# Submit Info #2972

Problem Lang User Status Time Memory
Partition Function cpp risujiroh AC 1439 ms 28.02 MiB

ケース詳細
Name Status Time Memory
0_00 AC 2 ms 0.67 MiB
100000_00 AC 300 ms 7.37 MiB
10000_00 AC 35 ms 1.52 MiB
1000_00 AC 4 ms 0.78 MiB
100_00 AC 0 ms 0.67 MiB
1_00 AC 3 ms 0.72 MiB
200000_00 AC 624 ms 13.77 MiB
300000_00 AC 1157 ms 26.21 MiB
400000_00 AC 1295 ms 27.60 MiB
500000_00 AC 1439 ms 28.02 MiB
example_00 AC 2 ms 0.72 MiB

#include <bits/stdc++.h> using namespace std; template <class T> vector<T> operator-(vector<T> a) { for (auto&& e : a) e = -e; return a; } template <class T> vector<T>& operator+=(vector<T>& l, const vector<T>& r) { l.resize(max(l.size(), r.size())); for (int i = 0; i < (int)r.size(); ++i) l[i] += r[i]; return l; } template <class T> vector<T> operator+(vector<T> l, const vector<T>& r) { return l += r; } template <class T> vector<T>& operator-=(vector<T>& l, const vector<T>& r) { l.resize(max(l.size(), r.size())); for (int i = 0; i < (int)r.size(); ++i) l[i] -= r[i]; return l; } template <class T> vector<T> operator-(vector<T> l, const vector<T>& r) { return l -= r; } template <class T> vector<T>& operator<<=(vector<T>& a, size_t n) { return a.insert(begin(a), n, 0), a; } template <class T> vector<T> operator<<(vector<T> a, size_t n) { return a <<= n; } template <class T> vector<T>& operator>>=(vector<T>& a, size_t n) { return a.erase(begin(a), begin(a) + min(a.size(), n)), a; } template <class T> vector<T> operator>>(vector<T> a, size_t n) { return a >>= n; } template <class T> vector<T> operator*(const vector<T>& l, const vector<T>& r) { if (l.empty() or r.empty()) return {}; vector<T> res(l.size() + r.size() - 1); for (int i = 0; i < (int)l.size(); ++i) for (int j = 0; j < (int)r.size(); ++j) res[i + j] += l[i] * r[j]; return res; } template <class T> vector<T>& operator*=(vector<T>& l, const vector<T>& r) { return l = l * r; } template <class T> vector<T> inverse(const vector<T>& a) { assert(not a.empty() and not (a[0] == 0)); vector<T> b{1 / a[0]}; while (b.size() < a.size()) { vector<T> x(begin(a), begin(a) + min(a.size(), 2 * b.size())); x *= b * b; b.resize(2 * b.size()); for (auto i = b.size() / 2; i < min(x.size(), b.size()); ++i) b[i] = -x[i]; } return {begin(b), begin(b) + a.size()}; } template <class T> vector<T> operator/(vector<T> l, vector<T> r) { if (l.size() < r.size()) return {}; reverse(begin(l), end(l)), reverse(begin(r), end(r)); int n = l.size() - r.size() + 1; l.resize(n), r.resize(n); l *= inverse(r); return {rend(l) - n, rend(l)}; } template <class T> vector<T>& operator/=(vector<T>& l, const vector<T>& r) { return l = l / r; } template <class T> vector<T> operator%(vector<T> l, const vector<T>& r) { if (l.size() < r.size()) return l; l -= l / r * r; return {begin(l), begin(l) + (r.size() - 1)}; } template <class T> vector<T>& operator%=(vector<T>& l, const vector<T>& r) { return l = l % r; } template <class T> vector<T> derivative(const vector<T>& a) { vector<T> res(max((int)a.size() - 1, 0)); for (int i = 0; i < (int)res.size(); ++i) res[i] = (i + 1) * a[i + 1]; return res; } template <class T> vector<T> primitive(const vector<T>& a) { vector<T> res(a.size() + 1); for (int i = 1; i < (int)res.size(); ++i) res[i] = a[i - 1] / i; return res; } template <class T> vector<T> logarithm(const vector<T>& a) { assert(not a.empty() and a[0] == 