#include using namespace std; #ifdef LOCAL #include "debug.h" #else #define DEBUG(...) #endif template > constexpr T power(T a, long long n, Op op = Op(), T e = {1}) { assert(n >= 0); while (n) { if (n & 1) e = op(e, a); if (n >>= 1) a = op(a, a); } return e; } template vector operator-(vector a) { for (auto&& e : a) e = -e; return a; } template vector& operator+=(vector& a, const vector& b) { a.resize(max(a.size(), b.size())); for (int i = 0; i < (int)b.size(); ++i) a[i] += b[i]; return a; } template vector operator+(vector a, const vector& b) { return a += b; } template vector& operator-=(vector& a, const vector& b) { a.resize(max(a.size(), b.size())); for (int i = 0; i < (int)b.size(); ++i) a[i] -= b[i]; return a; } template vector operator-(vector a, const vector& b) { return a -= b; } template vector& operator<<=(vector& a, size_t n) { return a.insert(begin(a), n, 0), a; } template vector operator<<(vector a, size_t n) { return a <<= n; } template vector& operator>>=(vector& a, size_t n) { return a.erase(begin(a), begin(a) + min(a.size(), n)), a; } template vector operator>>(vector a, size_t n) { return a >>= n; } // template vector operator*(const vector& a, const vector& b) { // if (a.empty() or b.empty()) return {}; // vector res(a.size() + b.size() - 1); // for (int i = 0; i < (int)a.size(); ++i) // for (int j = 0; j < (int)b.size(); ++j) res[i + j] += a[i] * b[j]; // return res; // } template vector& operator*=(vector& a, const vector& b) { return a = a * b; } template vector inverse(const vector& a) { assert(not a.empty() and not (a[0] == 0)); vector b{1 / a[0]}; while (b.size() < a.size()) { vector 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 vector operator/(vector a, vector b) { if (a.size() < b.size()) return {}; reverse(begin(a), end(a)), reverse(begin(b), end(b)); int n = a.size() - b.size() + 1; a.resize(n), b.resize(n); a *= inverse(b); return {rend(a) - n, rend(a)}; } template vector& operator/=(vector& a, const vector& b) { return a = a / b; } template vector operator%(vector a, const vector& b) { if (a.size() < b.size()) return a; a -= a / b * b; return {begin(a), begin(a) + (b.size() - 1)}; } template vector& operator%=(vector& a, const vector& b) { return a = a % b; } template vector derivative(const vector& a) { vector 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 vector primitive(const vector& a) { vector res(a.size() + 1); for (int i = 1; i < (int)res.size(); ++i) res[i] = a[i - 1] / i; return res; } template vector logarithm(const vector& a) { assert(not a.empty() and a[0] == 1); auto res = primitive(derivative(a) * inverse(a)); return {begin(res), begin(res) + a.size()}; } template vector exponent(const vector& a) { assert(a.empty() or a[0] == 0); vector b{1}; while (b.size() < a.size()) { vector 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 void ntt(vector& a, bool inverse) { int n = size(a); assert((n & (n - 1)) == 0); if (n < 2) return; assert((T::mod - 1) % n == 0); static vector w{1}, iw{1}; for (int m = size(w); m < n / 2; m *= 2) { static T root = 2; while (power(root, (T::mod - 1) / 2) == 1) root += 1; T dw = power(root, (T::mod - 1) / (4 * m)), idw = 1 / dw; w.resize(2 * m), iw.resize(2 * m); for (int i = 0; i < m; ++i) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * idw; } if (not inverse) { for (int m = n; m >>= 1; ) { for (int s = 0, k = 0; s < n; s += 2 * m, ++k) { for (int i = s, j = s + m; i < s + m; ++i, ++j) { T x = a[i], y = a[j] * w[k]; a[i] = x + y, a[j] = 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, j = s + m; i < s + m; ++i, ++j) { T x = a[i], y = a[j]; a[i] = x + y, a[j] = (x - y) * iw[k]; } } } auto inv = 1 / T(n); for (auto&& e : a) e *= inv; } } template vector operator*(vector a, vector b) { if (empty(a) or empty(b)) return {}; int n = size(a), m = size(b), sz = 1 << __lg(2 * (n + m - 1) - 1); a.resize(sz), ntt(a, false); b.resize(sz), ntt(b, false); for (int i = 0; i < sz; ++i) a[i] *= b[i]; ntt(a, true), a.resize(n + m - 1); return a; } template struct modular { using m = modular; static constexpr unsigned mod = M; unsigned v; modular(long long x = 0) : v((x %= mod) < 0 ? x + mod : x) {} m operator-() const { return m() -= *this; } m& operator+=(m b) { if ((int)(v += b.v - mod) < 0) v += mod; return *this; } m& operator-=(m b) { if ((int)(v -= b.v) < 0) v += mod; return *this; } m& operator*=(m b) { v = (uint64_t)v * b.v % mod; return *this; } m& operator/=(m b) { return *this *= power(b, mod - 2); } friend m operator+(m a, m b) { return a += b; } friend m operator-(m a, m b) { return a -= b; } friend m operator*(m a, m b) { return a *= b; } friend m operator/(m a, m b) { return a /= b; } friend bool operator==(m a, m b) { return a.v == b.v; } }; using mint = modular; vector operator*(const vector& a, const vector& b) { if (a.empty() or b.empty()) return {}; int n = a.size(), m = b.size(); static constexpr int mod0 = 998244353, mod1 = 1300234241, mod2 = 1484783617; using mint0 = modular; using mint1 = modular; using mint2 = modular; vector a0(n), b0(m); vector a1(n), b1(m); vector a2(n), b2(m); for (int i = 0; i < n; ++i) a0[i] = a[i].v, a1[i] = a[i].v, a2[i] = a[i].v; for (int j = 0; j < m; ++j) b0[j] = b[j].v, b1[j] = b[j].v, b2[j] = b[j].v; a0 = a0 * b0, a1 = a1 * b1, a2 = a2 * b2; static const mint1 im0 = 1 / mint1(mod0); static const mint2 im1 = 1 / mint2(mod1), im0m1 = im1 / mod0; static const mint m0 = mod0, m0m1 = m0 * mod1; vector res(n + m - 1); for (int i = 0; i < n + m - 1; ++i) { int y0 = a0[i].v; int y1 = (im0 * (a1[i] - y0)).v; int y2 = (im0m1 * (a2[i] - y0) - im1 * y1).v; res[i] = y0 + m0 * y1 + m0m1 * y2; } return res; } vector fact, inv_fact, minv; void prepare(int n) { fact.resize(n + 1), inv_fact.resize(n + 1), minv.resize(n + 1); for (int i = 0; i <= n; ++i) fact[i] = i ? fact[i - 1] * i : 1; inv_fact[n] = power(fact[n], mint::mod - 2); for (int i = n; i--; ) inv_fact[i] = (i + 1) * inv_fact[i + 1]; for (int i = 1; i <= n; ++i) minv[i] = inv_fact[i] * fact[i - 1]; } mint binom(int n, int k) { if (k < 0 or k > n) return 0; return fact[n] * inv_fact[k] * inv_fact[n - k]; } template <> mint& mint::operator/=(mint b) { return *this *= b.v < minv.size() ? minv[b.v] : power(b, mod - 2); } int main() { cin.tie(nullptr); ios::sync_with_stdio(false); int n; cin >> n; prepare(n + 1); auto z = power(13, (mint::mod - 1) / 4); vector f(n + 1), g(n + 1); for (int i = 1; i <= n; ++i) { f[i] = z * (i + 1) * (i + 1); g[i] = -f[i]; } f = exponent(f); g = exponent(g); f *= vector{fact[n]}; g *= vector{fact[n]}; f = (f + g) - (f - g) * vector{z}; f *= vector{minv[2]}; for (int i = 1; i <= n; ++i) { cout << f[i].v << '\n'; } }