#include using namespace std; using i64 = long long; #define rep(i,s,e) for(i64 (i) = (s);(i) < (e);(i)++) #define all(x) x.begin(),x.end() #define STRINGIFY(n) #n #define TOSTRING(n) STRINGIFY(n) #define PREFIX "#" TOSTRING(__LINE__) "| " #define debug(x) \ { \ std::cout << PREFIX << #x << " = " << x << std::endl; \ } std::ostream& output_indent(std::ostream& os, int ind) { for(int i = 0; i < ind; i++) os << " "; return os; } template std::ostream& operator<<(std::ostream& os, const std::pair& p); template std::ostream& operator<<(std::ostream& os, const std::vector& v); template std::ostream& operator<<(std::ostream& os, const std::pair& p) { return (os << "(" << p.first << ", " << p.second << ")"); } template std::ostream& operator<<(std::ostream& os, const std::vector& v) { os << "["; for(int i = 0;i < v.size();i++) os << v[i] << ", "; return (os << "]"); } template static inline std::vector ndvec(size_t&& n, T val) { return std::vector(n, std::forward(val)); } template static inline auto ndvec(size_t&& n, Tail&&... tail) { return std::vector(tail)...))>(n, ndvec(std::forward(tail)...)); } i64 gcd(i64 a, i64 b) { if(b == 0) return a; return gcd(b, a % b); } #include using i64 = long long; template struct modint { i64 a; constexpr modint(const i64 x = 0): a((x%M+M)%M){} constexpr i64 value() const { return a; } constexpr modint inv() const { return this->pow(M-2); } constexpr modint pow(i64 r) const { modint ans(1); modint aa = *this; while(r) { if(r & 1) ans *= aa; aa *= aa; r >>= 1; } return ans; } constexpr modint& operator=(const i64 r) { a = (r % M + M) % M; return *this; } constexpr modint& operator+=(const modint r) { a += r.a; if(a >= M) a -= M; return *this; } constexpr modint& operator-=(const modint r) { a -= r.a; if(a < 0) a += M; return *this; } constexpr modint& operator*=(const modint r) { a = a * r.a % M; return *this; } constexpr modint& operator/=(const modint r) { (*this) *= r.inv(); return *this; } constexpr modint operator+(const modint r) const { return modint(*this) += r; } constexpr modint operator-(const modint r) const { return modint(*this) -= r; } constexpr modint operator*(const modint r) const { return modint(*this) *= r; } constexpr modint operator/(const modint r) const { return modint(*this) /= r; } constexpr bool operator!=(const modint r) const { return this->value() != r.value(); } }; template std::ostream& operator<<(std::ostream& os, const modint& m) { os << m.value(); return os; } using fp = modint<998244353>; #include #include using i64 = long long; template std::tuple, std::vector, std::vector> build_factorial(int N) { std::vector fact(N); std::vector finv(N); std::vector inv(N); fact[0] = T(1); for(int i = 1;i < N;i++) { fact[i] = fact[i - 1] * T(i); } finv[N - 1] = T(1) / fact[N - 1]; for(int i = N - 1; i --> 0;) { finv[i] = finv[i + 1] * T(i + 1); } for(int i = 0;i < N;i++) { inv[i] = fact[i - 1] * finv[i]; } return std::make_tuple(std::move(fact), std::move(finv), std::move(inv)); } int main() { i64 N; cin >> N; auto [fact, finv, inv] = build_factorial(404040); rep(K,1,N + 1) { cout << fact[N - K] * fp(N - K + 1) * fact[K] * fp(N + 1) * fp(N + 1 - K) * fact[N] * finv[K - 1] * finv[N - K + 1] * inv[K + 1] << endl; } }