//line 1 "answer.cpp"
#if !__INCLUDE_LEVEL__
#include __FILE__
int main() {
    int n, h; input(n, h);
    using mint = atcoder::modint998244353;
    using Matrix = vector<vector<vector<mint>>>;
    auto pe = [&](vector<mint>& a, const vector<mint>& b) {
        while (sz(a) < sz(b)) a.push_back(mint(0));
        rep(i, sz(b)) a[i] += b[i];
    };
    auto matmul = [&](const Matrix &a, const Matrix &b) {
        Matrix result(3, vector(3, vector<mint>(0)));
        rep(i, 3) rep(j, 3) {
            rep(k, 3) pe(result[i][j], atcoder::convolution(a[i][k], b[k][j]));
            if (sz(result[i][j]) > h) result[i][j].resize(h);
        }
        return result;
    };
    auto pow = [&](Matrix a, int p) {
        Matrix result(3, vector(3, vector<mint>(0)));
        rep(i, 3) result[i][i] = {mint(1)};
        while (p > 0) {
            if (p & 1) result = matmul(result, a);
            a = matmul(a, a);
            p >>= 1;
        }
        return result;
    };
    vector<vector<vector<mint>>> a = {
        {{mint(2).inv()}, {mint(3).inv()}, {}},
        {{mint(0), mint(2).inv()}, {mint(0), mint(3).inv()}, {mint(0), mint(2) * mint(3).inv()}},
        {{}, {mint(0), mint(3).inv()}, {mint(0), mint(3).inv()}},
    };
    auto mat = pow(a, n-1);
    mint ans(0);
    rep(i, 3) rep(j, h) if (sz(mat[i][0]) > j) ans += mat[i][0][j] * 2;
    rep(i, 3) rep(j, h-1) if (sz(mat[i][1]) > j) ans += mat[i][1][j] * 2;
    rep(i, 3) rep(j, h-1) if (sz(mat[i][1]) > j) ans += mat[i][2][j];
    ans /= 5;
    ans = 1 - ans;
    print(ans.val());
}
#else
//line 2 "/home/seekworser/.cpp_lib/competitive_library/competitive/std/std.hpp"
#include <bits/stdc++.h>
#ifndef LOCAL_TEST
#pragma GCC target ("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#endif // LOCAL_TEST
using namespace std;
using std::cout;
// shorten typenames
using ll = long long;
using pii = pair<int, int>; using pll = pair<ll, ll>;
using vi = vector<int>;  using vvi = vector<vi>; using vvvi = vector<vvi>;
using vl = vector<ll>;  using vvl = vector<vl>; using vvvl = vector<vvl>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
using vs = vector<string>; using vvs = vector<vector<string>>; using vvvs = vector<vector<vector<string>>>;
template<typename T> vector<vector<T>> vv(int h, int w, T val = T()) { return vector(h, vector<T>(w, val)); }
template<typename T> vector<vector<vector<T>>> vvv(int h1, int h2, int h3, T val = T()) { return vector(h1, vector(h2, vector<T>(h3, val))); }
template<typename T> vector<vector<vector<vector<T>>>> vvvv(int h1, int h2, int h3, int h4, T val = T()) { return vector(h1, vector(h2, vector(h3, vector<T>(h4, val)))); }
template <class T> using priority_queue_min = priority_queue<T, vector<T>, greater<T>>;
// define CONSTANTS
constexpr double PI = 3.14159265358979323;
constexpr int INF = 100100111; constexpr ll INFL = 3300300300300300491LL;
float EPS = 1e-8; double EPSL = 1e-10;
template<typename T> bool eq(const T x, const T y) { return x == y; }
template<> bool eq<double>(const double x, const double y) { return (abs(x - y) < EPSL * x || abs(x - y) < EPSL); }
template<> bool eq<float>(const float x, const float y) { return abs(x - y) < EPS * x; }
template<typename T> bool neq(const T x, const T y) { return !(eq<T>(x, y)); }
template<typename T> bool ge(const T x, const T y) { return (eq<T>(x, y) || (x > y)); }
template<typename T> bool le(const T x, const T y) { return (eq<T>(x, y) || (x < y)); }
template<typename T> bool gt(const T x, const T y) { return !(le<T>(x, y)); }
template<typename T> bool lt(const T x, const T y) { return !(ge<T>(x, y)); }
constexpr int MODINT998244353 = 998244353;
constexpr int MODINT1000000007 = 1000000007;
// fasten io
struct Nyan { Nyan() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } nyan;
// define macros
#define all(a) (a).begin(), (a).end()
#define sz(x) ((ll)(x).size())
#define rep1(n) for(ll dummy_iter = 0LL; dummy_iter < n; ++dummy_iter) // 0,1,...,n-1
#define rep2(i, n) for(ll i = 0LL, i##_counter = 0LL; i##_counter < ll(n); ++(i##_counter), (i) = i##_counter) // i=0,1,...,n-1
#define rep3(i, s, t) for(ll i = ll(s), i##_counter = ll(s); i##_counter < ll(t); ++(i##_counter), (i) = (i##_counter)) // i=s,s+1,...,t-1
#define rep4(i, s, t, step) for(ll i##_counter = step > 0 ? ll(s) : -ll(s), i##_end = step > 0 ? ll(t) : -ll(t), i##_step = abs(step), i = ll(s); i##_counter < i##_end; i##_counter += i##_step, i = step > 0 ? i##_counter : -i##_counter) // i=s,s+step,...,<t
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define repe(a, v) for(auto& a : (v)) // iterate over all elements in v
#define smod(n, m) ((((n) % (m)) + (m)) % (m))
#define sdiv(n, m) (((n) - smod(n, m)) / (m))
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());}
int Yes(bool b=true) { cout << (b ? "Yes\n" : "No\n"); return 0; };
int YES(bool b=true) { cout << (b ? "YES\n" : "NO\n"); return 0; };
int No(bool b=true) {return Yes(!b);};
int NO(bool b=true) {return YES(!b);};
template<typename T, size_t N> T max(array<T, N>& a) { return *max_element(all(a)); };
template<typename T, size_t N> T min(array<T, N>& a) { return *min_element(all(a)); };
template<typename T> T max(vector<T>& a) { return *max_element(all(a)); };
template<typename T> T min(vector<T>& a) { return *min_element(all(a)); };
template<typename T> vector<T> vec_slice(const vector<T>& a, int l, int r) { vector<T> rev; rep(i, l, r) rev.push_back(a[i]); return rev; };
template<typename T> T sum(vector<T>& a, T zero = T(0)) { T rev = zero; rep(i, sz(a)) rev += a[i]; return rev; };
template<typename T> bool in_range(const T& val, const T& s, const T& t) { return s <= val && val < t; };

