//*
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
//*/

// #include <atcoder/all>
#include <bits/stdc++.h>

using namespace std;
// using namespace atcoder;

// #define _GLIBCXX_DEBUG

#define DEBUG(x) cerr << #x << ": " << x << endl;
#define DEBUG_VEC(v)                                        \
    cerr << #v << ":";                                      \
    for (int iiiiiiii = 0; iiiiiiii < v.size(); iiiiiiii++) \
        cerr << " " << v[iiiiiiii];                         \
    cerr << endl;
#define DEBUG_MAT(v)                                \
    cerr << #v << endl;                             \
    for (int iv = 0; iv < v.size(); iv++) {         \
        for (int jv = 0; jv < v[iv].size(); jv++) { \
            cerr << v[iv][jv] << " ";               \
        }                                           \
        cerr << endl;                               \
    }
typedef long long ll;
// #define int ll

#define vi vector<int>
#define vl vector<ll>
#define vii vector<vector<int>>
#define vll vector<vector<ll>>
#define vs vector<string>
#define pii pair<int, int>
#define pis pair<int, string>
#define psi pair<string, int>
#define pll pair<ll, ll>
template <class S, class T>
pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) {
    return pair<S, T>(s.first + t.first, s.second + t.second);
}
template <class S, class T>
pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first - t.first, s.second - t.second); }
template <class S, class T>
ostream &operator<<(ostream &os, pair<S, T> p) {
    os << "(" << p.first << ", " << p.second << ")";
    return os;
}
#define X first
#define Y second
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep1(i, n) for (int i = 1; i <= (int)(n); i++)
#define rrep(i, n) for (int i = (int)(n)-1; i >= 0; i--)
#define rrep1(i, n) for (int i = (int)(n); i > 0; i--)
#define REP(i, a, b) for (int i = a; i < b; i++)
#define in(x, a, b) (a <= x && x < b)
#define all(c) c.begin(), c.end()
void YES(bool t = true) {
    cout << (t ? "YES" : "NO") << endl;
}
void Yes(bool t = true) { cout << (t ? "Yes" : "No") << endl; }
void yes(bool t = true) { cout << (t ? "yes" : "no") << endl; }
void NO(bool t = true) { cout << (t ? "NO" : "YES") << endl; }
void No(bool t = true) { cout << (t ? "No" : "Yes") << endl; }
void no(bool t = true) { cout << (t ? "no" : "yes") << endl; }
template <class T>
bool chmax(T &a, const T &b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
bool chmin(T &a, const T &b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}
#define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end());
const ll inf = 1000000001;
const ll INF = (ll)1e18 + 1;
const long double pi = 3.1415926535897932384626433832795028841971L;
int popcount(ll t) { return __builtin_popcountll(t); }
// int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
// int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 };
vi dx = {0, 0, -1, 1}, dy = {-1, 1, 0, 0};
vi dx2 = {1, 1, 0, -1, -1, -1, 0, 1}, dy2 = {0, 1, 1, 1, 0, -1, -1, -1};
struct Setup_io {
    Setup_io() {
        ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
        cout << fixed << setprecision(25);
    }
} setup_io;
// const ll MOD = 1000000007;
const ll MOD = 998244353;
// #define mp make_pair
//#define endl '\n'

#include <cassert>
#include <numeric>
#include <type_traits>

#ifdef _MSC_VER
#include <intrin.h>
#endif

#include <utility>

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

struct barrett {
    unsigned int _m;
    unsigned long long im;

    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    unsigned int umod() const { return _m; }

    unsigned int mul(unsigned int a, unsigned int b) const {

        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x =
            (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned int v = (unsigned int)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};

constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0)
        d /= 2;
    constexpr long long bases[3] = {2, 7, 61};
    for (long long a : bases) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n>
constexpr bool is_prime = is_prime_constexpr(n);

constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};

    long long s = b, t = a;
    long long m0 = 0, m1 = 1;

