#pragma region Macros #pragma GCC optimize("O3") #include #define ll long long #define ld long double #define rep2(i, a, b) for(ll i = a; i <= b; ++i) #define rep(i, n) for(ll i = 0; i < n; ++i) #define rep3(i, a, b) for(ll i = a; i >= b; --i) #define pii pair #define pll pair #define pb push_back #define eb emplace_back #define vi vector #define vec vector #define vll vector #define vpi vector #define vpll vector #define overload2(_1, _2, name, ...) name #define vv(a, b) vector>(a, vector(b)) #define vv2(a, b, c) vector>(a, vector(b, c)) #define vvl(a, b) vector>(a, vector(b)) #define vvl2(a, b, c) vector>(a, vector(b, c)) #define vvv(a, b, c) vector(a) #define vvv2(a, b, c, d) vector(a) #define vvvl(a, b, c) vector(a) #define vvvl2(a, b, c, d) vector(a) #define fi first #define se second #define all(c) begin(c), end(c) #define ios ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0); #define lb(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define ub(c, x) distance((c).begin(), upper_bound(all(c), (x))) using namespace std; template using pq = priority_queue; template using pqg = priority_queue, greater>; #define Size(c) (int)(c).size() #define INT(...) \ int __VA_ARGS__; \ IN(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ IN(__VA_ARGS__) #define ULL(...) \ ull __VA_ARGS__; \ IN(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ IN(__VA_ARGS__) #define CHR(...) \ char __VA_ARGS__; \ IN(__VA_ARGS__) #define DBL(...) \ double __VA_ARGS__; \ IN(__VA_ARGS__) #define LD(...) \ ld __VA_ARGS__; \ IN(__VA_ARGS__) #define VEC(type, name, size) \ vector name(size); \ IN(name) #define VV(type, name, h, w) \ vector> name(h, vector(w)); \ IN(name) int scan() { return getchar(); } void scan(int &a) { cin >> a; } void scan(long long &a) { cin >> a; } void scan(char &a) { cin >> a; } void scan(double &a) { cin >> a; } void scan(long double &a) { cin >> a; } void scan(char a[]) { scanf("%s", a); } void scan(string &a) { cin >> a; } template void scan(vector &); template void scan(array &); template void scan(pair &); template void scan(T (&)[size]); template void scan(vector &a) { for(auto &i : a) scan(i); } template void scan(deque &a) { for(auto &i : a) scan(i); } template void scan(array &a) { for(auto &i : a) scan(i); } template void scan(pair &p) { scan(p.first); scan(p.second); } template void scan(T (&a)[size]) { for(auto &i : a) scan(i); } template void scan(T &a) { cin >> a; } void IN() {} template void IN(Head &head, Tail &... tail) { scan(head); IN(tail...); } string stin() { string s; cin >> s; return s; } template inline bool chmax(T &a, T b) { if(a < b) { a = b; return 1; } return 0; } template inline bool chmin(T &a, T b) { if(a > b) { a = b; return 1; } return 0; } vi iota(int n) { vi a(n); iota(all(a), 0); return a; } template void UNIQUE(vector &x) { sort(all(x)); x.erase(unique(all(x)), x.end()); } int in() { int x; cin >> x; return x; } ll lin() { unsigned long long x; cin >> x; return x; } void print() { putchar(' '); } void print(bool a) { cout << a; } void print(int a) { cout << a; } void print(long long a) { cout << a; } void print(char a) { cout << a; } void print(string &a) { cout << a; } void print(double a) { cout << a; } template void print(const vector &); template void print(const array &); template void print(const pair &p); template void print(const T (&)[size]); template void print(const vector &a) { if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end();) { cout << " "; print(*i); } cout << endl; } template void print(const deque &a) { if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end();) { cout << " "; print(*i); } } template void print(const array &a) { print(a[0]); for(auto i = a.begin(); ++i != a.end();) { cout << " "; print(*i); } } template void print(const pair &p) { cout << '('; print(p.first); cout << ","; print(p.second); cout << ')'; } template void print(set &x) { for(auto e : x) print(e), cout << " "; cout << endl; } template void print(multiset &x) { for(auto e : x) print(e), cout << " "; cout << endl; } template void print(const T (&a)[size]) { print(a[0]); for(auto i = a; ++i != end(a);) { cout << " "; print(*i); } } template void print(const T &a) { cout << a; } int out() { putchar('\n'); return 0; } template int out(const T &t) { print(t); putchar('\n'); return 0; } template int out(const Head &head, const Tail &... tail) { print(head); putchar(' '); out(tail...); return 0; } ll gcd(ll a, ll b) { while(b) { ll c = b; b = a % b; a = c; } return a; } ll lcm(ll a, ll b) { if(!a || !b) return 0; return a * b / gcd(a, b); } vector factor(ll x) { vector ans; for(ll i = 2; i * i <= x; i++) if(x % i == 0) { ans.push_back({i, 1}); while((x /= i) % i == 0) ans.back().second++; } if(x != 1) ans.push_back({x, 1}); return ans; } vector divisor(int x) { vector ans; for(int i = 1; i * i <= x; i++) if(x % i == 0) { ans.pb(i); if(i * i != x) ans.pb(x / i); } return ans; } int popcount(ll x) { return __builtin_popcountll(x); } mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); int rnd(int n) { return uniform_int_distribution(0, n - 1)(rng); } #define endl '\n' #ifdef _LOCAL #undef endl #define debug(x) \ cout << #x << ": "; \ print(x); \ cout << endl; void err() {} template void err(const T &t) { print(t); cout << " "; } template void err(const Head &head, const Tail &... tail) { print(head); putchar(' '); out(tail...); } #else #define debug(x) template void err(const T &...) {} #endif struct Setup_io { Setup_io() { ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0); cout << fixed << setprecision(15); } } setup_io; #pragma endregion // _______ここから編集!_______________ // exp of poly from https://judge.yosupo.jp/submission/2613 template vector operator-(vector a) { for(auto &&e : a) e = -e; return a; } template vector &operator+=(vector &l, const vector &r) { l.resize(max(l.size(), r.size())); for(int i = 0; i < (int)r.size(); ++i) l[i] += r[i]; return l; } template vector operator+(vector l, const vector &r) { return l += r; } template vector &operator-=(vector &l, const vector &r) { l.resize(max(l.size(), r.size())); for(int i = 0; i < (int)r.size(); ++i) l[i] -= r[i]; return l; } template vector operator-(vector l, const vector &r) { return l -= r; } 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 &l, const vector &r) { if(l.empty() or r.empty()) return {}; vector 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 vector &operator*=(vector &l, const vector &r) { return l = l * r; } 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 l, vector 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 vector &operator/=(vector &l, const vector &r) { return l = l / r; } template vector operator%(vector l, const vector &r) { if(l.size() < r.size()) return l; l -= l / r * r; return {begin(l), begin(l) + (r.size() - 1)}; } template vector &operator%=(vector &l, const vector &r) { return l = l % r; } 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 > T power(T a, long long n, F op = multiplies(), 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 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 void ntt(vector> &a, bool inverse) { static vector> dt(30), idt(30); if(dt[0] == 