROBLEM "https://atcoder.jp/contests/abc245/tasks/abc245_d" #include <iostream> #include <atcoder/modint> using mint = atcoder::modint998244353; #include "library/polynomial/fps_naive.hpp" int main() { int n, m; std::cin >> n >> m; suisen::FPSNaive<mint> a(n + 1), c(n + m + 1); for (auto &e : a) { int v; std::cin >> v; e = v; } for (auto &e : c) { int v; std::cin >> v; e = v; } auto [b, r] = c.div_mod(a); assert(r == suisen::FPSNaive<mint>{}); for (int i = 0; i <= m; ++i) { int v = b[i].val(); std::cout << (v > 100 ? v - mint::mod() : v) << " \n"[i == m]; } }
#line 1 "test/src/polynomial/fps_naive/abc245_d.test.cpp" #define PROBLEM "https://atcoder.jp/contests/abc245/tasks/abc245_d" #include <iostream> #include <atcoder/modint> using mint = atcoder::modint998244353; #line 1 "library/polynomial/fps_naive.hpp" #include <cassert> #include <cmath> #include <limits> #include <type_traits> #include <vector> #line 1 "library/type_traits/type_traits.hpp" #line 7 "library/type_traits/type_traits.hpp" namespace suisen { template <typename ...Constraints> using constraints_t = std::enable_if_t<std::conjunction_v<Constraints...>, std::nullptr_t>; template <typename T, typename = std::nullptr_t> struct bitnum { static constexpr int value = 0; }; template <typename T> struct bitnum<T, constraints_t<std::is_integral<T>>> { static constexpr int value = std::numeric_limits<std::make_unsigned_t<T>>::digits; }; template <typename T> static constexpr int bitnum_v = bitnum<T>::value; template <typename T, size_t n> struct is_nbit { static constexpr bool value = bitnum_v<T> == n; }; template <typename T, size_t n> static constexpr bool is_nbit_v = is_nbit<T, n>::value; template <typename T, typename = std::nullptr_t> struct safely_multipliable { using type = T; }; template <typename T> struct safely_multipliable<T, constraints_t<std::is_signed<T>, is_nbit<T, 32>>> { using type = long long; }; template <typename T> struct safely_multipliable<T, constraints_t<std::is_signed<T>, is_nbit<T, 64>>> { using type = __int128_t; }; template <typename T> struct safely_multipliable<T, constraints_t<std::is_unsigned<T>, is_nbit<T, 32>>> { using type = unsigned long long; }; template <typename T> struct safely_multipliable<T, constraints_t<std::is_unsigned<T>, is_nbit<T, 64>>> { using type = __uint128_t; }; template <typename T> using safely_multipliable_t = typename safely_multipliable<T>::type; template <typename T, typename = void> struct rec_value_type { using type = T; }; template <typename T> struct rec_value_type<T, std::void_t<typename T::value_type>> { using type = typename rec_value_type<typename T::value_type>::type; }; template <typename T> using rec_value_type_t = typename rec_value_type<T>::type; template <typename T> class is_iterable { template <typename T_> static auto test(T_ e) -> decltype(e.begin(), e.end(), std::true_type{}); static std::false_type test(...); public: static constexpr bool value = decltype(test(std::declval<T>()))::value; }; template <typename T> static constexpr bool is_iterable_v = is_iterable<T>::value; template <typename T> class is_writable { template <typename T_> static auto test(T_ e) -> decltype(std::declval<std::ostream&>() << e, std::true_type{}); static std::false_type test(...); public: static constexpr bool value = decltype(test(std::declval<T>()))::value; }; template <typename T> static constexpr bool is_writable_v = is_writable<T>::value; template <typename T> class is_readable { template <typename T_> static auto test(T_ e) -> decltype(std::declval<std::istream&>() >> e, std::true_type{}); static std::false_type test(...); public: static constexpr bool value = decltype(test(std::declval<T>()))::value; }; template <typename T> static constexpr bool is_readable_v = is_readable<T>::value; } // namespace