#line 2 "Library/src/stream.hpp"
#include <ctype.h>
#include <stdio.h>
#include <string>
#line 2 "Library/src/internal/type_traits.hpp"
#include <iostream>
#include <limits>
#include <numeric>
#include <typeinfo>
#include <cstdint>

namespace kyopro {
namespace internal {
template <typename... Args> struct first_enabled {};

template <typename T, typename... Args>
struct first_enabled<std::enable_if<true, T>, Args...> {
    using type = T;
};
template <typename T, typename... Args>
struct first_enabled<std::enable_if<false, T>, Args...>
    : first_enabled<Args...> {};
template <typename T, typename... Args> struct first_enabled<T, Args...> {
    using type = T;
};

template <typename... Args>
using first_enabled_t = typename first_enabled<Args...>::type;

template <int dgt, std::enable_if_t<dgt <= 128>* = nullptr> struct int_least {
    using type = first_enabled_t<std::enable_if<dgt <= 8, std::int8_t>,
                                 std::enable_if<dgt <= 16, std::int16_t>,
                                 std::enable_if<dgt <= 32, std::int32_t>,
                                 std::enable_if<dgt <= 64, std::int64_t>,
                                 std::enable_if<dgt <= 128, __int128_t>>;
};

template <int dgt, std::enable_if_t<dgt <= 128>* = nullptr> struct uint_least {
    using type = first_enabled_t<std::enable_if<dgt <= 8, std::uint8_t>,
                                 std::enable_if<dgt <= 16, std::uint16_t>,
                                 std::enable_if<dgt <= 32, std::uint32_t>,
                                 std::enable_if<dgt <= 64, std::uint64_t>,
                                 std::enable_if<dgt <= 128, __uint128_t>>;
};

template <int dgt> using int_least_t = typename int_least<dgt>::type;
template <int dgt> using uint_least_t = typename uint_least<dgt>::type;

template <typename T>
using double_size_uint_t = uint_least_t<2 * std::numeric_limits<T>::digits>;

template <typename T>
using double_size_int_t = int_least_t<2 * std::numeric_limits<T>::digits>;

struct modint_base {};
template <typename T> using is_modint = std::is_base_of<modint_base, T>;
template <typename T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;


// is_integral
template <typename T>
using is_integral_t =
    std::enable_if_t<std::is_integral_v<T> || std::is_same_v<T, __int128_t> ||
                   std::is_same_v<T, __uint128_t>>;
};  // namespace internal
};  // namespace kyopro

/**
 * @brief Type Traits
 * @see https://qiita.com/kazatsuyu/items/f8c3b304e7f8b35263d8
 */
#line 6 "Library/src/stream.hpp"

namespace kyopro {

inline void single_read(char& c) {
    c = getchar_unlocked();
    while (isspace(c)) c = getchar_unlocked();
}
template <typename T, internal::is_integral_t<T>* = nullptr>
inline void single_read(T& a) {
    a = 0;
    bool is_negative = false;
    char c = getchar_unlocked();
    while (isspace(c)) {
        c = getchar_unlocked();
    }
    if (c == '-') is_negative = true, c = getchar_unlocked();
    while (isdigit(c)) {
        a = 10 * a + (c - '0');
        c = getchar_unlocked();
    }
    if (is_negative) a *= -1;
}
template <typename T, internal::is_modint_t<T>* = nullptr>
inline void single_read(T& a) {
    long long x;
    single_read(x);
    a = T(x);
}
inline void single_read(std::string& str) noexcept {
    char c = getchar_unlocked();
    while (isspace(c)) c = getchar_unlocked();
    while (!isspace(c)) {
        str += c;
        c = getchar_unlocked();
    }
}
template<typename T>
inline void read(T& x) noexcept {single_read(x);}
template <typename Head, typename... Tail>
inline void read(Head& head, Tail&... tail) noexcept {
    single_read(head), read(tail...);
}

inline void single_write(char c) noexcept { putchar_unlocked(c); }
template <typename T, internal::is_integral_t<T>* = nullptr>
inline void single_write(T a) noexcept {
    if (!a) {
        putchar_unlocked('0');
        return;
    }
    if constexpr (std::is_signed_v<T>) {
        if (a < 0) putchar_unlocked('-'), a *= -1;
    }
    constexpr int d = std::numeric_limits<T>::digits10;
    char s[d + 1];
    int now = d + 1;
    while (a) {
        s[--now] = (char)'0' + a % 10;
        a /= 10;
    }
    while (now <= d) putchar_unlocked(s[now++]);
}
template <typename T, internal::is_modint_t<T>* = nullptr>
inline void single_write(T a) noexcept {
    single_write(a.val());
}
inline void single_write(const std::string& str) noexcept {
    for (auto c : str) {
        putchar_unlocked(c);
    }
}
template <typename T> inline void write(T x) noexcept { single_write(x); }
template <typename Head, typename... Tail>
inline void write(Head head, Tail... tail) noexcept {
    single_write(head);
    putchar_unlocked(' ');
    write(tail...);
}
template <typename... Args> inline void put(Args... x) noexcept {
    write(x...);
    putchar_unlocked('\n');
}
};  // namespace kyopro