0) { Modular root = 2; while(power(root, (Mod - 1) / 2) == 1) root += 1; for(int i = 0; i < 30; ++i) dt[i] = -power(root, (Mod - 1) >> (i + 2)), idt[i] = 1 / dt[i]; } int n = a.size(); assert((n & (n - 1)) == 0); if(not inverse) { for(int w = n; w >>= 1;) { Modular t = 1; for(int s = 0, k = 0; s < n; s += 2 * w) { for(int i = s, j = s + w; i < s + w; ++i, ++j) { auto x = a[i], y = a[j] * t; if(x.v >= Mod) x.v -= Mod; a[i].v = x.v + y.v, a[j].v = x.v + (Mod - y.v); } t *= dt[__builtin_ctz(++k)]; } } } else { for(int w = 1; w < n; w *= 2) { Modular t = 1; for(int s = 0, k = 0; s < n; s += 2 * w) { for(int i = s, j = s + w; i < s + w; ++i, ++j) { auto x = a[i], y = a[j]; a[i] = x + y, a[j].v = x.v + (Mod - y.v), a[j] *= t; } t *= idt[__builtin_ctz(++k)]; } } } auto c = 1 / Modular(inverse ? n : 1); for(auto &&e : a) e *= c; } template vector> operator*(vector> l, vector> 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 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; } template vector> inverse(const vector> &a) { assert(not a.empty() and not(a[0] == 0)); vector> b{1 / a[0]}; for(int m = 1; m < (int)a.size(); m *= 2) { vector> x(begin(a), begin(a) + min(a.size(), 2 * m)); auto y = b; x.resize(2 * m), ntt(x, false); y.resize(2 * m), ntt(y, false); for(int i = 0; i < 2 * m; ++i) x[i] *= y[i]; ntt(x, true); fill(begin(x), begin(x) + m, 0); ntt(x, false); for(int i = 0; i < 2 * m; ++i) x[i] *= -y[i]; ntt(x, true); b.insert(end(b), begin(x) + m, end(x)); } return {begin(b), begin(b) + a.size()}; } template vector> exponent(const vector> &a) { assert(a.empty() or a[0] == 0); vector> b{1, 1 < a.size() ? a[1] : 0}, c{1}, z1, z2{1, 1}; for(int m = 2; m < (int)a.size(); m *= 2) { auto y = b; y.resize(2 * m), ntt(y, false); z1 = z2; vector> z(m); for(int i = 0; i < m; ++i) z[i] = y[i] * z1[i]; ntt(z, true); fill(begin(z), begin(z) + m / 2, 0); ntt(z, false); for(int i = 0; i < m; ++i) z[i] *= -z1[i]; ntt(z, true); c.insert(end(c), begin(z) + m / 2, end(z)); z2 = c, z2.resize(2 * m), ntt(z2, false); vector> x(begin(a), begin(a) + min(a.size(), m)); x = derivative(x), x.push_back(0), ntt(x, false); for(int i = 0; i < m; ++i) x[i] *= y[i]; ntt(x, true); x -= derivative(b); x.resize(2 * m); for(int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = 0; ntt(x, false); for(int i = 0; i < 2 * m; ++i) x[i] *= z2[i]; ntt(x, true); x = primitive(x), x.pop_back(); for(int i = m; i < min(a.size(), 2 * m); ++i) x[i] += a[i]; fill(begin(x), begin(x) + m, 0); ntt(x, false); for(int i = 0; i < 2 * m; ++i) x[i] *= y[i]; ntt(x, true); b.insert(end(b), begin(x) + m, end(x)); } return {begin(b), begin(b) + a.size()}; } constexpr long long mod = 1e9 + 9; using Mint = Modular; 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 ? i * fact[i - 1] : 1; inv_fact[n] = 1 / fact[n]; for(int i = n; i; --i) inv_fact[i - 1] = i * inv_fact[i]; 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 r) { return *this *= r.v < minv.size() ? minv[r.v] : power(r, mod - 2); } ll modpow(ll x, ll n, ll mod) { ll res = 1; while(n) { if(n & 1) res = res * x % mod; x = x * x % mod; n >>= 1; } return res; } main() { INT(n); ll a = 430477711, b = 569522298; vector f1(n + 1), f2(n + 1); rep2(i, 1, n) f1[i] = (i + 1) * (i + 1) % mod * a; rep2(i, 1, n) f2[i] = (i + 1) * (i + 1) % mod * b; prepare(2 * (n + 1)); f1 = exponent(f1); f2 = exponent(f2); ll p = 1; rep2(i, 1, n) p = p * i % mod; rep2(i, 1, n) f1[i] *= p, f2[i] *= p; Mint I = modpow(b - a, mod - 2, mod); rep2(i, 1, n) { Mint c = (f2[i] - f1[i]) * I; cout << (c.v + (f1[i] - c * a).v) % mod << endl; } }