suisen #line 11 "library/polynomial/fps_naive.hpp" #line 1 "library/math/modint_extension.hpp" #line 5 "library/math/modint_extension.hpp" #include <optional> /** * refernce: https://37zigen.com/tonelli-shanks-algorithm/ * calculates x s.t. x^2 = a mod p in O((log p)^2). */ template <typename mint> std::optional<mint> safe_sqrt(mint a) { static int p = mint::mod(); if (a == 0) return std::make_optional(0); if (p == 2) return std::make_optional(a); if (a.pow((p - 1) / 2) != 1) return std::nullopt; mint b = 1; while (b.pow((p - 1) / 2) == 1) ++b; static int tlz = __builtin_ctz(p - 1), q = (p - 1) >> tlz; mint x = a.pow((q + 1) / 2); b = b.pow(q); for (int shift = 2; x * x != a; ++shift) { mint e = a.inv() * x * x; if (e.pow(1 << (tlz - shift)) != 1) x *= b; b *= b; } return std::make_optional(x); } /** * calculates x s.t. x^2 = a mod p in O((log p)^2). * if not exists, raises runtime error. */ template <typename mint> auto sqrt(mint a) -> decltype(mint::mod(), mint()) { return *safe_sqrt(a); } template <typename mint> auto log(mint a) -> decltype(mint::mod(), mint()) { assert(a == 1); return 0; } template <typename mint> auto exp(mint a) -> decltype(mint::mod(), mint()) { assert(a == 0); return 1; } template <typename mint, typename T> auto pow(mint a, T b) -> decltype(mint::mod(), mint()) { return a.pow(b); } template <typename mint> auto inv(mint a) -> decltype(mint::mod(), mint()) { return a.inv(); } #line 1 "library/math/inv_mods.hpp" #line 5 "library/math/inv_mods.hpp" namespace suisen { template <typename mint> class inv_mods { public: inv_mods() = default; inv_mods(int n) { ensure(n); } const mint& operator[](int i) const { ensure(i); return invs[i]; } static void ensure(int n) { int sz = invs.size(); if (sz < 2) invs = { 0, 1 }, sz = 2; if (sz < n + 1) { invs.resize(n + 1); for (int i = sz; i <= n; ++i) invs[i] = mint(mod - mod / i) * invs[mod % i]; } } private: static std::vector<mint> invs; static constexpr int mod = mint::mod(); }; template <typename mint> std::vector<mint> inv_mods<mint>::invs{}; template <typename mint> std::vector<mint> get_invs(const std::vector<mint>& vs) { const int n = vs.size(); mint p = 1; for (auto& e : vs) { p *= e; assert(e != 0); } mint ip = p.inv(); std::vector<mint> rp(n + 1); rp[n] = 1; for (int i = n - 1; i >= 0; --i) { rp[i] = rp[i + 1] * vs[i]; } std::vector<mint> res(n); for (int i = 0; i < n; ++i) { res[i] = ip * rp[i + 1]; ip *= vs[i]; } return res; } } #line 14 "library/polynomial/fps_naive.hpp" namespace suisen { template <typename T> struct FPSNaive : std::vector<T> { static inline int MAX_SIZE = std::numeric_limits<int>::max() / 2; using value_type = T; using element_type = rec_value_type_t<T>; using std::vector<value_type>::vector; FPSNaive(const std::initializer_list<value_type> l) : std::vector<value_type>::vector(l) {} FPSNaive(const std::vector<value_type>& v) : std::vector<value_type>::vector(v) {} static void set_max_size(int n) { FPSNaive<T>::MAX_SIZE = n; } const value_type operator[](int n) const { return n <= deg() ? unsafe_get(n) : value_type{ 0 }; } value_type& operator[](int n) { return ensure_deg(n), unsafe_get(n); } int size() const { return std::vector<value_type>::size(); } int deg() const { return size() - 1; } int normalize() { while (size() and this->back() == value_type{ 0 }) this->pop_back(); return deg(); } FPSNaive& cut_inplace(int n) { if (size() > n) this->resize(std::max(0, n)); return *this; } FPSNaive cut(int n) const { FPSNaive f = FPSNaive(*this).cut_inplace(n); return f; } FPSNaive operator+() const { return FPSNaive(*this); } FPSNaive operator-() const { FPSNaive f(*this); for (auto& e : f) e = -e; return f; } FPSNaive& operator++() { return ++(*this)[0], * this; } FPSNaive& operator--() { return --(*this)[0], * this; } FPSNaive& operator+=(const