template <class T> inline vector<T>& operator--(vector<T>& v) { repe(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repe(x, v) ++x; return v; }

ll powm(ll a, ll n, ll mod=INFL) {
    ll res = 1;
    while (n > 0) {
        if (n & 1) res = (res * a) % mod;
        if (n > 1) a = (a * a) % mod;
        n >>= 1;
    }
    return res;
}
ll sqrtll(ll x) {
    assert(x >= 0);
    ll rev = sqrt(x);
    while(rev * rev > x) --rev;
    while((rev+1) * (rev+1)<=x) ++rev;
    return rev;
}
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; }
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; }
int digit(ll x, int d=10) { int rev=0; while (x > 0) { rev++; x /= d;}; return rev; }
/**
 * @brief std.hpp
 * @docs docs/std/std.md
 */
//line 2 "/home/seekworser/.cpp_lib/competitive_library/atcoder/convolution.hpp"

//line 6 "/home/seekworser/.cpp_lib/competitive_library/atcoder/convolution.hpp"
#include <type_traits>
//line 8 "/home/seekworser/.cpp_lib/competitive_library/atcoder/convolution.hpp"

//line 2 "/home/seekworser/.cpp_lib/competitive_library/atcoder/internal_bit.hpp"
#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
constexpr int bsf_constexpr(unsigned int n) {
    int x = 0;
    while (!(n & (1 << x))) x++;
    return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}