    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b

        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0)
        x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m>
constexpr int primitive_root = primitive_root_constexpr(m);

unsigned long long floor_sum_unsigned(unsigned long long n,
                                      unsigned long long m,
                                      unsigned long long a,
                                      unsigned long long b) {
    unsigned long long ans = 0;
    while (true) {
        if (a >= m) {
            ans += n * (n - 1) / 2 * (a / m);
            a %= m;
        }
        if (b >= m) {
            ans += n * (b / m);
            b %= m;
        }

        unsigned long long y_max = a * n + b;
        if (y_max < m) break;
        n = (unsigned long long)(y_max / m);
        b = (unsigned long long)(y_max % m);
        std::swap(m, a);
    }
    return ans;
}

} // namespace internal

} // namespace atcoder

#include <cassert>
#include <numeric>
#include <type_traits>

namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                  is_signed_int128<T>::value ||
                                                  is_unsigned_int128<T>::value,
                                              std::true_type,
                                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

#else

template <class T>
using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T>
using to_unsigned_t = typename to_unsigned<T>::type;

} // namespace internal

} // namespace atcoder

namespace atcoder {

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T>
using is_modint = std::is_base_of<modint_base, T>;
template <class T>
using is_modint_t = std::enable_if_t<is_modint<T>::value>;

} // namespace internal

template <int m, std::enable_if_t<(1 <= m)> * = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;

  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    static_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T> * = nullptr>
    static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T> * = nullptr>
    static_modint(T v) {
        _v = (unsigned int)(v % umod());
    }

    unsigned int val() const { return _v; }

    mint &operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint &operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint &operator+=(const mint &rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint &operator-=(const mint &rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    mint &operator*=(const mint &rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }

    friend mint operator+(const mint &lhs, const mint &rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint &lhs, const mint &rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint &lhs, const mint &rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint &lhs, const mint &rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint &lhs, const mint &rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint &lhs, const mint &rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = internal::is_prime<m>;
};

template <int id>
struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;

  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T> * = nullptr>
    dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T> * = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }

    unsigned int val() const { return _v; }

    mint &operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint &operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint &operator+=(const mint &rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint &operator-=(const mint &rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint &operator*=(const mint &rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }

    friend mint operator+(const mint &lhs, const mint &rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint &lhs, const mint &rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint &lhs, const mint &rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint &lhs, const mint &rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint &lhs, const mint &rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint &lhs, const mint &rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id>
internal::barrett dynamic_modint<id>::bt(998244353);

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class>
struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

} // namespace internal

} // namespace atcoder

using namespace atcoder;

// using mint = modint998244353;

template <uint32_t mod>
struct LazyMontgomeryModInt {
    using mint = LazyMontgomeryModInt;
    using i32 = int32_t;
    using u32 = uint32_t;
    using u64 = uint64_t;

    static constexpr u32 get_r() {
        u32 ret = mod;
        for (i32 i = 0; i < 4; ++i)
            ret *= 2 - mod * ret;
        return ret;
    }

    static constexpr u32 r = get_r();
    static constexpr u32 n2 = -u64(mod) % mod;
    static_assert(r * mod == 1, "invalid, r * mod != 1");
    static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
    static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");

    u32 a;

    constexpr LazyMontgomeryModInt() : a(0) {}
    constexpr LazyMontgomeryModInt(const int64_t &b)
        : a(reduce(u64(b % mod + mod) * n2)){};

    static constexpr u32 reduce(const u64 &b) {
        return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
    }

    constexpr mint &operator+=(const mint &b) {
        if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
        return *this;
    }

    constexpr mint &operator-=(const mint &b) {
        if (i32(a -= b.a) < 0) a += 2 * mod;
        return *this;
    }

    constexpr mint &operator*=(const mint &b) {
        a = reduce(u64(a) * b.a);
        return *this;
    }

    constexpr mint &operator/=(const mint &b) {
        *this *= b.inverse();
        return *this;
    }

    constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
    constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
    constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
    constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
    constexpr bool operator==(const mint &b) const {
        return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
    }
    constexpr bool operator!=(const mint &b) const {
        return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
    }
    constexpr mint operator-() const { return mint() - mint(*this); }

