#ifndef LOCAL #define FAST_IO #endif // ============ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define OVERRIDE(a, b, c, d, ...) d #define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i) #define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i) #define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__) #define PER(i, n) for (i32 i = (i32)(n) - 1; i >= 0; --i) #define ALL(x) begin(x), end(x) using namespace std; using u32 = unsigned int; using u64 = unsigned long long; using i32 = signed int; using i64 = signed long long; using f64 = double; using f80 = long double; template using Vec = vector; template bool chmin(T &x, const T &y) { if (x > y) { x = y; return true; } return false; } template bool chmax(T &x, const T &y) { if (x < y) { x = y; return true; } return false; } #ifdef INT128 using u128 = __uint128_t; using i128 = __int128_t; istream &operator>>(istream &is, i128 &x) { i64 v; is >> v; x = v; return is; } ostream &operator<<(ostream &os, i128 x) { os << (i64)x; return os; } istream &operator>>(istream &is, u128 &x) { u64 v; is >> v; x = v; return is; } ostream &operator<<(ostream &os, u128 x) { os << (u64)x; return os; } #endif [[maybe_unused]] constexpr i32 INF = 1000000100; [[maybe_unused]] constexpr i64 INF64 = 3000000000000000100; struct SetUpIO { SetUpIO() { #ifdef FAST_IO ios::sync_with_stdio(false); cin.tie(nullptr); #endif cout << fixed << setprecision(15); } } set_up_io; // ============ #ifdef DEBUGF #else #define DBG(x) (void) 0 #endif #include using M = atcoder::modint998244353; M pwk[30001]; M f[30001], invf[30001]; M f2[30001], invf2[30001]; M s0[30001], s1[30001], s2[30001], s3[30001], s4[30001]; M ans[30001]; int main() { i32 k; cin >> k; i32 n = 30000; REP(i, n + 1) { pwk[i] = M(i).pow(k); } f[0] = M(1); REP(i, 1, n + 1) { f[i] = f[i - 1] * M(i); } invf[n] = f[n].inv(); PER(i, n) { invf[i] = invf[i + 1] * M(i + 1); } REP(i, n + 1) { f2[i] = f[i] * f[i]; invf2[i] = invf[i] * invf[i]; } REP(a_, 1, n + 1) { M a = M::raw(a_); M a2 = a * a; M a3 = a2 * a; M a4 = a3 * a; if (a_ >= 3) { i32 rem_max = 2 * a_ - 3; i32 i_max = min(n, rem_max + a_ - 3); REP(i, a_, i_max + 1) { i32 rem = i + 3 - a_; M coeff = pwk[a_ - 2] * f2[i] * invf2[a_]; M sum; sum += s0[rem]; sum += a * s1[rem]; sum += a2 * s2[rem]; sum += a3 * s3[rem]; sum += a4 * s4[rem]; ans[i] += coeff * sum; } } if (a_ >= 2) { i32 b_ = a_; REP(c_, 1, b_) { if (b_ + c_ >= n + 1) { break; } i32 idx = b_ + c_; M coeff = invf2[b_] * invf2[c_] * M::raw((b_ - c_) * (b_ - c_)); M bpc = M::raw(b_ + c_); M bc = M::raw(b_ * c_); s0[idx] += coeff * bc * bc; s1[idx] -= coeff * M::raw(2) * bc * bpc; s2[idx] += coeff * (bpc * bpc + M::raw(2) * bc); s3[idx] -= coeff * M::raw(2) * bpc; s4[idx] += coeff; } } } cout << n << '\n'; REP(i, 1, n + 1) { cout << ans[i].val() << " \n"[i == n]; } }