Submit Info #29844

Problem Lang User Status Time Memory
Polynomial Taylor Shift cpp hitonanode AC 990 ms 30.00 MiB

ケース詳細
Name Status Time Memory
example_00 AC 0 ms 0.62 MiB
example_01 AC 1 ms 0.67 MiB
fft_killer_00 AC 990 ms 30.00 MiB
fft_killer_01 AC 990 ms 29.92 MiB
max_random_00 AC 983 ms 29.93 MiB
max_random_01 AC 982 ms 29.92 MiB
medium_00 AC 4 ms 0.74 MiB
medium_01 AC 13 ms 1.17 MiB
medium_02 AC 12 ms 1.17 MiB
medium_all_zero_00 AC 4 ms 0.80 MiB
medium_c_zero_00 AC 2 ms 0.66 MiB
random_00 AC 950 ms 28.45 MiB
random_01 AC 964 ms 29.24 MiB
random_02 AC 110 ms 4.16 MiB
small_00 AC 3 ms 0.67 MiB
small_01 AC 1 ms 0.68 MiB
small_02 AC 1 ms 0.59 MiB
small_03 AC 1 ms 0.63 MiB
small_04 AC 1 ms 0.67 MiB
small_05 AC 2 ms 0.68 MiB
small_06 AC 3 ms 0.67 MiB
small_07 AC 1 ms 0.66 MiB
small_08 AC 1 ms 0.66 MiB
small_09 AC 1 ms 0.66 MiB
small_10 AC 1 ms 0.36 MiB
small_11 AC 2 ms 0.61 MiB
small_12 AC 1 ms 0.62 MiB
small_13 AC 1 ms 0.67 MiB
small_14 AC 1 ms 0.64 MiB
small_15 AC 1 ms 0.66 MiB

#include <iostream> #include <vector> #include <set> // CUT begin template <int mod> struct ModInt { using lint = long long; static int get_mod() { return mod; } static int get_primitive_root() { static int primitive_root = 0; if (!primitive_root) { primitive_root = [&](){ std::set<int> fac; int v = mod - 1; for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i; if (v > 1) fac.insert(v); for (int g = 1; g < mod; g++) { bool ok = true; for (auto i : fac) if (ModInt(g).power((mod - 1) / i) == 1) { ok = false; break; } if (ok) return g; } return -1; }(); } return primitive_root; } int val; constexpr ModInt() : val(0) {} constexpr ModInt &_setval(lint v) { val = (v >= mod ? v - mod : v); return *this; } constexpr ModInt(lint v) { _setval(v % mod + mod); } explicit operator bool() const { return val != 0; } constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); } constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); } constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); } constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); } constexpr ModInt operator-() const { return ModInt()._setval(mod - val); } constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; } constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; } constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; } constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; } friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); } friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); } friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); } friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); } constexpr bool operator==(const ModInt &x) const { return val == x.val; } constexpr bool operator!=(const ModInt &x) const { return val != x.val; } bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map<ModInt, T> friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; is >> t; x = ModInt(t); return is; } friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val; return os; } constexpr lint power(lint n) const { lint ans = 1, tmp = this->val; while (n) { if (n & 1) ans = ans * tmp % mod; tmp = tmp * tmp % mod; n /= 2; } return ans; } constexpr lint inv() const { return this->power(mod - 2); } constexpr ModInt operator^(lint n) const { return ModInt(this->power(n)); } constexpr ModInt &operator^=(lint n) { return *this = *this ^ n; } inline ModInt fac() const { static std::vector<ModInt> facs; int l0 = facs.size(); if (l0 > this->val) return facs[this->val]; facs.resize(this->val + 1); for (int i = l0; i <= this->val; i++) facs[i] = (i == 0 ? ModInt(1) : facs[i - 1] * ModInt(i)); return facs[this->val]; } ModInt doublefac() const { lint k = (this->val + 1) / 2; if (this->val & 1) return ModInt(k * 2).fac() / ModInt(2).power(k) / ModInt(k).fac(); else return ModInt(k).fac() * ModInt(2).power(k); } ModInt nCr(const ModInt &r) const { if (this->val < r.val) return ModInt(0); return this->fac() / ((*this - r).fac() * r.fac()); } ModInt sqrt() const { if (val == 0) return 0; if (mod == 2) return val; if (power((mod - 1) / 2) != 1) return 0; ModInt b = 1; while (b.power((mod - 1) / 2) == 1) b += 1; int e = 0, m = mod - 1; while (m % 2 == 0) m >>= 1, e++; ModInt x = power((m - 1) / 2), y = (*this) * x * x; x *= (*this); ModInt z = b.power(m); while (y != 1) { int j = 0; ModInt t = y; while (t != 1) j++, t *= t; z = z.power(1LL << (e - j - 1)); x *= z, z *= z, y *= z; e = j; } return ModInt(std::min(x.val, mod - x.val)); } }; // constexpr lint MOD = 998244353; // using mint = ModInt<MOD>; #include <algorithm> #include <array> #include <cassert> #include <tuple> #include <vector> // CUT begin // Integer convolution for arbitrary mod // with NTT (and Garner's algorithm) for ModInt / ModIntRuntime class. // We skip Garner's algorithm if `skip_garner` is true or mod is in `nttprimes`. // input: a (size: n), b (size: m) // return: vector (size: n + m - 1) template <typename MODINT> std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner = false); constexpr int nttprimes[3] = {998244353, 167772161, 469762049}; // Integer FFT (Fast Fourier Transform) for ModInt class // (Also known as Number Theoretic Transform, NTT) // is_inverse: inverse transform // ** Input size must be 2^n ** template <typename MODINT> void ntt(std::vector<MODINT> &a, bool is_inverse = false) { int n = a.size(); if (n == 1) return; static const int mod = MODINT::get_mod(); static const MODINT root = MODINT::get_primitive_root(); assert(__builtin_popcount(n) == 1 and (mod - 1) % n == 0); static std::vector<MODINT> w{1}, iw{1}; for (int m = w.size(); m < n / 2; m *= 2) { MODINT dw = root.power((mod - 1) / (4 * m)), dwinv = 1 / dw; w.resize(m * 2), iw.resize(m * 2); for (int i = 0; i < m; i++) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * dwinv; } if (!is_inverse) { for (int m = n; m >>= 1;) { for (int s = 0, k = 0; s < n; s += 2 * m, k++) { for (int i = s; i < s + m; i++) { MODINT x = a[i], y = a[i + m] * w[k]; a[i] = x + y, a[i + m] = x - y; } } } } else { for (int m = 1; m < n; m *= 2) { for (int s = 0, k = 0; s < n; s += 2 * m, k++) { for (int i = s; i < s + m; i++) { MODINT x = a[i], y = a[i + m]; a[i] = x + y, a[i + m] = (x - y) * iw[k]; } } } int n_inv = MODINT(n).inv(); for (auto &v : a) v *= n_inv; } } template <int MOD> std::vector<ModInt<MOD>> nttconv_(const std::vector<int> &a, const std::vector<int> &b) { int sz = a.size(); assert(a.size() == b.size() and __builtin_popcount(sz) == 1); std::vector<ModInt<MOD>> ap(sz), bp(sz); for (int i = 0; i < sz; i++) ap[i] = a[i], bp[i] = b[i]; ntt(ap, false); if (a == b) bp = ap; else ntt(bp, false); for (int i = 0; i < sz; i++) ap[i] *= bp[i]; ntt(ap, true); return ap; } long long garner_ntt_(int r0, int r1, int r2, int mod) { using mint2 = ModInt<nttprimes[2]>; static const long long m01 = 1LL * nttprimes[0] * nttprimes[1]; static const long long m0_inv_m1 = ModInt<nttprimes[1]>(nttprimes[0]).inv(); static const long long m01_inv_m2 = mint2(m01).inv(); int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1]; auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * m01_inv_m2; return (r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val) % mod; } template <typename MODINT> std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner) { int sz = 1, n = a.size(), m = b.size(); while (sz < n + m) sz <<= 1; if (sz <= 16) { std::vector<MODINT> ret(n + m - 1); for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) ret[i + j] += a[i] * b[j]; } return ret; } int mod = MODINT::get_mod(); if (skip_garner or std::find(std::begin(nttprimes), std::end(nttprimes), mod) != std::end(nttprimes)) { a.resize(sz), b.resize(sz); if (a == b) { ntt(a, false); b = a; } else ntt(a, false), ntt(b, false); for (int i = 0; i < sz; i++) a[i] *= b[i]; ntt(a, true); a.resize(n + m - 1); } else { std::vector<int> ai(sz), bi(sz); for (int i = 0; i < n; i++) ai[i] = a[i].val; for (int i = 0; i < m; i++) bi[i] = b[i].val; auto ntt0 = nttconv_<nttprimes[0]>(ai, bi); auto ntt1 = nttconv_<nttprimes[1]>(ai, bi); auto ntt2 = nttconv_<nttprimes[2]>(ai, bi); a.resize(n + m - 1); for (int i = 0; i < n + m - 1; i++) { a[i] = garner_ntt_(ntt0[i].val, ntt1[i].val, ntt2[i].val, mod); } } return a; } #include <algorithm> #include <cassert> #include <vector> using namespace std; // CUT begin // Formal Power Series (形式的冪級数) based on ModInt<mod> / ModIntRuntime // Reference: <https://ei1333.github.io/luzhiled/snippets/math/formal-power-series.html> template<typename T> struct FormalPowerSeries : vector<T> { using vector<T>::vector; using P = FormalPowerSeries; void shrink() { while (this->size() and 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 T &v) const { return P(*this) /= v; } 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 < (int)r.size(); i++) (*this)[i] += r[i]; shrink(); return *this; } P &operator+=(const