    constexpr mint pow(u64 n) const {
        mint ret(1), mul(*this);
        while (n > 0) {
            if (n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }

    constexpr mint inverse() const { return pow(mod - 2); }

    friend ostream &operator<<(ostream &os, const mint &b) {
        return os << b.get();
    }

    friend istream &operator>>(istream &is, mint &b) {
        int64_t t;
        is >> t;
        b = LazyMontgomeryModInt<mod>(t);
        return (is);
    }

    constexpr u32 get() const {
        u32 ret = reduce(a);
        return ret >= mod ? ret - mod : ret;
    }

    static constexpr u32 get_mod() { return mod; }
};

template <typename mint>
struct NTT {
    static constexpr uint32_t get_pr() {
        uint32_t _mod = mint::get_mod();
        using u64 = uint64_t;
        u64 ds[32] = {};
        int idx = 0;
        u64 m = _mod - 1;
        for (u64 i = 2; i * i <= m; ++i) {
            if (m % i == 0) {
                ds[idx++] = i;
                while (m % i == 0)
                    m /= i;
            }
        }
        if (m != 1) ds[idx++] = m;

        uint32_t _pr = 2;
        while (1) {
            int flg = 1;
            for (int i = 0; i < idx; ++i) {
                u64 a = _pr, b = (_mod - 1) / ds[i], r = 1;
                while (b) {
                    if (b & 1) r = r * a % _mod;
                    a = a * a % _mod;
                    b >>= 1;
                }
                if (r == 1) {
                    flg = 0;
                    break;
                }
            }
            if (flg == 1) break;
            ++_pr;
        }
        return _pr;
    };

    static constexpr uint32_t mod = mint::get_mod();
    static constexpr uint32_t pr = get_pr();
    static constexpr int level = __builtin_ctzll(mod - 1);
    mint dw[level], dy[level];

    void setwy(int k) {
        mint w[level], y[level];
        w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));
        y[k - 1] = w[k - 1].inverse();
        for (int i = k - 2; i > 0; --i)
            w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];
        dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];
        for (int i = 3; i < k; ++i) {
            dw[i] = dw[i - 1] * y[i - 2] * w[i];
            dy[i] = dy[i - 1] * w[i - 2] * y[i];
        }
    }

    NTT() { setwy(level); }

    void fft4(vector<mint> &a, int k) {
        if ((int)a.size() <= 1) return;
        if (k == 1) {
            mint a1 = a[1];
            a[1] = a[0] - a[1];
            a[0] = a[0] + a1;
            return;
        }
        if (k & 1) {
            int v = 1 << (k - 1);
            for (int j = 0; j < v; ++j) {
                mint ajv = a[j + v];
                a[j + v] = a[j] - ajv;
                a[j] += ajv;
            }
        }
        int u = 1 << (2 + (k & 1));
        int v = 1 << (k - 2 - (k & 1));
        mint one = mint(1);
        mint imag = dw[1];
        while (v) {
            // jh = 0
            {
                int j0 = 0;
                int j1 = v;
                int j2 = j1 + v;
                int j3 = j2 + v;
                for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
                    mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
                    mint t0p2 = t0 + t2, t1p3 = t1 + t3;
                    mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
                    a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;
                    a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;
                }
            }
            // jh >= 1
            mint ww = one, xx = one * dw[2], wx = one;
            for (int jh = 4; jh < u;) {
                ww = xx * xx, wx = ww * xx;
                int j0 = jh * v;
                int je = j0 + v;
                int j2 = je + v;
                for (; j0 < je; ++j0, ++j2) {
                    mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,
                         t3 = a[j2 + v] * wx;
                    mint t0p2 = t0 + t2, t1p3 = t1 + t3;
                    mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
                    a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;
                    a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;
                }
                xx *= dw[__builtin_ctzll((jh += 4))];
            }
            u <<= 2;
            v >>= 2;
        }
    }

