Submit Info #25778

Problem Lang User Status Time Memory
Stirling Number of the First Kind cpp tonegawa AC 830 ms 113.50 MiB

ケース詳細
Name Status Time Memory
0_00 AC 1 ms 0.67 MiB
1_00 AC 1 ms 0.67 MiB
262143_00 AC 398 ms 56.62 MiB
262144_00 AC 428 ms 57.52 MiB
2_00 AC 1 ms 0.67 MiB
491519_00 AC 814 ms 109.89 MiB
499999_00 AC 830 ms 113.50 MiB
500000_00 AC 830 ms 113.49 MiB
5000_00 AC 7 ms 1.55 MiB
example_00 AC 4 ms 0.65 MiB

#include <iostream> #include <string> #include <vector> #include <array> #include <queue> #include <deque> #include <algorithm> #include <set> #include <map> #include <bitset> #include <cmath> #include <functional> #include <cassert> #include <iomanip> #define vll vector<ll> #define vvvl vector<vvl> #define vvl vector<vector<ll>> #define VV(a, b, c, d) vector<vector<d>>(a, vector<d>(b, c)) #define VVV(a, b, c, d) vector<vvl>(a, vvl(b, vll (c, d))); #define re(c, b) for(ll c=0;c<b;c++) #define all(obj) (obj).begin(), (obj).end() typedef long long ll; typedef long double ld; using namespace std; #include <numeric> #include <type_traits> namespace internal{ template <class T> using is_integral = typename std::is_integral<T>; template <class T> using is_signed_int = typename std::conditional<is_integral<T>::value && std::is_signed<T>::value, std::true_type, std::false_type>::type; template <class T> using is_unsigned_int = typename std::conditional<is_integral<T>::value && std::is_unsigned<T>::value, std::true_type, std::false_type>::type; template <class T> using to_unsigned = typename std::conditional<is_signed_int<T>::value, std::make_unsigned<T>, std::common_type<T>>::type; template <class T> using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>; template <class T> using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>; template <class T> using to_unsigned_t = typename to_unsigned<T>::type; //<internal_math> constexpr long long safe_mod(long long x, long long m) { x %= m; if (x < 0) x += m; return x; } struct barrett { unsigned int _m; unsigned long long im; barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {} unsigned int umod() const { return _m; } unsigned int mul(unsigned int a, unsigned int b) const { unsigned long long z = a; z *= b; unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64); unsigned int v = (unsigned int)(z - x * _m); if (_m <= v) v += _m; return v; } }; constexpr long long pow_mod_constexpr(long long x, long long n, int m) { if (m == 1) return 0; unsigned int _m = (unsigned int)(m); unsigned long long r = 1; unsigned long long y = safe_mod(x, m); while (n) { if (n & 1) r = (r * y) % _m; y = (y * y) % _m; n >>= 1; } return r; } constexpr bool is_prime_constexpr(int n) { if (n <= 1) return false; if (n == 2 || n == 7 || n == 61) return true; if (n % 2 == 0) return false; long long d = n - 1; while (d % 2 == 0) d /= 2; constexpr long long bases[3] = {2, 7, 61}; for (long long a : bases) { long long t = d; long long y = pow_mod_constexpr(a, t, n); while (t != n - 1 && y != 1 && y != n - 1) { y = y * y % n; t <<= 1; } if (y != n - 1 && t % 2 == 0) { return false; } } return true; } template <int n> constexpr bool is_prime = is_prime_constexpr(n); constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) { a = safe_mod(a, b); if (a == 0) return {b, 0}; long long s = b, t = a; long long m0 = 0, m1 = 1; while (t) { long long u = s / t; s -= t * u; m0 -= m1 * u; auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } if (m0 < 0) m0 += b / s; return {s, m0}; } constexpr int