}  // namespace internal

}  // namespace atcoder
//line 5 "/home/seekworser/.cpp_lib/competitive_library/atcoder/modint.hpp"

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

//line 3 "/home/seekworser/.cpp_lib/competitive_library/atcoder/internal_math.hpp"

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

namespace atcoder {

namespace internal {

// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
    unsigned int _m;
    unsigned long long im;

    // @param m `1 <= m < 2^31`
    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    // @return m
    unsigned int umod() const { return _m; }

    // @param a `0 <= a < m`
    // @param b `0 <= b < m`
    // @return `a * b % m`
    unsigned int mul(unsigned int a, unsigned int b) const {
        // [1] m = 1
        // a = b = im = 0, so okay

        // [2] m >= 2
        // im = ceil(2^64 / m)
        // -> im * m = 2^64 + r (0 <= r < m)
        // let z = a*b = c*m + d (0 <= c, d < m)
        // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
        // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
        // ((ab * im) >> 64) == c or c + 1
        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;
    }
};

// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
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;
}

// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
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);

// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
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};

    // Contracts:
    // [1] s - m0 * a = 0 (mod b)
    // [2] t - m1 * a = 0 (mod b)
    // [3] s * |m1| + t * |m0| <= b
    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

        // [3]:
        // (s - t * u) * |m1| + t * |m0 - m1 * u|
        // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
        // = s * |m1| + t * |m0| <= b

        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    // by [3]: |m0| <= b/g
    // by g != b: |m0| < b/g
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
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);

// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
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;
        // y_max < m * (n + 1)
        // floor(y_max / m) <= n
        n = (unsigned long long)(y_max / m);
        b = (unsigned long long)(y_max % m);
        std::swap(m, a);
    }
    return ans;
}

}  // namespace internal

}  // namespace atcoder
//line 5 "/home/seekworser/.cpp_lib/competitive_library/atcoder/internal_type_traits.hpp"

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
//line 12 "/home/seekworser/.cpp_lib/competitive_library/atcoder/modint.hpp"

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 mint& rhs) { (*this)._v = rhs.val(); return *this; }

    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 mint& rhs) { (*this)._v = rhs.val(); return *this; }

    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
//line 11 "/home/seekworser/.cpp_lib/competitive_library/atcoder/convolution.hpp"

namespace atcoder {

namespace internal {

template <class mint,
          int g = internal::primitive_root<mint::mod()>,
          internal::is_static_modint_t<mint>* = nullptr>
struct fft_info {
    static constexpr int rank2 = bsf_constexpr(mint::mod() - 1);
    std::array<mint, rank2 + 1> root;   // root[i]^(2^i) == 1
    std::array<mint, rank2 + 1> iroot;  // root[i] * iroot[i] == 1

    std::array<mint, std::max(0, rank2 - 2 + 1)> rate2;
    std::array<mint, std::max(0, rank2 - 2 + 1)> irate2;

    std::array<mint, std::max(0, rank2 - 3 + 1)> rate3;
    std::array<mint, std::max(0, rank2 - 3 + 1)> irate3;

    fft_info() {
        root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
        iroot[rank2] = root[rank2].inv();
        for (int i = rank2 - 1; i >= 0; i--) {
            root[i] = root[i + 1] * root[i + 1];
            iroot[i] = iroot[i + 1] * iroot[i + 1];
        }

        {
            mint prod = 1, iprod = 1;
            for (int i = 0; i <= rank2 - 2; i++) {
                rate2[i] = root[i + 2] * prod;
                irate2[i] = iroot[i + 2] * iprod;
                prod *= iroot[i + 2];
                iprod *= root[i + 2];
            }
        }
        {
            mint prod = 1, iprod = 1;
            for (int i = 0; i <= rank2 - 3; i++) {
                rate3[i] = root[i + 3] * prod;
                irate3[i] = iroot[i + 3] * iprod;
                prod *= iroot[i + 3];
                iprod *= root[i + 3];
            }
        }
    }
};