    void ifft4(vector<mint> &a, int k) {
        if ((int)a.size() <= 1) return;
        if (k == 1) {
            mint a1 = a[1];
            a[1] = a[0] - a[1];
            a[0] = a[0] + a1;
            return;
        }
        int u = 1 << (k - 2);
        int v = 1;
        mint one = mint(1);
        mint imag = dy[1];
        while (u) {
            // jh = 0
            {
                int j0 = 0;
                int j1 = v;
                int j2 = v + v;
                int j3 = j2 + v;
                for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
                    mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
                    mint t0p1 = t0 + t1, t2p3 = t2 + t3;
                    mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;
                    a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;
                    a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;
                }
            }
            // jh >= 1
            mint ww = one, xx = one * dy[2], yy = one;
            u <<= 2;
            for (int jh = 4; jh < u;) {
                ww = xx * xx, yy = xx * imag;
                int j0 = jh * v;
                int je = j0 + v;
                int j2 = je + v;
                for (; j0 < je; ++j0, ++j2) {
                    mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];
                    mint t0p1 = t0 + t1, t2p3 = t2 + t3;
                    mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
                    a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;
                    a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;
                }
                xx *= dy[__builtin_ctzll(jh += 4)];
            }
            u >>= 4;
            v <<= 2;
        }
        if (k & 1) {
            u = 1 << (k - 1);
            for (int j = 0; j < u; ++j) {
                mint ajv = a[j] - a[j + u];
                a[j] += a[j + u];
                a[j + u] = ajv;
            }
        }
    }

    void ntt(vector<mint> &a) {
        if ((int)a.size() <= 1) return;
        fft4(a, __builtin_ctz(a.size()));
    }

    void intt(vector<mint> &a) {
        if ((int)a.size() <= 1) return;
        ifft4(a, __builtin_ctz(a.size()));
        mint iv = mint(a.size()).inverse();
        for (auto &x : a)
            x *= iv;
    }

    vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
        int l = a.size() + b.size() - 1;
        if (min<int>(a.size(), b.size()) <= 40) {
            vector<mint> s(l);
            for (int i = 0; i < (int)a.size(); ++i)
                for (int j = 0; j < (int)b.size(); ++j)
                    s[i + j] += a[i] * b[j];
            return s;
        }
        int k = 2, M = 4;
        while (M < l)
            M <<= 1, ++k;
        setwy(k);
        vector<mint> s(M), t(M);
        for (int i = 0; i < (int)a.size(); ++i)
            s[i] = a[i];
        for (int i = 0; i < (int)b.size(); ++i)
            t[i] = b[i];
        fft4(s, k);
        fft4(t, k);
        for (int i = 0; i < M; ++i)
            s[i] *= t[i];
        ifft4(s, k);
        s.resize(l);
        mint invm = mint(M).inverse();
        for (int i = 0; i < l; ++i)
            s[i] *= invm;
        return s;
    }

    void ntt_doubling(vector<mint> &a) {
        int M = (int)a.size();
        auto b = a;
        intt(b);
        mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));
        for (int i = 0; i < M; i++)
            b[i] *= r, r *= zeta;
        ntt(b);
        copy(begin(b), end(b), back_inserter(a));
    }
};

namespace ArbitraryNTT {
using i64 = int64_t;
using u128 = __uint128_t;
constexpr int32_t m0 = 167772161;
constexpr int32_t m1 = 469762049;
constexpr int32_t m2 = 754974721;
using mint0 = LazyMontgomeryModInt<m0>;
using mint1 = LazyMontgomeryModInt<m1>;
using mint2 = LazyMontgomeryModInt<m2>;
constexpr int r01 = mint1(m0).inverse().get();
constexpr int r02 = mint2(m0).inverse().get();
constexpr int r12 = mint2(m1).inverse().get();
constexpr int r02r12 = i64(r02) * r12 % m2;
constexpr i64 w1 = m0;
constexpr i64 w2 = i64(m0) * m1;

template <typename T, typename submint>
vector<submint> mul(const vector<T> &a, const vector<T> &b) {
    static NTT<submint> ntt;
    vector<submint> s(a.size()), t(b.size());
    for (int i = 0; i < (int)a.size(); ++i)
        s[i] = i64(a[i] % submint::get_mod());
    for (int i = 0; i < (int)b.size(); ++i)
        t[i] = i64(b[i] % submint::get_mod());
    return ntt.multiply(s, t);
}