value_type x) { return (*this)[0] += x, *this; } FPSNaive& operator-=(const value_type x) { return (*this)[0] -= x, *this; } FPSNaive& operator+=(const FPSNaive& g) { ensure_deg(g.deg()); for (int i = 0; i <= g.deg(); ++i) unsafe_get(i) += g.unsafe_get(i); return *this; } FPSNaive& operator-=(const FPSNaive& g) { ensure_deg(g.deg()); for (int i = 0; i <= g.deg(); ++i) unsafe_get(i) -= g.unsafe_get(i); return *this; } FPSNaive& operator*=(const FPSNaive& g) { return *this = *this * g; } FPSNaive& operator*=(const value_type x) { for (auto& e : *this) e *= x; return *this; } FPSNaive& operator/=(const FPSNaive& g) { return *this = *this / g; } FPSNaive& operator%=(const FPSNaive& g) { return *this = *this % g; } FPSNaive& operator<<=(const int shamt) { this->insert(this->begin(), shamt, value_type{ 0 }); return *this; } FPSNaive& operator>>=(const int shamt) { if (shamt > size()) this->clear(); else this->erase(this->begin(), this->begin() + shamt); return *this; } friend FPSNaive operator+(FPSNaive f, const FPSNaive& g) { f += g; return f; } friend FPSNaive operator+(FPSNaive f, const value_type& x) { f += x; return f; } friend FPSNaive operator-(FPSNaive f, const FPSNaive& g) { f -= g; return f; } friend FPSNaive operator-(FPSNaive f, const value_type& x) { f -= x; return f; } friend FPSNaive operator*(const FPSNaive& f, const FPSNaive& g) { if (f.empty() or g.empty()) return FPSNaive{}; const int n = f.size(), m = g.size(); FPSNaive h(std::min(MAX_SIZE, n + m - 1)); for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) { if (i + j >= MAX_SIZE) break; h.unsafe_get(i + j) += f.unsafe_get(i) * g.unsafe_get(j); } return h; } friend FPSNaive operator*(FPSNaive f, const value_type& x) { f *= x; return f; } friend FPSNaive operator/(FPSNaive f, const FPSNaive& g) { return std::move(f.div_mod(g).first); } friend FPSNaive operator%(FPSNaive f, const FPSNaive& g) { return std::move(f.div_mod(g).second); } friend FPSNaive operator*(const value_type x, FPSNaive f) { f *= x; return f; } friend FPSNaive operator<<(FPSNaive f, const int shamt) { f <<= shamt; return f; } friend FPSNaive operator>>(FPSNaive f, const int shamt) { f >>= shamt; return f; } std::pair<FPSNaive, FPSNaive> div_mod(FPSNaive g) const { FPSNaive f = *this; const int fd = f.normalize(), gd = g.normalize(); assert(gd >= 0); if (fd < gd) return { FPSNaive{}, f }; if (gd == 0) return { f *= g.unsafe_get(0).inv(), FPSNaive{} }; const int k = f.deg() - gd; value_type head_inv = g.unsafe_get(gd).inv(); FPSNaive q(k + 1); for (int i = k; i >= 0; --i) { value_type div = f.unsafe_get(i + gd) * head_inv; q.unsafe_get(i) = div; for (int j = 0; j <= gd; ++j) f.unsafe_get(i + j) -= div * g.unsafe_get(j); } f.cut_inplace(gd); f.normalize(); return { q, f }; } friend bool operator==(const FPSNaive& f, const FPSNaive& g) { const int n = f.size(), m = g.size(); if (n < m) return g == f; for (int i = 0; i < m; ++i) if (f.unsafe_get(i) != g.unsafe_get(i)) return false; for (int i = m; i < n; ++i) if (f.unsafe_get(i) != 0) return false; return true; } friend bool operator!=(const FPSNaive& f, const FPSNaive& g) { return not (f == g); } FPSNaive mul(const FPSNaive& g, int n = -1) const { if (n < 0) n = size(); if (this->empty() or g.empty()) return FPSNaive{}; const int m = size(), k = g.size(); FPSNaive h(std::min(n, m + k - 1)); for (int i = 0; i < m; ++i) { for (int j = 0, jr = std::min(k, n - i); j < jr; ++j) { h.unsafe_get(i + j) += unsafe_get(i) * g.unsafe_get(j); } } return h; } FPSNaive diff() const { if (this->empty()) return {}; FPSNaive g(size() - 1); for (int i = 1; i <= deg(); ++i) g.unsafe_get(i - 1) = unsafe_get(i) * i; return g; } FPSNaive intg() const { const int n = size(); FPSNaive g(n + 1); for (int i = 0; i < n; ++i) g.unsafe_get(i + 1) = unsafe_get(i) * invs[i + 1]; if (g.deg() > MAX_SIZE) g.cut_inplace(MAX_SIZE); return g; } FPSNaive inv(int n = -1) const { if (n < 0) n = size(); FPSNaive g(n); const value_type inv_f0 = ::inv(unsafe_get(0)); g.unsafe_get(0) = inv_f0; for (int i = 1; i < n; ++i) { for (int j = 1; j <= i; ++j) g.unsafe_get(i) -= g.unsafe_get(i - j) * (*this)[j]; g.unsafe_get(i) *= inv_f0; } return g; } FPSNaive exp(int n = -1) const { if (n < 0) n = size(); assert(unsafe_get(0) == value_type{ 0 }); FPSNaive g(n); g.unsafe_get(0) = value_type{ 1 }; for (int i = 1; i < n; ++i) { for (int j = 1; j <= i; ++j) g.unsafe_get(i) += j * g.unsafe_get(i - j) * (*this)[j]; g.unsafe_get(i) *= invs[i]; } return g; } FPSNaive log(int n = -1) const { if (n < 0) n = size(); assert(unsafe_get(0) == value_type{ 1 }); FPSNaive g(n); g.unsafe_get(0) = value_type{ 0 }; for (int i = 1; i < n; ++i) { g.unsafe_get(i) = i * (*this)[i]; for (int j = 1; j < i; ++j) g.unsafe_get(i) -= (i - j) * g.unsafe_get(i - j) * (*this)[j]; g.unsafe_get(i) *= invs[i]; } return g; } FPSNaive pow(const long long k, int n = -1) const { if (n < 0) n = size(); if (k == 0) { FPSNaive res(n); res[0] = 1; return res; } int z = 0; while (z < size() and unsafe_get(z) == value_type{ 0 }) ++z; if (z == size() or z > (n - 1) / k) return FPSNaive(n, 0); const int m = n - z * k; FPSNaive g(m); const value_type inv_f0 = ::inv(unsafe_get(z)); g.unsafe_get(0) = unsafe_get(z).pow(k); for (int i = 1; i < m; ++i) { for (int j = 1; j <= i; ++j) g.unsafe_get(i) += (element_type{ k } *j - (i - j)) * g.unsafe_get(i - j) * (*this)[z + j]; g.unsafe_get(i) *= inv_f0 * invs[i]; } g <<= z * k; return g; } std::optional<FPSNaive> safe_sqrt(int n = -1) const { if (n < 0) n = size(); int dl = 0; while (dl < size() and unsafe_get(dl) == value_type{ 0 }) ++dl; if (dl == size()) return FPSNaive(n, 0); if (dl & 1) return std::nullopt; const int m = n - dl / 2; FPSNaive g(m); auto opt_g0 = ::safe_sqrt((*this)[dl]); if (not opt_g0.has_value()) return std::nullopt; g.unsafe_get(0) = *opt_g0; value_type inv_2g0 = ::inv(2 * g.unsafe_get(0)); for (int i = 1; i < m; ++i) { g.unsafe_get(i) = (*this)[dl + i]; for (int j = 1; j < i; ++j) g.unsafe_get(i) -= g.unsafe_get(j) * g.unsafe_get(i - j); g.unsafe_get(i) *= inv_2g0; } g <<= dl / 2; return g; } FPSNaive sqrt(int n = -1) const { if (n < 0) n = size(); return *safe_sqrt(n); } value_type eval(value_type x) const { value_type y = 0; for (int i = size() - 1; i >= 0; --i) y = y * x + unsafe_get(i); return y; } private: static inline inv_mods<element_type> invs; void ensure_deg(int d) { if (deg() < d) this->resize(d + 1, value_type{ 0 }); } const value_type& unsafe_get(int i) const { return std::vector<value_type>::operator[](i); } value_type& unsafe_get(int i) { return std::vector<value_type>::operator[](i); } }; } // namespace suisen template <typename mint> suisen::FPSNaive<mint> sqrt(suisen::FPSNaive<mint> a) { return a.sqrt(); } template <typename mint> suisen::FPSNaive<mint> log(suisen::FPSNaive<mint> a) { return a.log(); } template <typename mint> suisen::FPSNaive<mint> exp(suisen::FPSNaive<mint> a) { return a.exp(); } template <typename mint, typename T> suisen::FPSNaive<mint> pow(suisen::FPSNaive<mint> a, T b) { return a.pow(b); } template <typename mint> suisen::FPSNaive<mint> inv(suisen::FPSNaive<mint> a) { return a.inv(); } #line 8 "test/src/polynomial/fps_naive/abc245_d.test.cpp" int main() { int n, m; std::cin >> n >> m; suisen::FPSNaive<mint> a(n + 1), c(n + m + 1); for (auto &e : a) { int v; std::cin >> v; e = v; } for (auto &e : c) { int v; std::cin >> v; e = v; } auto [b, r] = c.div_mod(a); assert(r == suisen::FPSNaive<mint>{}); for (int i = 0; i <= m; ++i) { int v = b[i].val(); std::cout << (v > 100 ? v - mint::mod() : v) << " \n"[i == m]; } }