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
    int n = int(a.size());
    int h = internal::ceil_pow2(n);

    static const fft_info<mint> info;

    int len = 0;  // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
    while (len < h) {
        if (h - len == 1) {
            int p = 1 << (h - len - 1);
            mint rot = 1;
            for (int s = 0; s < (1 << len); s++) {
                int offset = s << (h - len);
                for (int i = 0; i < p; i++) {
                    auto l = a[i + offset];
                    auto r = a[i + offset + p] * rot;
                    a[i + offset] = l + r;
                    a[i + offset + p] = l - r;
                }
                if (s + 1 != (1 << len))
                    rot *= info.rate2[bsf(~(unsigned int)(s))];
            }
            len++;
        } else {
            // 4-base
            int p = 1 << (h - len - 2);
            mint rot = 1, imag = info.root[2];
            for (int s = 0; s < (1 << len); s++) {
                mint rot2 = rot * rot;
                mint rot3 = rot2 * rot;
                int offset = s << (h - len);
                for (int i = 0; i < p; i++) {
                    auto mod2 = 1ULL * mint::mod() * mint::mod();
                    auto a0 = 1ULL * a[i + offset].val();
                    auto a1 = 1ULL * a[i + offset + p].val() * rot.val();
                    auto a2 = 1ULL * a[i + offset + 2 * p].val() * rot2.val();
                    auto a3 = 1ULL * a[i + offset + 3 * p].val() * rot3.val();
                    auto a1na3imag =
                        1ULL * mint(a1 + mod2 - a3).val() * imag.val();
                    auto na2 = mod2 - a2;
                    a[i + offset] = a0 + a2 + a1 + a3;
                    a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
                    a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
                    a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
                }
                if (s + 1 != (1 << len))
                    rot *= info.rate3[bsf(~(unsigned int)(s))];
            }
            len += 2;
        }
    }
}

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
    int n = int(a.size());
    int h = internal::ceil_pow2(n);

    static const fft_info<mint> info;

    int len = h;  // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
    while (len) {
        if (len == 1) {
            int p = 1 << (h - len);
            mint irot = 1;
            for (int s = 0; s < (1 << (len - 1)); s++) {
                int offset = s << (h - len + 1);
                for (int i = 0; i < p; i++) {
                    auto l = a[i + offset];
                    auto r = a[i + offset + p];
                    a[i + offset] = l + r;
                    a[i + offset + p] =
                        (unsigned long long)(mint::mod() + l.val() - r.val()) *
                        irot.val();
                    ;
                }
                if (s + 1 != (1 << (len - 1)))
                    irot *= info.irate2[bsf(~(unsigned int)(s))];
            }
            len--;
        } else {
            // 4-base
            int p = 1 << (h - len);
            mint irot = 1, iimag = info.iroot[2];
            for (int s = 0; s < (1 << (len - 2)); s++) {
                mint irot2 = irot * irot;
                mint irot3 = irot2 * irot;
                int offset = s << (h - len + 2);
                for (int i = 0; i < p; i++) {
                    auto a0 = 1ULL * a[i + offset + 0 * p].val();
                    auto a1 = 1ULL * a[i + offset + 1 * p].val();
                    auto a2 = 1ULL * a[i + offset + 2 * p].val();
                    auto a3 = 1ULL * a[i + offset + 3 * p].val();

                    auto a2na3iimag =
                        1ULL *
                        mint((mint::mod() + a2 - a3) * iimag.val()).val();

                    a[i + offset] = a0 + a1 + a2 + a3;
                    a[i + offset + 1 * p] =
                        (a0 + (mint::mod() - a1) + a2na3iimag) * irot.val();
                    a[i + offset + 2 * p] =
                        (a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) *
                        irot2.val();
                    a[i + offset + 3 * p] =
                        (a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) *
                        irot3.val();
                }
                if (s + 1 != (1 << (len - 2)))
                    irot *= info.irate3[bsf(~(unsigned int)(s))];
            }
            len -= 2;
        }
    }
}