T &v) { if (this->empty()) this->resize(1); (*this)[0] += v; shrink(); return *this; } P &operator-=(const P &r) { if (r.size() > this->size()) this->resize(r.size()); for (int i = 0; i < (int)r.size(); i++) (*this)[i] -= r[i]; shrink(); return *this; } P &operator-=(const T &v) { if (this->empty()) this->resize(1); (*this)[0] -= v; shrink(); return *this; } P &operator*=(const T &v) { for (auto &x : (*this)) x *= v; shrink(); return *this; } P &operator*=(const P &r) { if (this->empty() || r.empty()) this->clear(); else { auto ret = nttconv(*this, r); *this = P(ret.begin(), ret.end()); } return *this; } P &operator%=(const P &r) { *this -= *this / r * r; shrink(); return *this; } P operator-() const { P ret = *this; for (auto &v : ret) v = -v; return ret; } P &operator/=(const T &v) { assert(v != T(0)); for (auto &x : (*this)) x /= v; return *this; } P &operator/=(const P &r) { if (this->size() < r.size()) { this->clear(); return *this; } int n = (int)this->size() - r.size() + 1; return *this = (reversed().pre(n) * r.reversed().inv(n)).pre(n).reversed(n); } P pre(int sz) const { P ret(this->begin(), this->begin() + min((int)this->size(), sz)); ret.shrink(); return ret; } P operator>>(int sz) const { if ((int)this->size() <= sz) return {}; return P(this->begin() + sz, this->end()); } P operator<<(int sz) const { if (this->empty()) return {}; P ret(*this); ret.insert(ret.begin(), sz, T(0)); return ret; } P reversed(int deg = -1) const { assert(deg >= -1); P ret(*this); if (deg != -1) ret.resize(deg, T(0)); reverse(ret.begin(), ret.end()); ret.shrink(); return ret; } P differential() const { // formal derivative (differential) of f.p.s. 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; } P 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; } P inv(int deg) const { assert(deg >= -1); assert(this->size() and ((*this)[0]) != T(0)); // Requirement: F(0) != 0 const int n = this->size(); if (deg == -1) deg = n; 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); } ret = ret.pre(deg); ret.shrink(); return ret; } P log(int deg = -1) const { assert(deg >= -1); assert(this->size() and ((*this)[0]) == T(1)); // Requirement: F(0) = 1 const int n = (int)this->size(); if (deg == 0) return {}; if (deg == -1) deg = n; return (this->differential() * this->inv(deg)).pre(deg - 1).integral(); } P sqrt(int deg = -1) const { assert(deg >= -1); const int n = (int)this->size(); if (deg == -1) deg = n; if (this->empty()) return {}; if ((*this)[0] == T(0)) { for (int i = 1; i < n; i++) if ((*this)[i] != T(0)) { if ((i & 1) or deg - i / 2 <= 0) return {}; return (*this >> i).sqrt(deg - i / 2) << (i / 2); } return {}; } T sqrtf0 = (*this)[0].sqrt(); if (sqrtf0 == T(0)) return {}; P y = (*this) / (*this)[0], ret({T(1)}); T inv2 = T(1) / T(2); for (int i = 1; i < deg; i <<= 1) { ret = (ret + y.pre(i << 1) * ret.inv(i << 1)) * inv2; } return ret.pre(deg) * sqrtf0; } P exp(int deg = -1) const { assert(deg >= -1); assert(this->empty() or ((*this)[0]) == T(0)); // Requirement: F(0) = 0 const int n = (int)this->size(); if (deg == -1) deg = n; 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); } P pow(long long int k, int deg = -1) const { assert(deg >= -1); 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 C(*this * rev); P D(n - i); for (int j = i; j < n; j++) D[j - i] = C[j]; D = (D.log(deg) * T(k)).exp(deg) * (*this)[i].power(k); P E(deg); if (k * (i > 0) > deg or k * i > deg) return {}; long long int S = i * k; for (int j = 0; j + S < deg and j < (int)D.size(); j++) E[j + S] = D[j]; E.shrink(); return E; } } return *this; } P shift(long long c) const { const int n = (int)this->size(); P ret = *this; for (int i = 0; i < n; i++) { ret[i] *= T(i).fac(); } reverse(ret.begin(), ret.end()); P exp_cx = P({ 0, c }).exp(n); ret = (ret * exp_cx).pre(n); reverse(ret.begin(), ret.end()); for (int i = 0; i < n; i++) { ret[i] /= T(i).fac(); } return ret; } T coeff(int i) const { if ((int)this->size() <= i or i < 0) return T(0); return (*this)[i]; } T eval(T x) const { T ret = 0, w = 1; for (auto &v : *this) ret += w * v, w *= x; return ret; } }; #include <iostream> using namespace std; using mint = ModInt<998244353>; int main() { cin.tie(nullptr), ios::sync_with_stdio(false); int N, c; cin >> N >> c; FormalPowerSeries<ModInt<998244353>> f(N); for (auto &x : f) { cin >> x; } f = f.shift(c); for (int i = 0; i < N; i++) { cout << f.coeff(i) << (i < N - 1 ? ' ' : '\n'); } }