1); auto res = primitive(derivative(a) * inverse(a)); return {begin(res), begin(res) + a.size()}; } template <class T> vector<T> exponent(const vector<T>& a) { assert(a.empty() or a[0] == 0); vector<T> b{1}; while (b.size() < a.size()) { vector<T> x(begin(a), begin(a) + min(a.size(), 2 * b.size())); x[0] += 1; b.resize(2 * b.size()); x -= logarithm(b); x *= {begin(b), begin(b) + b.size() / 2}; for (auto i = b.size() / 2; i < min(x.size(), b.size()); ++i) b[i] = x[i]; } return {begin(b), begin(b) + a.size()}; } template <class T, class F = multiplies<T>> T power(T a, long long n, F op = multiplies<T>(), T e = {1}) { assert(n >= 0); T res = e; while (n) { if (n & 1) res = op(res, a); if (n >>= 1) a = op(a, a); } return res; } template <unsigned Mod> struct Modular { using M = Modular; unsigned v; Modular(long long a = 0) : v((a %= Mod) < 0 ? a + Mod : a) {} M operator-() const { return M() -= *this; } M& operator+=(M r) { if ((v += r.v) >= Mod) v -= Mod; return *this; } M& operator-=(M r) { if ((v += Mod - r.v) >= Mod) v -= Mod; return *this; } M& operator*=(M r) { v = (uint64_t)v * r.v % Mod; return *this; } M& operator/=(M r) { return *this *= power(r, Mod - 2); } friend M operator+(M l, M r) { return l += r; } friend M operator-(M l, M r) { return l -= r; } friend M operator*(M l, M r) { return l *= r; } friend M operator/(M l, M r) { return l /= r; } friend bool operator==(M l, M r) { return l.v == r.v; } }; template <unsigned Mod> void ntt(vector<Modular<Mod>>& a, bool inverse) { static vector<Modular<Mod>> dw(30), idw(30); if (dw[0] == 0) { Modular<Mod> root = 2; while (power(root, (Mod - 1) / 2) == 1) root += 1; for (int i = 0; i < 30; ++i) dw[i] = -power(root, (Mod - 1) >> (i + 2)), idw[i] = 1 / dw[i]; } int n = a.size(); assert((n & (n - 1)) == 0); if (not inverse) { for (int m = n; m >>= 1; ) { Modular<Mod> w = 1; for (int s = 0, k = 0; s < n; s += 2 * m) { for (int i = s, j = s + m; i < s + m; ++i, ++j) { auto x = a[i], y = a[j] * w; if (x.v >= Mod) x.v -= Mod; a[i].v = x.v + y.v, a[j].v = x.v + (Mod - y.v); } w *= dw[__builtin_ctz(++k)]; } } } else { for (int m = 1; m < n; m *= 2) { Modular<Mod> w = 1; for (int s = 0, k = 0; s < n; s += 2 * m) { for (int i = s, j = s + m; i < s + m; ++i, ++j) { auto x = a[i], y = a[j]; a[i] = x + y, a[j].v = x.v + (Mod - y.v), a[j] *= w; } w *= idw[__builtin_ctz(++k)]; } } } auto c = 1 / Modular<Mod>(inverse ? n : 1); for (auto&& e : a) e *= c; } template <unsigned Mod> vector<Modular<Mod>> operator*(vector<Modular<Mod>> l, vector<Modular<Mod>> r) { if (l.empty() or r.empty()) return {}; int n = l.size(), m = r.size(), sz = 1 << __lg(2 * (n + m - 1) - 1); if (min(n, m) < 30) { vector<long long> res(n + m - 1); for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) res[i + j] += (l[i] * r[j]).v; return {begin(res), end(res)}; } bool eq = l == r; l.resize(sz), ntt(l, false); if (eq) r = l; else r.resize(sz), ntt(r, false); for (int i = 0; i < sz; ++i) l[i] *= r[i]; ntt(l, true), l.resize(n + m - 1); return l; } constexpr long long mod = 998244353; using Mint = Modular<mod>; int main() { cin.tie(nullptr); ios::sync_with_stdio(false); int n; cin >> n; vector<Mint> f(n + 1); for (int i = 1; i <= n; ++i) { for (int j = 1; i * j <= n; ++j) { f[i * j] += 1 / Mint(j); } } f = exponent(f); for (int i = 0; i <= n; ++i) { cout << f[i].v << " \n"[i == n]; } }