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution_naive(const std::vector<mint>& a,
                                    const std::vector<mint>& b) {
    int n = int(a.size()), m = int(b.size());
    std::vector<mint> ans(n + m - 1);
    if (n < m) {
        for (int j = 0; j < m; j++) {
            for (int i = 0; i < n; i++) {
                ans[i + j] += a[i] * b[j];
            }
        }
    } else {
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                ans[i + j] += a[i] * b[j];
            }
        }
    }
    return ans;
}

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) {
    int n = int(a.size()), m = int(b.size());
    int z = 1 << internal::ceil_pow2(n + m - 1);
    a.resize(z);
    internal::butterfly(a);
    b.resize(z);
    internal::butterfly(b);
    for (int i = 0; i < z; i++) {
        a[i] *= b[i];
    }
    internal::butterfly_inv(a);
    a.resize(n + m - 1);
    mint iz = mint(z).inv();
    for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
    return a;
}

}  // namespace internal

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint>&& a, std::vector<mint>&& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    if (std::min(n, m) <= 60) return convolution_naive(a, b);
    return internal::convolution_fft(a, b);
}

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(const std::vector<mint>& a,
                              const std::vector<mint>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    if (std::min(n, m) <= 60) return convolution_naive(a, b);
    return internal::convolution_fft(a, b);
}

template <unsigned int mod = 998244353,
          class T,
          std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};

    using mint = static_modint<mod>;
    std::vector<mint> a2(n), b2(m);
    for (int i = 0; i < n; i++) {
        a2[i] = mint(a[i]);
    }
    for (int i = 0; i < m; i++) {
        b2[i] = mint(b[i]);
    }
    auto c2 = convolution(move(a2), move(b2));
    std::vector<T> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
        c[i] = c2[i].val();
    }
    return c;
}

std::vector<long long> convolution_ll(const std::vector<long long>& a,
                                      const std::vector<long long>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};

    static constexpr unsigned long long MOD1 = 754974721;  // 2^24
    static constexpr unsigned long long MOD2 = 167772161;  // 2^25
    static constexpr unsigned long long MOD3 = 469762049;  // 2^26
    static constexpr unsigned long long M2M3 = MOD2 * MOD3;
    static constexpr unsigned long long M1M3 = MOD1 * MOD3;
    static constexpr unsigned long long M1M2 = MOD1 * MOD2;
    static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;

    static constexpr unsigned long long i1 =
        internal::inv_gcd(MOD2 * MOD3, MOD1).second;
    static constexpr unsigned long long i2 =
        internal::inv_gcd(MOD1 * MOD3, MOD2).second;
    static constexpr unsigned long long i3 =
        internal::inv_gcd(MOD1 * MOD2, MOD3).second;

    auto c1 = convolution<MOD1>(a, b);
    auto c2 = convolution<MOD2>(a, b);
    auto c3 = convolution<MOD3>(a, b);

    std::vector<long long> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
        unsigned long long x = 0;
        x += (c1[i] * i1) % MOD1 * M2M3;
        x += (c2[i] * i2) % MOD2 * M1M3;
        x += (c3[i] * i3) % MOD3 * M1M2;
        // B = 2^63, -B <= x, r(real value) < B
        // (x, x - M, x - 2M, or x - 3M) = r (mod 2B)
        // r = c1[i] (mod MOD1)
        // focus on MOD1
        // r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)
        // r = x,
        //     x - M' + (0 or 2B),
        //     x - 2M' + (0, 2B or 4B),
        //     x - 3M' + (0, 2B, 4B or 6B) (without mod!)
        // (r - x) = 0, (0)
        //           - M' + (0 or 2B), (1)
        //           -2M' + (0 or 2B or 4B), (2)
        //           -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)
        // we checked that
        //   ((1) mod MOD1) mod 5 = 2
        //   ((2) mod MOD1) mod 5 = 3
        //   ((3) mod MOD1) mod 5 = 4
        long long diff =
            c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
        if (diff < 0) diff += MOD1;
        static constexpr unsigned long long offset[5] = {
            0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
        x -= offset[diff % 5];
        c[i] = x;
    }

