Submit Info #58895

Problem Lang User Status Time Memory
Multipoint Evaluation cpp tokusakurai AC 1204 ms 27.20 MiB

ケース詳細
Name Status Time Memory
example_00 AC 3 ms 0.67 MiB
example_01 AC 2 ms 0.68 MiB
max_random_00 AC 1204 ms 27.18 MiB
max_random_01 AC 1197 ms 27.20 MiB
random_00 AC 219 ms 11.40 MiB
random_01 AC 203 ms 8.59 MiB
random_02 AC 1032 ms 23.69 MiB
zero_00 AC 1 ms 0.68 MiB

#include <bits/stdc++.h> using namespace std; struct io_setup { io_setup() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout << fixed << setprecision(15); } } io_setup; const int MOD = 998244353; template <int mod> struct Mod_Int { int x; Mod_Int() : x(0) {} Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} static int get_mod() { return mod; } Mod_Int &operator+=(const Mod_Int &p) { if ((x += p.x) >= mod) x -= mod; return *this; } Mod_Int &operator-=(const Mod_Int &p) { if ((x += mod - p.x) >= mod) x -= mod; return *this; } Mod_Int &operator*=(const Mod_Int &p) { x = (int)(1LL * x * p.x % mod); return *this; } Mod_Int &operator/=(const Mod_Int &p) { *this *= p.inverse(); return *this; } Mod_Int &operator++() { return *this += Mod_Int(1); } Mod_Int operator++(int) { Mod_Int tmp = *this; ++*this; return tmp; } Mod_Int &operator--() { return *this -= Mod_Int(1); } Mod_Int operator--(int) { Mod_Int tmp = *this; --*this; return tmp; } Mod_Int operator-() const { return Mod_Int(-x); } Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; } Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; } Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; } Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; } bool operator==(const Mod_Int &p) const { return x == p.x; } bool operator!=(const Mod_Int &p) const { return x != p.x; } Mod_Int inverse() const { assert(*this != Mod_Int(0)); return pow(mod - 2); } Mod_Int pow(long long k) const { Mod_Int now = *this, ret = 1; for (; k > 0; k >>= 1, now *= now) { if (k & 1) ret *= now; } return ret; } friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; } friend istream &operator>>(istream &is, Mod_Int &p) { long long a; is >> a; p = Mod_Int<mod>(a); return is; } }; using mint = Mod_Int<MOD>; template <typename T> struct Number_Theoretic_Transform { static int max_base; static T root; static vector<T> r, ir; Number_Theoretic_Transform() {} static void init() { if (!r.empty()) return; int mod = T::get_mod(); int tmp = mod - 1; root = 2; while (root.pow(tmp >> 1) == 1) root++; max_base = 0; while (tmp % 2 == 0) tmp >>= 1, max_base++; r.resize(max_base), ir.resize(max_base); for (int i = 0; i < max_base; i++) { r[i] = -root.pow((mod - 1) >> (i + 2)); // r[i]:=1の2^(i+2)乗根 ir[i] = r[i].inverse(); // ir[i]:=1/r[i] } } static void ntt(vector<T> &a) { init(); int n = a.size(); assert((n & (n - 1)) == 0); assert(n <= (1 << max_base)); for (int k = n; k >>= 1;) { T w = 1; for (int s = 0, t = 0; s < n; s += 2 * k) { for (int i = s, j = s + k; i < s + k; i++, j++) { T x = a[i], y = w * a[j]; a[i] = x + y, a[j] = x - y; } w *= r[__builtin_ctz(++t)]; } } } static void intt(vector<T> &a) { init(); int n = a.size(); assert((n & (n - 1)) == 0); assert(n <= (1 << max_base)); for (int k = 1; k < n; k <<= 1) { T w = 1; for (int s = 0, t = 0; s < n; s += 2 * k) { for (int i = s, j = s + k; i < s + k; i++, j++) { T x = a[i], y = a[j]; a[i] = x + y, a[j] = w * (x - y); } w *= ir[__builtin_ctz(++t)]; } } T inv = T(n).inverse(); for (auto &e : a) e *= inv; } static vector<T> convolve(vector<T> a, vector<T> b) { int k = (int)a.size() + (int)b.size() - 1, n = 1; while (n < k) n <<= 1; a.resize(n), b.resize(n); ntt(a), ntt(b); for (int i = 0; i < n; i++) a[i] *= b[i]; intt(a), a.resize(k); return a; } }; template <typename T> int Number_Theoretic_Transform<T>::max_base = 0; template <typename T> T Number_Theoretic_Transform<T>::root = T(); template <typename T> vector<T> Number_Theoretic_Transform<T>::r = vector<T>(); template <typename T> vector<T> Number_Theoretic_Transform<T>::ir = vector<T>(); using NTT = Number_Theoretic_Transform<mint>; template <typename T> struct Formal_Power_Series : vector<T> { using NTT_ = Number_Theoretic_Transform<T>; using vector<T>::vector; Formal_Power_Series(const