#include <bits/stdc++.h>
#include <atcoder/convolution>
#include <atcoder/modint>

using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
using isize = std::ptrdiff_t;
using usize = std::size_t;

class rep {
    struct Iter {
        usize itr;
        constexpr Iter(const usize pos) noexcept : itr(pos) {}
        constexpr void operator++() noexcept { ++itr; }
        constexpr bool operator!=(const Iter& other) const noexcept { return itr != other.itr; }
        constexpr usize operator*() const noexcept { return itr; }
    };
    const Iter first, last;

  public:
    explicit constexpr rep(const usize first, const usize last) noexcept : first(first), last(std::max(first, last)) {}
    constexpr Iter begin() const noexcept { return first; }
    constexpr Iter end() const noexcept { return last; }
};

class revrep {
    struct Iter {
        usize itr;
        constexpr Iter(const usize pos) noexcept : itr(pos) {}
        constexpr void operator++() noexcept { --itr; }
        constexpr bool operator!=(const Iter& other) const noexcept { return itr != other.itr; }
        constexpr usize operator*() const noexcept { return itr; }
    };
    const Iter first, last;

  public:
    explicit constexpr revrep(const usize first, const usize last) noexcept
        : first(last - 1), last(std::min(first, last) - 1) {}
    constexpr Iter begin() const noexcept { return first; }
    constexpr Iter end() const noexcept { return last; }
};

template <class T> using Vec = std::vector<T>;

using Fp = atcoder::modint998244353;

const auto INV2 = Fp(1) / Fp(2);

void main_() {
    usize N;
    std::cin >> N;
    Vec<Fp> A(N);
    for (auto& x : A) {
        u32 y;
        std::cin >> y;
        x = y;
    }
    Vec<Fp> C(N);
    {
        Vec<Fp> more(N);
        more[N - 1] = Fp(1);
        for (const auto i : revrep(1, N)) {
            more[i - 1] = more[i] * Fp(i);
        }
        Vec<Fp> pow2(2 * N);
        pow2[0] = 1;
        for (const auto i : rep(1, 2 * N)) {
            pow2[i] = pow2[i - 1] * 2;
        }
        Fp sum;
        for (const auto i : rep(0, N - 1)) {
            sum += (more[i] - more[i + 1] * INV2) * pow2[2 * ((N - 1) - i) + i];
            C[i] = sum;
        }
        for (const auto i : rep(0, N)) {
            C[N - 1] += more[i] * pow2[2 * ((N - 1) - i) + i];
        }
    }
    A.resize(2 * N);
    C.resize(2 * N);
    for (const auto i : rep(0, N)) {
        A[2 * N - i - 1] = A[i];
        C[2 * N - i - 1] = C[i];
    }
    const auto N2 = 2 * N;
    std::reverse(C.begin(), C.end());
    auto F = atcoder::convolution(A, C);
    for (const auto i : rep(N2, F.size())) {
        F[i - N2] += F[i];
    }
    F.resize(N2);
    std::reverse(F.begin(), F.end());
    const usize K = std::min(N2, (usize)(7.5 * std::sqrt(N)));
    Vec<Vec<Fp>> D_base(K + 1);
    D_base[0] = {Fp(1)};
    for (const auto i : rep(1, K + 1)) {
        D_base[i].resize(D_base[i - 1].size() + 2);
        for (const auto j : rep(0, D_base[i - 1].size())) {
            D_base[i][j] += D_base[i - 1][j];
            D_base[i][j + 1] += D_base[i - 1][j] * Fp((isize)N - 3);
            D_base[i][j + 2] += D_base[i - 1][j];
        }
    }
    Vec<typename Vec<Fp>::const_iterator> D(K);
    for (const auto i : rep(0, K)) {
        D[i] = D_base[i].cbegin() + (D_base[i].size() / 2);
    }
    for (const auto i : rep(0, N + 1)) {
        if (i % K == 0 and i != 0) {
            const auto tmp = atcoder::convolution(F, D_base[K]);
            F.assign(N2, 0);
            for (const auto i : rep(0, tmp.size())) {
                F[(i + N2 - K) % N2] += tmp[i];
            }
        }
        Fp ans;
        const isize width = i % K;
        for (isize i = -width; i <= width; i += 1) {
            ans += F[i < 0 ? i + N2 : i] * D[width][i];
        }
        std::cout << (ans * INV2).val() << '\n';
    }
}

int main() {
    std::ios_base::sync_with_stdio(false);
    std::cin.tie(nullptr);
    main_();
    return 0;
}