primitive_root_constexpr(int m) { if (m == 2) return 1; if (m == 167772161) return 3; if (m == 469762049) return 3; if (m == 754974721) return 11; if (m == 998244353) return 3; int divs[20] = {}; divs[0] = 2; int cnt = 1; int x = (m - 1) / 2; while (x % 2 == 0) x /= 2; for (int i = 3; (long long)(i)*i <= x; i += 2) { if (x % i == 0) { divs[cnt++] = i; while (x % i == 0) { x /= i; } } } if (x > 1) divs[cnt++] = x; for (int g = 2;; g++) { bool ok = true; for (int i = 0; i < cnt; i++) { if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) { ok = false; break; } } if (ok) return g; } } template <int m> constexpr int primitive_root = primitive_root_constexpr(m); //<internal_bit> int ceil_pow2(int n) { int x = 0; while ((1U << x) < (unsigned int)(n)) x++; return x; } int bsf(unsigned int n) { return __builtin_ctz(n); } //<modint> struct modint_base {}; struct static_modint_base : modint_base {}; template <class T> using is_modint = std::is_base_of<modint_base, T>; template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>; template <int m, std::enable_if_t<(1 <= m)>* = nullptr> struct static_modint : internal::static_modint_base { using mint = static_modint; public: static constexpr int mod() { return m; } static mint raw(int v) { mint x; x._v = v; return x; } static_modint() : _v(0) {} template <class T, internal::is_signed_int_t<T>* = nullptr> static_modint(T v) { long long x = (long long)(v % (long long)(umod())); if (x < 0) x += umod(); _v = (unsigned int)(x); } template <class T, internal::is_unsigned_int_t<T>* = nullptr> static_modint(T v) { _v = (unsigned int)(v % umod()); } static_modint(bool v) { _v = ((unsigned int)(v) % umod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v -= rhs._v; if (_v >= umod()) _v += umod(); return *this; } mint& operator*=(const mint& rhs) { unsigned long long z = _v; z *= rhs._v; _v = (unsigned int)(z % umod()); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { if (prime) { assert(_v); return pow(umod() - 2); } else { auto eg = internal::inv_gcd(_v, m); assert(eg.first == 1); return eg.second; } } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static constexpr unsigned int umod() { return m; } static constexpr bool prime = internal::is_prime<m>; }; template <int id> struct dynamic_modint : internal::modint_base { using mint = dynamic_modint; public: static int mod() { return (int)(bt.umod()); } static void set_mod(int m) { assert(1 <= m); bt = internal::barrett(m); } static mint raw(int v) { mint x; x._v = v; return x; } dynamic_modint() : _v(0) {} template <class T, internal::is_signed_int_t<T>* = nullptr> dynamic_modint(T v) { long long x = (long long)(v % (long long)(mod())); if (x < 0) x += mod(); _v = (unsigned int)(x); } template <class T, internal::is_unsigned_int_t<T>* = nullptr> dynamic_modint(T v) { _v = (unsigned int)(v % mod()); } dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v += mod() - rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator*=(const mint& rhs) { _v = bt.mul(_v, rhs._v); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { auto eg = internal::inv_gcd(_v, mod()); assert(eg.first == 1); return eg.second; } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static internal::barrett bt; static unsigned int umod() { return bt.umod(); } }; template <int id> internal::barrett dynamic_modint<id>::bt = 998244353; //using modint998244353 = static_modint<998244353>; //using modint1000000007 = static_modint<1000000007>; //using modint = dynamic_modint<-1>; template <class T> using is_static_modint = std::is_base_of<internal::static_modint_base, T>; template <class T> using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>; template <class> struct is_dynamic_modint : public std::false_type {}; template <int id> struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {}; template <class T> using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>; //<conbovution> template <class mint, internal::is_static_modint_t<mint>* = nullptr> void butterfly(std::vector<mint>& a) { static constexpr int g = internal::primitive_root<mint::mod()>; int n = int(a.size()); int h = internal::ceil_pow2(n); static bool first = true; static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i] if (first) { first = false; mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1 int cnt2 = bsf(mint::mod() - 1); mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv(); for (int i = cnt2; i >= 2; i--) { // e^(2^i) == 1 es[i - 2] = e; ies[i - 2] = ie; e *= e; ie *= ie; } mint now = 1; for (int i = 0; i <= cnt2 - 2; i++) { sum_e[i] = es[i] * now; now *= ies[i]; } } for (int ph = 1; ph <= h; ph++) { int w = 1 << (ph - 1), p = 1 << (h - ph); mint now = 1; for (int s = 0; s < w; s++) { int offset = s << (h - ph + 1); for (int i = 0; i < p; i++) { auto l = a[i + offset]; auto r = a[i + offset + p] * now; a[i + offset] = l + r; a[i + offset + p] = l - r; } now *= sum_e[internal::bsf(~(unsigned int)(s))]; } } } template <class mint, internal::is_static_modint_t<mint>* = nullptr> void butterfly_inv(std::vector<mint>& a) { static constexpr int g = internal::primitive_root<mint::mod()>; int n = int(a.size()); int h = internal::ceil_pow2(n); static bool first = true; static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i] if (first) { first = false; mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1 int cnt2 = bsf(mint::mod() - 1); mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv(); for (int i = cnt2; i >= 2; i--) { // e^(2^i) == 1 es[i - 2] = e; ies[i - 2] = ie; e *= e; ie *= ie; } mint now = 1; for (int i = 0; i <= cnt2 - 2; i++) { sum_ie[i] = ies[i] * now; now *= es[i]; } } for (int ph = h; ph >= 1; ph--) { int w = 1 << (ph - 1), p = 1 << (h - ph); mint inow = 1; for (int s = 0; s < w; s++) { int offset = s << (h - ph + 1); for (int i = 0; i < p; i++) { auto l = a[i + offset]; auto r = a[i + offset + p]; a[i + offset] = l + r; a[i + offset + p] = (unsigned long long)(mint::mod() + l.val() - r.val()) * inow.val(); } inow *= sum_ie[internal::bsf(~(unsigned int)(s))]; } } } template <class mint, internal::is_static_modint_t<mint>* = nullptr> std::vector<mint> _convolution(std::vector<mint> a, std::vector<mint> b) { int n = int(a.size()), m = int(b.size()); if (!n || !m) return {}; if (std::min(n, m) <= 60) { if (n < m) { std::swap(n, m); std::swap(a, b); } std::vector<mint> ans(n + m - 1); for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) { ans[i + j] += a[i] * b[j]; } } return ans; } int z = 1 << internal::ceil_pow2(n + m - 1); a.resize(z); internal::butterfly(a); b.resize(z); internal::butterfly(b); for (int i = 0; i < z; i++) { a[i] *= b[i]; } internal::butterfly_inv(a); a.resize(n + m - 1); mint iz = mint(z).inv(); for (int i = 0; i < n + m - 1; i++) a[i] *= iz; return a; } template <unsigned int mod = 998244353, class T, std::enable_if_t<internal::is_integral<T>::value>* = nullptr> std::vector<T> _convolution(const std::vector<T>& a, const std::vector<T>& b) { int n = int(a.size()), m = int(b.size()); if (!n || !m) return {}; using mint = internal::static_modint<mod>; std::vector<mint> a2(n), b2(m); for (int i = 0; i < n; i++) { a2[i] = mint(a[i]); } for (int i = 0; i < m; i++) { b2[i] = mint(b[i]); } auto c2 = _convolution(move(a2), move(b2)); std::vector<T> c(n + m - 1); for (int i = 0; i < n + m - 1; i++) { c[i] = c2[i].val(); } return c; } std::vector<long long> convolution_ll(const std::vector<long long>& a, const std::vector<long long>& b) { int n = int(a.size()), m = int(b.size()); if (!n || !m) return {}; static constexpr unsigned long long MOD1 = 754974721; // 2^24 static constexpr unsigned long long MOD2 = 167772161; // 2^25 static constexpr unsigned long long MOD3 = 469762049; // 2^26 static constexpr unsigned long long M2M3 = MOD2 * MOD3; static constexpr unsigned long long M1M3 = MOD1 * MOD3; static constexpr unsigned long long M1M2 = MOD1 * MOD2; static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3; static constexpr unsigned long long i1 = internal::inv_gcd(MOD2 * MOD3, MOD1).second; static constexpr unsigned long long i2 = internal::inv_gcd(MOD1 * MOD3, MOD2).second; static constexpr unsigned long long i3 = internal::inv_gcd(MOD1 * MOD2, MOD3).second; auto c1 = internal::_convolution<MOD1>(a, b); auto c2 = internal::_convolution<MOD2>(a, b); auto c3 = internal::_convolution<MOD3>(a, b); std::vector<long long> c(n + m - 1); for (int i = 0; i < n + m - 1; i++) { unsigned long long x = 0; x += (c1[i] * i1) % MOD1 * M2M3; x += (c2[i] * i2) % MOD2 * M1M3; x += (c3[i] * i3) % MOD3 * M1M2; long long diff = c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1)); if (diff < 0) diff += MOD1; static constexpr unsigned long long offset[5] = { 0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3}; x -= offset[diff % 5]; c[i] = x; } return c; } } ll mpow(ll a, ll b, ll MOD = -1){ ll ret = 1, num = a; while(b>0){ if(b%2) ret = (ret*num)%MOD; num = (num*num)%MOD; b /= 2; } return ret; } vector<ll> int32mod_conv(vector<ll> a, vector<ll> b, ll MOD, int MAXSIZE=-1){ if(MAXSIZE!=-1){ if(a.size()>MAXSIZE) a.resize(MAXSIZE); if(b.size()>MAXSIZE) b.resize(MAXSIZE); } if(MOD==998244353) return internal::_convolution<998244353, ll>(a, b); vector<ll> A = internal::_convolution<167772161>(a, b); vector<ll> B = internal::_convolution<469762049>(a, b); vector<ll> C = internal::_convolution<1224736769>(a, b); ll N = A.size(); vector<ll> ret(N); ll x = 167772161, y = 469762049, z = 1224736769; ll ix = mpow(x, y-2, y); ll ixy = mpow((x*y)%z, z-2, z); for(int i=0;i<N;i++){ ll v = ((B[i] - A[i])*ix)%y; if(v<0) v += y; ll xxv = A[i]+x*v; v = ((C[i] - (xxv%z))*ixy)%z; if(v<0) v += z; ret[i] = ((xxv%MOD) + ((x*y)%MOD)*v)%MOD; } if(MAXSIZE!=-1&&(int)ret.size()>MAXSIZE) ret.resize(MAXSIZE); return ret; } //using modint998244353 = internal::static_modint<998244353>; //using modint1000000007 = internal::static_modint<1000000007>; //using modint = internal::dynamic_modint<-1>; template<ll MOD, int MAXSIZE=-1> struct StaticModFPS: vector<ll>{ using vector<ll>::vector; using fps = StaticModFPS<MOD, MAXSIZE>; StaticModFPS(vector<ll> v){ int n = v.size(); this->resize(n); for(int i=0;i<n;i++){ (*this)[i] = v[i] % MOD; if((*this)[i] < 0) (*this)[i] += MOD; } } fps operator *= (const fps &vr) { *this = int32mod_conv(*this, vr, MOD); return *this; } fps operator /= (fps &vr){ return (*this) *= vr.inv(); } fps operator += (const fps &vr){ int n = this->size(); int m = vr.size(); if(n < m) this->resize(m); for(int