vector<T> &v) : vector<T>(v) {} Formal_Power_Series pre(int n) const { return Formal_Power_Series(begin(*this), begin(*this) + min((int)this->size(), n)); } Formal_Power_Series rev(int deg = -1) const { Formal_Power_Series ret = *this; if (deg != -1) ret.resize(deg, T(0)); reverse(begin(ret), end(ret)); return ret; } void normalize() { while (!this->empty() && this->back() == 0) this->pop_back(); } Formal_Power_Series operator-() const { Formal_Power_Series ret = *this; for (int i = 0; i < (int)ret.size(); i++) ret[i] = -ret[i]; return ret; } Formal_Power_Series &operator+=(const T &x) { if (this->empty()) this->resize(1); (*this)[0] += x; return *this; } Formal_Power_Series &operator+=(const Formal_Power_Series &v) { if (v.size() > this->size()) this->resize(v.size()); for (int i = 0; i < (int)v.size(); i++) (*this)[i] += v[i]; this->normalize(); return *this; } Formal_Power_Series &operator-=(const T &x) { if (this->empty()) this->resize(1); *this[0] -= x; return *this; } Formal_Power_Series &operator-=(const Formal_Power_Series &v) { if (v.size() > this->size()) this->resize(v.size()); for (int i = 0; i < (int)v.size(); i++) (*this)[i] -= v[i]; this->normalize(); return *this; } Formal_Power_Series &operator*=(const T &x) { for (int i = 0; i < (int)this->size(); i++) (*this)[i] *= x; return *this; } Formal_Power_Series &operator*=(const Formal_Power_Series &v) { if (this->empty() || empty(v)) { this->clear(); return *this; } return *this = NTT_::convolve(*this, v); } Formal_Power_Series &operator/=(const T &x) { assert(x != 0); T inv = x.inverse(); for (int i = 0; i < (int)this->size(); i++) (*this)[i] *= inv; return *this; } Formal_Power_Series &operator/=(const Formal_Power_Series &v) { if (v.size() > this->size()) { this->clear(); return *this; } int n = this->size() - (int)v.size() + 1; return *this = (rev().pre(n) * v.rev().inv(n)).pre(n).rev(n); } Formal_Power_Series &operator%=(const Formal_Power_Series &v) { return *this -= (*this / v) * v; } Formal_Power_Series &operator<<=(int x) { Formal_Power_Series ret(x, 0); ret.insert(end(ret), begin(*this), end(*this)); return *this = ret; } Formal_Power_Series &operator>>=(int x) { Formal_Power_Series ret; ret.insert(end(ret), begin(*this) + x, end(*this)); return *this = ret; } Formal_Power_Series operator+(const T &x) const { return Formal_Power_Series(*this) += x; } Formal_Power_Series operator+(const Formal_Power_Series &v) const { return Formal_Power_Series(*this) += v; } Formal_Power_Series operator-(const T &x) const { return Formal_Power_Series(*this) -= x; } Formal_Power_Series operator-(const Formal_Power_Series &v) const { return Formal_Power_Series(*this) -= v; } Formal_Power_Series operator*(const T &x) const { return Formal_Power_Series(*this) *= x; } Formal_Power_Series operator*(const Formal_Power_Series &v) const { return Formal_Power_Series(*this) *= v; } Formal_Power_Series operator/(const T &x) const { return Formal_Power_Series(*this) /= x; } Formal_Power_Series operator/(const Formal_Power_Series &v) const { return Formal_Power_Series(*this) /= v; } Formal_Power_Series operator%(const Formal_Power_Series &v) const { return Formal_Power_Series(*this) %= v; } Formal_Power_Series operator<<(int x) const { return Formal_Power_Series(*this) <<= x; } Formal_Power_Series operator>>(int x) const { return Formal_Power_Series(*this) >>= x; } T val(const T &x) const { T ret = 0; for (int i = (int)this->size() - 1; i >= 0; i--) ret *= x, ret += (*this)[i]; return ret; } Formal_Power_Series diff() const { // df/dx int n = this->size(); Formal_Power_Series ret(n - 1); for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * i; return ret; } Formal_Power_Series integral() const { // ∫fdx int n = this->size(); Formal_Power_Series ret(n + 1); for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / (i + 1); return ret; } Formal_Power_Series inv(int deg) const { // 1/f (f[0] != 0) assert((*this)[0] != T(0)); Formal_Power_Series ret(1, (*this)[0].inverse()); for (int i = 1; i < deg; i <<= 1) { Formal_Power_Series f = pre(2 * i), g = ret; f.resize(2 * i), g.resize(2 * i); NTT_::ntt(f), NTT_::ntt(g); Formal_Power_Series h(2 * i); for (int j = 0; j < 2 * i; j++) h[j] = f[j] * g[j]; NTT_::intt(h); for (int j = 0; j < i; j++) h[j] = 0; NTT_::ntt(h); for (int j = 0; j < 2 * i; j++) h[j] *= g[j]; NTT_::intt(h); for (int j = 0; j < i; j++) h[j] = 0; ret -= h; } ret.resize(deg); return ret; } Formal_Power_Series inv() const { return inv(this->size()); } Formal_Power_Series log(int deg) const { // log(f) (f[0] = 1) assert((*this)[0] == 1); Formal_Power_Series ret = (diff() * inv(deg)).pre(deg - 1).integral(); ret.resize(deg); return ret; } Formal_Power_Series log() const { return log(this->size()); } Formal_Power_Series exp(int deg) const { // exp(f) (f[0] = 0) assert((*this)[0] == 0); Formal_Power_Series inv; inv.reserve(deg + 1); inv.push_back(0), inv.push_back(1); auto inplace_integral = [&](Formal_Power_Series &F) -> void { int n = F.size(); int 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), 0); for (int i = 1; i <= n; i++) F[i] *= inv[i]; }; auto inplace_diff = [](Formal_Power_Series &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; } }; Formal_Power_Series ret{1, this->size() > 1 ? (*this)[1] : 0}, c{1}, z1, z2{1, 1}; for (int m = 2; m < deg; m *= 2) { auto y = ret; y.resize(2 * m); NTT_::ntt(y); z1 = z2; Formal_Power_Series z(m); for (int i = 0; i < m; i++) z[i] = y[i] * z1[i]; NTT_::intt(z); fill(begin(z), begin(z) + m / 2, 0); NTT_::ntt(z); for (int i = 0; i < m; i++) z[i] *= -z1[i]; NTT_::intt(z); c.insert(end(c), begin(z) + m / 2, end(z)); z2 = c, z2.resize(2 * m); NTT_::ntt(z2); Formal_Power_Series x(begin(*this), begin(*this) + min((int)this->size(), m)); inplace_diff(x); x.push_back(0); NTT_::ntt(x); for (int i = 0; i < m; i++) x[i] *= y[i]; NTT_::intt(x); x -= ret.diff(), x.resize(2 * m); for (int i = 0; i < m - 1; i++) x[m + i] = x[i], x[i] = 0; NTT_::ntt(x); for (int i = 0; i < 2 * m; i++) x[i] *= z2[i]; NTT_::intt(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, 0); NTT_::ntt(x); for (int i = 0; i < 2 * m; i++) x[i] *= y[i]; NTT_::intt(x); ret.insert(end(ret), begin(x) + m, end(x)); } ret.resize(deg); return ret; } Formal_Power_Series exp() const { return exp(this->size()); } Formal_Power_Series pow(long long k, int deg) const { // f^k int n = this->size(); for (int i = 0; i < n; i++) { if ((*this)[i] == 0) continue; T rev = (*this)[i].inverse(); Formal_Power_Series C(*this * rev), D(n - i, 0); for (int j = i; j < n; j++) D[j - i] = C[j]; D = (D.log() * k).exp() * ((*this)[i].pow(k)); Formal_Power_Series E(deg, 0); if (i > 0 && k > deg / i) return E; long long S = i * k; for (int j = 0; j + S < deg && j < D.size(); j++) E[j + S] = D[j]; E.resize(deg); return E; } return Formal_Power_Series(deg, 0); } Formal_Power_Series pow(long long k) const { return pow(k, this->size()); } Formal_Power_Series Taylor_shift(T c) const { int n = this->size(); vector<T> ifac(n, 1); Formal_Power_Series f(n), g(n); for (int i = 0; i < n; i++) { f[n - 1 - i] = (*this)[i] * ifac[n - 1]; if (i < n - 1) ifac[n - 1] *= i + 1; } ifac[n - 1] = ifac[n - 1].inverse(); for (int i = n - 1; i > 0; i--) ifac[i - 1] = ifac[i] * i; T pw = 1; for (int i = 0; i < n; i++) { g[i] = pw * ifac[i]; pw *= c; } f *= g; Formal_Power_Series b(n); for (int i = 0; i < n; i++) b[i] = f[n - 1 - i] * ifac[i]; return b; } }; using fps = Formal_Power_Series<mint>; template <typename T> vector<Formal_Power_Series<T>> subproduct_tree(const vector<T> &xs) { int n = xs.size(); int k = 1; while (k < n) k <<= 1; vector<Formal_Power_Series<T>> g(2 * k, {1}); for (int i = 0; i < n; i++) g[k + i] = {-xs[i], 1}; for (int i = k - 1; i > 0; i--) g[i] = g[2 * i] * g[2 * i + 1]; return g; } template <typename T> vector<T> multipoint_evaluation(const Formal_Power_Series<T> &f, const vector<T> &xs) { vector<Formal_Power_Series<T>> g = subproduct_tree(xs); int n = xs.size(), k = g.size() / 2; g[1] = f % g[1]; for (int i = 2; i < k + n; i++) g[i] = g[i / 2] % g[i]; vector<T> ys(n); for (int i = 0; i < n; i++) ys[i] = g[k + i].empty() ? 0 : g[k + i][0]; return ys; } int main() { int N, M; cin >> N >> M; fps f(N, 1); vector<mint> xs(M, 1); for (int i = 0; i < N; i++) cin >> f[i]; for (int i = 0; i < M; i++) cin >> xs[i]; vector<mint> ys = multipoint_evaluation(f, xs); for (int i = 0; i < M; i++) cout << ys[i] << (i == M - 1 ? '\n' : ' '); }