/**
 * @brief Fast IO(高速入出力)
 */
#line 2 "Library/src/template.hpp"
#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (n); i++)
#define all(x) std::begin(x), std::end(x)
#define popcount(x) __builtin_popcountll(x)
using i128 = __int128_t;
using ll = long long;
using ld = long double;
using graph = std::vector<std::vector<int>>;
using P = std::pair<int, int>;
constexpr int inf = std::numeric_limits<int>::max() / 2;
constexpr ll infl = std::numeric_limits<ll>::max() / 2;
const long double pi = acosl(-1);
constexpr int dx[] = {1, 0, -1, 0, 1, -1, -1, 1, 0};
constexpr int dy[] = {0, 1, 0, -1, 1, 1, -1, -1, 0};
template <typename T1, typename T2> constexpr inline bool chmax(T1& a, T2 b) {
    return a < b && (a = b, true);
}
template <typename T1, typename T2> constexpr inline bool chmin(T1& a, T2 b) {
    return a > b && (a = b, true);
}

/**
 * @brief Template
*/
#line 3 "b.cpp"

using namespace std;
using namespace kyopro;

#line 4 "verify/verify-yuki/yuki-0215-nth-term.test.cpp"
//
#line 2 "fps/arbitrary-fps.hpp"

#line 2 "ntt/arbitrary-ntt.hpp"

#line 2 "modint/montgomery-modint.hpp"

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(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
    static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
    static_assert(r * mod == 1, "this code has bugs.");

    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 operator+() const { return 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 {
        int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
        while (y > 0) {
            t = x / y;
            x -= t * y, u -= t * v;
            tmp = x, x = y, y = tmp;
            tmp = u, u = v, v = tmp;
        }
        return mint{u};
    }

    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; }
};
#line 2 "ntt/ntt.hpp"

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);
        for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i];
        fft4(s, k);
        if (a.size() == b.size() && a == b) {
            for (int i = 0; i < M; ++i) s[i] *= s[i];
        } else {
            vector<mint> t(M);
            for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i];
            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));
    }
};
#line 5 "ntt/arbitrary-ntt.hpp"

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
#line 2 "fps/formal-power-series.hpp"

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;
    }

    // 前 sz 項を取ってくる。sz に足りない項は 0 埋めする
    FPS pre(int sz) const {
        FPS ret(begin(*this), begin(*this) + min((int)this->size(), sz));
        if ((int)ret.size() < sz) ret.resize(sz);
        return ret;
    }

    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).empty() && (*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;

/**
 * @brief 多項式/形式的冪級数ライブラリ
 * @docs docs/fps/formal-power-series.md
 */
#line 5 "fps/arbitrary-fps.hpp"

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);
}
#line 7 "verify/verify-yuki/yuki-0215-nth-term.test.cpp"
using mint = LazyMontgomeryModInt<998244353>;
using vm = vector<mint>;
using vvm = vector<vm>;
using fps = FormalPowerSeries<mint>;

#line 2 "fps/nth-term.hpp"

#line 2 "fps/berlekamp-massey.hpp"

template <typename mint> vector<mint> BerlekampMassey(const vector<mint>& s) {
    const int N = (int)s.size();
    vector<mint> b, c;
    b.reserve(N + 1);
    c.reserve(N + 1);
    b.push_back(mint(1));
    c.push_back(mint(1));
    mint y = mint(1);
    for (int ed = 1; ed <= N; ed++) {
        int l = int(c.size()), m = int(b.size());
        mint x = 0;
        for (int i = 0; i < l; i++) x += c[i] * s[ed - l + i];
        b.emplace_back(mint(0));
        m++;
        if (x == mint(0)) continue;
        mint freq = x / y;
        if (l < m) {
            auto tmp = c;
            c.insert(begin(c), m - l, mint(0));
            for (int i = 0; i < m; i++) c[m - 1 - i] -= freq * b[m - 1 - i];
            b = tmp;
            y = x;
        } else {
            for (int i = 0; i < m; i++) c[l - 1 - i] -= freq * b[m - 1 - i];
        }
    }
    reverse(begin(c), end(c));
    return c;
}
#line 2 "fps/kitamasa.hpp"

