# Submit Info #3330

Problem Lang User Status Time Memory
Partition Function cpp satashun AC 1785 ms 49.01 MiB

ケース詳細
Name Status Time Memory
0_00 AC 15 ms 12.05 MiB
100000_00 AC 367 ms 21.70 MiB
10000_00 AC 50 ms 13.30 MiB
1000_00 AC 19 ms 12.17 MiB
100_00 AC 18 ms 12.17 MiB
1_00 AC 13 ms 12.11 MiB
200000_00 AC 779 ms 30.24 MiB
300000_00 AC 1585 ms 47.50 MiB
400000_00 AC 1657 ms 48.27 MiB
500000_00 AC 1785 ms 49.01 MiB
example_00 AC 17 ms 12.05 MiB

#include <bits/stdc++.h> using namespace std; typedef pair<int, int> pii; typedef long long ll; template<class T> using V = vector<T>; template<class T> using VV = V<V<T>>; #define pb push_back #define eb emplace_back #define mp make_pair #define fi first #define se second #define rep(i,n) rep2(i,0,n) #define rep2(i,m,n) for(int i=m;i<(n);i++) #define ALL(c) (c).begin(),(c).end() #ifdef LOCAL #define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl #else #define dump(x) true #endif constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n-1); } template<class T, class U> void chmin(T& t, const U& u) { if (t > u) t = u; } template<class T, class U> void chmax(T& t, const U& u) { if (t < u) t = u; } template<class T, class U> ostream& operator<<(ostream& os, const pair<T, U>& p) { os<<"("<<p.first<<","<<p.second<<")"; return os; } template<class T> ostream& operator<<(ostream& os, const vector<T>& v) { os<<"{"; rep(i, v.size()) { if (i) os<<","; os<<v[i]; } os<<"}"; return os; } template <unsigned int MOD> struct ModInt { using uint = unsigned int; using ull = unsigned long long; using M = ModInt; uint v; ModInt(ll _v = 0) { set_norm(_v % MOD + MOD); } M& set_norm(uint _v) { //[0, MOD * 2)->[0, MOD) v = (_v < MOD) ? _v : _v - MOD; return *this; } explicit operator bool() const { return v != 0; } M operator+(const M& a) const { return M().set_norm(v + a.v); } M operator-(const M& a) const { return M().set_norm(v + MOD - a.v); } M operator*(const M& a) const { return M().set_norm(ull(v) * a.v % MOD); } M operator/(const M& a) const { return *this * a.inv(); } M& operator+=(const M& a) { return *this = *this + a; } M& operator-=(const M& a) { return *this = *this - a; } M& operator*=(const M& a) { return *this = *this * a; } M& operator/=(const M& a) { return *this = *this / a; } M operator-() const { return M() - *this; } M& operator++(int) { return *this = *this + 1; } M& operator--(int) { return *this = *this - 1; } M pow(ll n) const { if (n < 0) return inv().pow(-n); M x = *this, res = 1; while (n) { if (n & 1) res *= x; x *= x; n >>= 1; } return res; } M inv() const { ll a = v, b = MOD, p = 1, q = 0, t; while (b != 0) { t = a / b; swap(a -= t * b, b); swap(p -= t * q, q); } return M(p); } bool operator==(const M& a) const { return v == a.v; } bool operator!=(const M& a) const { return v != a.v; } friend ostream& operator<<(ostream& os, const M& a) { return os << a.v; } static int get_mod() { return MOD; } }; using Mint = ModInt<998244353>; //depend on ModInt, must use NTT friendly mod template<class D> struct NumberTheoreticTransform { D root; V<D> roots = {0, 1}; V<int> rev = {0, 1}; int base = 1, max_base = -1; void init() { int mod = D::get_mod(); int tmp = mod - 1; max_base = 0; while (tmp % 2 == 0) { tmp /= 2; max_base++; } root = 2; while (true) { if (root.pow(1 << max_base).v == 1) { if (root.pow(1 << (max_base - 1)).v != 1) { break; } } root++; } } void ensure_base(int nbase) { if (max_base == -1) init(); if (nbase <= base) return; assert(nbase <= max_base); 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); while (base < nbase) { D 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; } ++base; } } void ntt(V<D> &a, bool inv = false) { int n = a.size(); //assert((n & (n - 1)) == 0); 