template <typename T>
vector<int> multiply(const vector<T> &s, const vector<T> &t, int mod) {
    auto d0 = mul<T, mint0>(s, t);
    auto d1 = mul<T, mint1>(s, t);
    auto d2 = mul<T, mint2>(s, t);
    int n = d0.size();
    vector<int> ret(n);
    const int W1 = w1 % mod;
    const int W2 = w2 % mod;
    for (int i = 0; i < n; i++) {
        int n1 = d1[i].get(), n2 = d2[i].get(), a = d0[i].get();
        int b = i64(n1 + m1 - a) * r01 % m1;
        int c = (i64(n2 + m2 - a) * r02r12 + i64(m2 - b) * r12) % m2;
        ret[i] = (i64(a) + i64(b) * W1 + i64(c) * W2) % mod;
    }
    return ret;
}

template <typename mint>
vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
    if (a.size() == 0 && b.size() == 0) return {};
    if (min<int>(a.size(), b.size()) < 128) {
        vector<mint> ret(a.size() + b.size() - 1);
        for (int i = 0; i < (int)a.size(); ++i)
            for (int j = 0; j < (int)b.size(); ++j)
                ret[i + j] += a[i] * b[j];
        return ret;
    }
    vector<int> s(a.size()), t(b.size());
    for (int i = 0; i < (int)a.size(); ++i)
        s[i] = a[i].get();
    for (int i = 0; i < (int)b.size(); ++i)
        t[i] = b[i].get();
    vector<int> u = multiply<int>(s, t, mint::get_mod());
    vector<mint> ret(u.size());
    for (int i = 0; i < (int)u.size(); ++i)
        ret[i] = mint(u[i]);
    return ret;
}

template <typename T>
vector<u128> multiply_u128(const vector<T> &s, const vector<T> &t) {
    if (s.size() == 0 && t.size() == 0) return {};
    if (min<int>(s.size(), t.size()) < 128) {
        vector<u128> ret(s.size() + t.size() - 1);
        for (int i = 0; i < (int)s.size(); ++i)
            for (int j = 0; j < (int)t.size(); ++j)
                ret[i + j] += i64(s[i]) * t[j];
        return ret;
    }
    auto d0 = mul<T, mint0>(s, t);
    auto d1 = mul<T, mint1>(s, t);
    auto d2 = mul<T, mint2>(s, t);
    int n = d0.size();
    vector<u128> ret(n);
    for (int i = 0; i < n; i++) {
        i64 n1 = d1[i].get(), n2 = d2[i].get();
        i64 a = d0[i].get();
        i64 b = (n1 + m1 - a) * r01 % m1;
        i64 c = ((n2 + m2 - a) * r02r12 + (m2 - b) * r12) % m2;
        ret[i] = a + b * w1 + u128(c) * w2;
    }
    return ret;
}
} // namespace ArbitraryNTT

// https://nyaannyaan.github.io/library/fps/formal-power-series.hpp.html
template <typename mint>
struct FormalPowerSeries : vector<mint> {
    using vector<mint>::vector;
    using FPS = FormalPowerSeries;

    FPS &operator+=(const FPS &r) {
        if (r.size() > this->size()) this->resize(r.size());
        for (int i = 0; i < (int)r.size(); i++)
            (*this)[i] += r[i];
        return *this;
    }

    FPS &operator+=(const mint &r) {
        if (this->empty()) this->resize(1);
        (*this)[0] += r;
        return *this;
    }

    FPS &operator-=(const FPS &r) {
        if (r.size() > this->size()) this->resize(r.size());
        for (int i = 0; i < (int)r.size(); i++)
            (*this)[i] -= r[i];
        return *this;
    }

    FPS &operator-=(const mint &r) {
        if (this->empty()) this->resize(1);
        (*this)[0] -= r;
        return *this;
    }

    FPS &operator*=(const mint &v) {
        for (int k = 0; k < (int)this->size(); k++)
            (*this)[k] *= v;
        return *this;
    }