    return c;
}

}  // namespace atcoder
//line 3 "/home/seekworser/.cpp_lib/competitive_library/competitive/std/io.hpp"
// overload operators (prototypes)
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p);
template <class T> inline istream& operator>>(istream& is, vector<T>& v);
template <class T, class U> inline ostream& operator<<(ostream& os, const pair<T, U>& p);
template <class T> inline ostream& operator<<(ostream& os, const vector<T>& v);
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp);
template <typename T> ostream &operator<<(ostream &os, const set<T> &st);
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st);
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T> &st);
template <typename T> ostream &operator<<(ostream &os, queue<T> q);
template <typename T> ostream &operator<<(ostream &os, deque<T> q);
template <typename T> ostream &operator<<(ostream &os, stack<T> st);
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq);

// overload operators
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repe(x, v) is >> x; return is; }
template <class T, class U> inline ostream& operator<<(ostream& os, const pair<T, U>& p) { os << p.first << " " << p.second; return os; }
template <class T> inline ostream& operator<<(ostream& os, const vector<T>& v) { rep(i, sz(v)) { os << v.at(i); if (i != sz(v) - 1) os << " "; } return os; }
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp) { for (auto &[key, val] : mp) { os << key << ":" << val << " "; } return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T> &st) { ll cnt = 0; for (auto &e : st) { os << e << (++cnt != (int)st.size() ? " " : ""); } return os; }
template <typename T> ostream &operator<<(ostream &os, queue<T> q) { while (q.size()) { os << q.front() << " "; q.pop(); } return os; }
template <typename T> ostream &operator<<(ostream &os, deque<T> q) { while (q.size()) { os << q.front(); q.pop_front(); if (q.size()) os << " "; } return os; }
template <typename T> ostream &operator<<(ostream &os, stack<T> st) { while (st.size()) { os << st.top() << " "; st.pop(); } return os; }
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq) { while (pq.size()) { os << pq.top() << " "; pq.pop(); } return os; }

template <typename T> int print_sep_end(string sep, string end, const T& val) { (void)sep; cout << val << end; return 0; };
template <typename T1, typename... T2> int print_sep_end(string sep, string end, const T1 &val, const T2 &...remain) {
    cout << val << sep;
    print_sep_end(sep, end, remain...);
    return 0;
};
template <typename... T> int print(const T &...args) { print_sep_end(" ", "\n", args...); return 0; };
template <typename... T> void flush() { cout << flush; };
template <typename... T> int print_and_flush(const T &...args) { print(args...); flush(); return 0; };
#define debug(...) debug_func(0, #__VA_ARGS__, __VA_ARGS__) // debug print
template <typename T> void input(T &a) { cin >> a; };
template <typename T1, typename... T2> void input(T1&a, T2 &...b) { cin >> a; input(b...); };
#ifdef LOCAL_TEST
template <typename T> void debug_func(int i, const T name) { (void)i; (void)name; cerr << endl; }
template <typename T1, typename T2, typename... T3> void debug_func(int i, const T1 &name, const T2 &a, const T3 &...b) {
    int scope = 0;
    for ( ; (scope != 0 || name[i] != ',') && name[i] != '\0'; i++ ) {
        cerr << name[i];
        if (name[i] == '(' || name[i] == '{') scope++;
        if (name[i] == ')' || name[i] == '}') scope--;
    }
    cerr << ":" << a << " ";
    debug_func(i + 1, name, b...);
}
template <typename T1, typename T2, typename... T3> void debug_func(int i, const T1 &name, T2 &a, T3 &...b) {
    int scope = 0;
    for ( ; (scope != 0 || name[i] != ',') && name[i] != '\0'; i++ ) {
        cerr << name[i];
        if (name[i] == '(' || name[i] == '{') scope++;
        if (name[i] == ')' || name[i] == '}') scope--;
    }
    cerr << ":" << a << " ";
    debug_func(i + 1, name, b...);
}
#endif
#ifndef LOCAL_TEST
template <typename... T>
void debug_func(T &...) {}
template <typename... T>
void debug_func(const T &...) {}
#endif
/**
 * @brief io.hpp
 * @docs docs/std/io.md
 */
//line 47 "answer.cpp"
#endif