#line 4 "fps/kitamasa.hpp"

template <typename mint>
mint LinearRecurrence(long long k,
                      FormalPowerSeries<mint> Q,
                      FormalPowerSeries<mint> P) {
    Q.shrink();
    mint ret = 0;
    if (P.size() >= Q.size()) {
        auto R = P / Q;
        P -= R * Q;
        P.shrink();
        if (k < (int)R.size()) ret += R[k];
    }
    if ((int)P.size() == 0) return ret;

    FormalPowerSeries<mint>::set_fft();
    if (FormalPowerSeries<mint>::ntt_ptr == nullptr) {
        P.resize((int)Q.size() - 1);
        while (k) {
            auto Q2 = Q;
            for (int i = 1; i < (int)Q2.size(); i += 2) Q2[i] = -Q2[i];
            auto S = P * Q2;
            auto T = Q * Q2;
            if (k & 1) {
                for (int i = 1; i < (int)S.size(); i += 2) P[i >> 1] = S[i];
                for (int i = 0; i < (int)T.size(); i += 2) Q[i >> 1] = T[i];
            } else {
                for (int i = 0; i < (int)S.size(); i += 2) P[i >> 1] = S[i];
                for (int i = 0; i < (int)T.size(); i += 2) Q[i >> 1] = T[i];
            }
            k >>= 1;
        }
        return ret + P[0];
    } else {
        int N = 1;
        while (N < (int)Q.size()) N <<= 1;

        P.resize(2 * N);
        Q.resize(2 * N);
        P.ntt();
        Q.ntt();
        vector<mint> S(2 * N), T(2 * N);

        vector<int> btr(N);
        for (int i = 0, logn = __builtin_ctz(N); i < (1 << logn); i++) {
            btr[i] = (btr[i >> 1] >> 1) + ((i & 1) << (logn - 1));
        }
        mint dw = mint(FormalPowerSeries<mint>::ntt_pr())
                      .inverse()
                      .pow((mint::get_mod() - 1) / (2 * N));

        while (k) {
            mint inv2 = mint(2).inverse();

            // even degree of Q(x)Q(-x)
            T.resize(N);
            for (int i = 0; i < N; i++)
                T[i] = Q[(i << 1) | 0] * Q[(i << 1) | 1];

            S.resize(N);
            if (k & 1) {
                // odd degree of P(x)Q(-x)
                for (auto& i : btr) {
                    S[i] = (P[(i << 1) | 0] * Q[(i << 1) | 1] -
                            P[(i << 1) | 1] * Q[(i << 1) | 0]) *
                           inv2;
                    inv2 *= dw;
                }
            } else {
                // even degree of P(x)Q(-x)
                for (int i = 0; i < N; i++) {
                    S[i] = (P[(i << 1) | 0] * Q[(i << 1) | 1] +
                            P[(i << 1) | 1] * Q[(i << 1) | 0]) *
                           inv2;
                }
            }
            swap(P, S);
            swap(Q, T);
            k >>= 1;
            if (k < N) break;
            P.ntt_doubling();
            Q.ntt_doubling();
        }
        P.intt();
        Q.intt();
        return ret + (P * (Q.inv()))[k];
    }
}

template <typename mint>
mint kitamasa(long long N,
              FormalPowerSeries<mint> Q,
              FormalPowerSeries<mint> a) {
    assert(!Q.empty() && Q[0] != 0);
    if (N < (int)a.size()) return a[N];
    assert((int)a.size() >= int(Q.size()) - 1);
    auto P = a.pre((int)Q.size() - 1) * Q;
    P.resize(Q.size() - 1);
    return LinearRecurrence<mint>(N, Q, P);
}

/**
 * @brief 線形漸化式の高速計算
 * @docs docs/fps/kitamasa.md
 */
#line 5 "fps/nth-term.hpp"

template <typename mint> mint nth_term(long long n, const vector<mint>& s) {
    using fps = FormalPowerSeries<mint>;
    auto bm = BerlekampMassey<mint>(s);
    return kitamasa(n, fps{begin(bm), end(bm)}, fps{begin(s), end(s)});
}


int main() {
    ll n, k;
    read(n, k);
    vector<mint> f(2 * k + 30);
    f[0] = f[1] = mint(1);
    for (int i = 2; i < (int)f.size();++i){
        f[i] = f[i - 1] + f[i - 2];
    }
    rep(i, (int)f.size()) f[i] = f[i].pow(k);
    rep(i, (int)f.size() - 1) f[i + 1] += f[i];
    put(nth_term(n - 1, f).get());
}