    FPS &operator/=(const FPS &r) {
        if (this->size() < r.size()) {
            this->clear();
            return *this;
        }
        int n = this->size() - r.size() + 1;
        if ((int)r.size() <= 64) {
            FPS f(*this), g(r);
            g.shrink();
            mint coeff = g.back().inverse();
            for (auto &x : g)
                x *= coeff;
            int deg = (int)f.size() - (int)g.size() + 1;
            int gs = g.size();
            FPS quo(deg);
            for (int i = deg - 1; i >= 0; i--) {
                quo[i] = f[i + gs - 1];
                for (int j = 0; j < gs; j++)
                    f[i + j] -= quo[i] * g[j];
            }
            *this = quo * coeff;
            this->resize(n, mint(0));
            return *this;
        }
        return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev();
    }

    FPS &operator%=(const FPS &r) {
        *this -= *this / r * r;
        shrink();
        return *this;
    }

    FPS operator+(const FPS &r) const { return FPS(*this) += r; }
    FPS operator+(const mint &v) const { return FPS(*this) += v; }
    FPS operator-(const FPS &r) const { return FPS(*this) -= r; }
    FPS operator-(const mint &v) const { return FPS(*this) -= v; }
    FPS operator*(const FPS &r) const { return FPS(*this) *= r; }
    FPS operator*(const mint &v) const { return FPS(*this) *= v; }
    FPS operator/(const FPS &r) const { return FPS(*this) /= r; }
    FPS operator%(const FPS &r) const { return FPS(*this) %= r; }
    FPS operator-() const {
        FPS ret(this->size());
        for (int i = 0; i < (int)this->size(); i++)
            ret[i] = -(*this)[i];
        return ret;
    }

    void shrink() {
        while (this->size() && this->back() == mint(0))
            this->pop_back();
    }

    FPS rev() const {
        FPS ret(*this);
        reverse(begin(ret), end(ret));
        return ret;
    }

    FPS dot(FPS r) const {
        FPS ret(min(this->size(), r.size()));
        for (int i = 0; i < (int)ret.size(); i++)
            ret[i] = (*this)[i] * r[i];
        return ret;
    }

    FPS pre(int sz) const {
        return FPS(begin(*this), begin(*this) + min((int)this->size(), sz));
    }

    FPS operator>>(int sz) const {
        if ((int)this->size() <= sz) return {};
        FPS ret(*this);
        ret.erase(ret.begin(), ret.begin() + sz);
        return ret;
    }

    FPS operator<<(int sz) const {
        FPS ret(*this);
        ret.insert(ret.begin(), sz, mint(0));
        return ret;
    }

    FPS diff() const {
        const int n = (int)this->size();
        FPS ret(max(0, n - 1));
        mint one(1), coeff(1);
        for (int i = 1; i < n; i++) {
            ret[i - 1] = (*this)[i] * coeff;
            coeff += one;
        }
        return ret;
    }

    FPS integral() const {
        const int n = (int)this->size();
        FPS ret(n + 1);
        ret[0] = mint(0);
        if (n > 0) ret[1] = mint(1);
        auto mod = mint::get_mod();
        for (int i = 2; i <= n; i++)
            ret[i] = (-ret[mod % i]) * (mod / i);
        for (int i = 0; i < n; i++)
            ret[i + 1] *= (*this)[i];
        return ret;
    }

    mint eval(mint x) const {
        mint r = 0, w = 1;
        for (auto &v : *this)
            r += w * v, w *= x;
        return r;
    }

    FPS log(int deg = -1) const {
        assert((*this)[0] == mint(1));
        if (deg == -1) deg = (int)this->size();
        return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
    }