i=0;i<m;i++) { (*this)[i] += vr[i]; if((*this)[i] >= MOD) (*this)[i] -= MOD; } return *this; } fps operator -= (const fps &vr){ int n = this->size(); int m = vr.size(); if(n < m) this->resize(m); for(int i=0;i<m;i++) { (*this)[i] -= vr[i]; if((*this)[i] < 0) (*this)[i] += MOD; } return *this; } fps operator += (const ll &vr){ int n = this->size(); ll r = vr % MOD; if(r < 0) r += MOD; for(int i=0;i<n;i++){ (*this)[i] += r; if((*this)[i] >= MOD) (*this)[i] -= MOD; } return *this; } fps operator -= (const ll &vr){ int n = this->size(); ll r = vr % MOD; if(r<0) r += MOD; for(int i=0;i<n;i++){ (*this[i]) -= r; if((*this[i]) < 0) (*this)[i] += MOD; } return *this; } fps operator *= (const ll &vr){ int n = this->size(); ll r = vr % MOD; if(r<0) r += MOD; for(int i=0;i<n;i++){ (*this)[i] = ((*this)[i] * r)%MOD; } return *this; } fps operator /= (const ll &vr){ ll r = vr % MOD; if(r < 0) r += MOD; assert(r!=0); r = mpow(r, MOD-2, MOD); int n = (int)this->size(); for(int i=0;i<n;i++) (*this)[i] = ((*this)[i] * r)%MOD; return *this; } fps operator + (const fps& vr){return fps(*this) += vr;} fps operator - (const fps& vr){return fps(*this) -= vr;} fps operator * (const fps& vr){return fps(*this) *= vr;} fps operator / (const fps& vr){return fps(*this) /= vr;} fps operator + (const ll& vr){return fps(*this) += vr;} fps operator - (const ll& vr){return fps(*this) -= vr;} fps operator * (const ll& vr){return fps(*this) *= vr;} fps operator / (const ll& vr){return fps(*this) /= vr;} void debug(int printsize = 20){ int n = min(20, (int)this->size()); for(int i=0;i<n;i++){ if(i==n-1) printf("%lld\n", (*this)[i]); else printf("%lld ", (*this)[i]); } } void print(){ int n = (int)this->size(); for(int i=0;i<n;i++){ if(i==n-1) printf("%lld\n", (*this)[i]); else printf("%lld ", (*this)[i]); } } fps prefix(int deg){ int n = min((int)this->size(), deg); return fps(this->begin(), this->begin() + n); } fps inv(int deg=-1){ assert((*this)[0]!=0); int n = this->size(); if(deg==-1) deg = n; fps ret({mpow((*this)[0], MOD-2, MOD)}); for(int i=1;i<deg;i<<=1) { ret = ((ret + ret) - (ret * ret * prefix(i << 1))).prefix(i << 1); } return ret.prefix(deg); } }; // The generating function of the partition number // π{k=1, ∞} (1 / (1-x^k)) // f(x) := π{k=1, ∞} (1-x^k) // ∑P(i)x^i = 1/f(x) // Euler's pentagonal number theorem // f(x) = 1 - x - x^2 + x^5 + x^7 - x^12 - ... // = 1 + ∑{k=1, ∞}((-1)^k * x^a ) + ∑{k=1, ∞}((-1)^k * x^b) // s.t. a = k(3k-1)/2, b = k(3k+1)/2 template<ll MOD> StaticModFPS<MOD> PartitionNumber(int n){ StaticModFPS<MOD> ret(n+1); ret[0] = 1; for(int i=1;(i*(3*i-1))/2 <= n;i++){ int sign = (i&1 ? MOD-1 : 1); int x = (i*(3*i-1))/2; int y = (i*(3*i+1))/2; if(x <= n) ret[x] = (ret[x] + sign)%MOD; if(y <= n) ret[y] = (ret[y] + sign)%MOD; } return ret.inv(); } //∑{k=0, n} S(n, k)x^k = x(x-1)(x-2)....(x-(n-1)) // x x-1 x-2 x-3 x-4 x-5 x-6 x-7 x-8 x-9 // d = 1 x(x-1) (x-2)(x-3) (x-4)(x-5) (x-6)(x-7) (x-8)(x-9) // d = 2 x(x-1)(x-2)(x-3))(x-4) (x-4)(x-5)(x-6)(x-7) (x-8)(x-9) // d = 4 x(x-1)(x-2)(x-3)...(x-7) (x-8)(x-9) // d = 8 x(x-1)(x-2)(x-3)... (x-8)(x-9) template<ll MOD> StaticModFPS<MOD> StirlingNumber1st(int n){ if(n==0) return StaticModFPS<MOD>{1}; StaticModFPS<MOD> ret(n+1); vector<StaticModFPS<MOD>> v(n, StaticModFPS<MOD>(2, 0)); for(int i=0;i<n;i++) v[i][1] = 1, v[i][0] = (MOD - i)%MOD; for(int d=1;d<n;d<<=1){ for(int j=0;j<n;j+=2*d){ if(j + d < n) v[j] *= v[j + d]; } } return v[0]; } int main(){ int n;scanf("%d", &n); auto t = StirlingNumber1st<998244353>(n); t.print(); }