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 += 2 * k) { for (int j = 0; j < k; j++) { D x = a[i + j]; D y = a[i + j + k] * roots[j + k]; a[i + j] = x + y; a[i + j + k] = x - y; } } } int v = D(n).inv().v; if (inv) { reverse(a.begin() + 1, a.end()); for (int i = 0; i < n; i++) { a[i] *= v; } } } V<D> mul(V<D> a, V<D> b) { int s = a.size() + b.size() - 1; int nbase = 1; while ((1 << nbase) < s) nbase++; int sz = 1 << nbase; a.resize(sz); b.resize(sz); ntt(a); ntt(b); for (int i = 0; i < sz; i++) { a[i] *= b[i]; } ntt(a, true); a.resize(s); return a; } }; NumberTheoreticTransform<Mint> ntt; template<class D> struct Poly : public V<D> { Poly() {} template<class...Args> Poly(Args...args):V<D>(args...){} Poly(initializer_list<D>init):V<D>(init.begin(),init.end()){} int size() const { return V<D>::size(); } D at(int p) const { return (p < this->size() ? (*this)[p] : D(0)); } Poly operator+(const Poly& r) const { auto n = max(size(), r.size()); V<D> tmp(n); for (int i = 0; i < n; ++i) { tmp[i] = at(i) + r.at(i); } return tmp; } Poly operator-(const Poly& r) const { auto n = max(size(), r.size()); V<D> tmp(n); for (int i = 0; i < n; ++i) { tmp[i] = at(i) - r.at(i); } return tmp; } Poly operator*(const D& k) const { int n = size(); V<D> tmp(n); for (int i = 0; i < n; ++i) { tmp[i] = at(i) * k; } return tmp; } Poly operator*(const Poly& r) const { Poly a = *this; Poly b = r; auto v = ntt.mul(a, b); return v; } Poly pref(int len) const { return Poly(this->begin(), this->begin() + min(this->size(), len)); } Poly diff() const { V<D> res(max(0, size() - 1)); for (int i = 1; i < size(); ++i) { res[i - 1] = at(i) * i; } return res; } Poly inte() const { V<D> res(size() + 1); for (int i = 0; i < size(); ++i) { res[i + 1] = at(i) / (D)(i + 1); } return res; } //f * f.inv(m) === 1 mod (x^m) //f_0 ^ -1 must exist Poly inv(int m) const { Poly res = Poly({D(1) / at(0)}); for (int i = 1; i < m; i *= 2) { res = (res * D(2) - res * res * pref(i * 2)).pref(i * 2); } return res.pref(m); } //f_0 = 1 must hold Poly log(int n) const { auto f = pref(n); return (f.diff() * f.inv(n - 1)).pref(n - 1).inte(); } //f_0 = 0 must hold Poly exp(int n) const { auto h = diff(); Poly f = {1}, g = {1}; for (int m = 1; m < n; m *= 2) { g = (g * D(2) - f * g * g).pref(m); auto q = h.pref(m - 1); auto w = (q + g * (f.diff() - f * q)).pref(m * 2 - 1); f = (f + f * (*this - w.inte())).pref(m * 2); } return f.pref(n); } //f_0 = 1 must hold Poly sqrt(int n) const { Poly g({}); return g; } Poly& operator+=(const Poly& r) { return *this = *this + r; } Poly& operator-=(const Poly& r) { return *this = *this - r; } Poly& operator*=(const D& r) { return *this = *this * r; } Poly& operator*=(const Poly& r) { return *this = *this * r; } Poly& operator/=(const Poly& r) { return *this = *this / r; } Poly& operator/=(const D &r) {return *this = *this / r; } Poly& operator%=(const Poly& r) { return *this = *this % r; } friend ostream& operator<<(ostream& os, const Poly& pl) { if (pl.size() == 0) return os << "0"; for (int i = 0; i < pl.size(); ++i) { if (pl[i]) { os << pl[i] << "x^" << i; if (i + 1 != pl.size()) os << ","; } } return os; } }; const int maxv = 1000010; Mint fact[maxv], finv[maxv], inv[maxv]; void init() { fact[0] = 1; for (int i = 1; i < maxv; ++i) { fact[i] = fact[i-1] * i; } finv[maxv-1] = fact[maxv-1].inv(); for (int i = maxv - 2; i >= 0; --i) { finv[i] = finv[i+1] * (i+1); } for (int i = 1; i < maxv; ++i) { inv[i] = finv[i] * fact[i-1]; } } int main() { init(); int N; scanf("%d", &N); ++N; Poly<Mint> a(N); for (int i = 1; i < N; ++i) { for (int j = 1; i * j < N; ++j) { a[i * j] += inv[j]; } } auto ans = a.exp(N); for (int i = 0; i < N; ++i) { printf("%d%c", ans[i].v, i == N-1 ? '\n' : ' '); } return 0; }