    FPS pow(int64_t k, int deg = -1) const {
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        if (k == 0) {
            FPS ret(deg);
            if (deg) ret[0] = 1;
            return ret;
        }
        for (int i = 0; i < n; i++) {
            if ((*this)[i] != mint(0)) {
                mint rev = mint(1) / (*this)[i];
                FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg);
                ret *= (*this)[i].pow(k);
                ret = (ret << (i * k)).pre(deg);
                if ((int)ret.size() < deg) ret.resize(deg, mint(0));
                return ret;
            }
            if (__int128_t(i + 1) * k >= deg) return FPS(deg, mint(0));
        }
        return FPS(deg, mint(0));
    }

    static void *ntt_ptr;
    static void set_fft();
    FPS &operator*=(const FPS &r);
    void ntt();
    void intt();
    void ntt_doubling();
    static int ntt_pr();
    FPS inv(int deg = -1) const;
    FPS exp(int deg = -1) const;
};
template <typename mint>
void *FormalPowerSeries<mint>::ntt_ptr = nullptr;

template <typename mint>
void FormalPowerSeries<mint>::set_fft() {
    ntt_ptr = nullptr;
}

template <typename mint>
void FormalPowerSeries<mint>::ntt() {
    exit(1);
}

template <typename mint>
void FormalPowerSeries<mint>::intt() {
    exit(1);
}

template <typename mint>
void FormalPowerSeries<mint>::ntt_doubling() {
    exit(1);
}

template <typename mint>
int FormalPowerSeries<mint>::ntt_pr() {
    exit(1);
}

template <typename mint>
FormalPowerSeries<mint> &FormalPowerSeries<mint>::operator*=(
    const FormalPowerSeries<mint> &r) {
    if (this->empty() || r.empty()) {
        this->clear();
        return *this;
    }
    auto ret = ArbitraryNTT::multiply(*this, r);
    return *this = FormalPowerSeries<mint>(ret.begin(), ret.end());
}

template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::inv(int deg) const {
    assert((*this)[0] != mint(0));
    if (deg == -1) deg = (*this).size();
    FormalPowerSeries<mint> ret({mint(1) / (*this)[0]});
    for (int i = 1; i < deg; i <<= 1)
        ret = (ret + ret - ret * ret * (*this).pre(i << 1)).pre(i << 1);
    return ret.pre(deg);
}

template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::exp(int deg) const {
    assert((*this).size() == 0 || (*this)[0] == mint(0));
    if (deg == -1) deg = (int)this->size();
    FormalPowerSeries<mint> ret({mint(1)});
    for (int i = 1; i < deg; i <<= 1) {
        ret = (ret * (pre(i << 1) + mint(1) - ret.log(i << 1))).pre(i << 1);
    }
    return ret.pre(deg);
}

using mint = LazyMontgomeryModInt<998244353>;
using FPS = FormalPowerSeries<mint>;

FPS mul(int x, FPS dp) {
    FPS ndp = dp;
    rrep(i, dp.size()) {
        ndp[i] += dp[(i - x + dp.size()) % dp.size()];
    }
    return ndp;
}

// vector<mint> div(int x, vector<mint> dp) {
//     if (x == 0) {
//         rep(i, dp.size()) {
//             dp[i] /= 2;
//         }
//         return dp;
//     }

//     for (int i = 0; i * x < dp.size(); i++) {
//         vector<mint> ndp = dp;
//         if (i % 2 == 0) {
//             ndp = mul(i * x, dp);
//         } else {
//             rrep(j, dp.size()) {
//                 ndp[j] += dp[(j - i * x + dp.size()) % dp.size()];
//             }
//         }
//         swap(dp, ndp);
//     }
//     return dp;
// }

signed main() {
    int n, m, k;
    cin >> n >> m >> k;

    vi a(n);
    rep(i, n) {
        cin >> a[i];
    }

    FPS dp(k);
    dp[0] = 1;
    rep(i, m) {
        dp = mul(a[i], dp);

        // rep(i, k) {
        //     cout << dp[i].val() << " ";
        // }
        // cout << endl;
    }
    cout << dp[0] - 1 << endl;

    for (int i = m; i < n; i++) {
        dp = mul(a[i], dp);

        FPS div(a[i - m] + 1);
        div[0] = 1;
        div[a[i - m]] = 1;
        dp = dp * div.inv();
        dp.resize(k);

        cout << dp[0] - 1 << endl;
    }
}