#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif


template <int md> struct ModInt {
    using lint = long long;
    constexpr static int mod() { return md; }
    static int get_primitive_root() {
        static int primitive_root = 0;
        if (!primitive_root) {
            primitive_root = [&]() {
                std::set<int> fac;
                int v = md - 1;
                for (lint i = 2; i * i <= v; i++)
                    while (v % i == 0) fac.insert(i), v /= i;
                if (v > 1) fac.insert(v);
                for (int g = 1; g < md; g++) {
                    bool ok = true;
                    for (auto i : fac)
                        if (ModInt(g).pow((md - 1) / i) == 1) {
                            ok = false;
                            break;
                        }
                    if (ok) return g;
                }
                return -1;
            }();
        }
        return primitive_root;
    }
    int val_;
    int val() const noexcept { return val_; }
    constexpr ModInt() : val_(0) {}
    constexpr ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; }
    constexpr ModInt(lint v) { _setval(v % md + md); }
    constexpr explicit operator bool() const { return val_ != 0; }
    constexpr ModInt operator+(const ModInt &x) const {
        return ModInt()._setval((lint)val_ + x.val_);
    }
    constexpr ModInt operator-(const ModInt &x) const {
        return ModInt()._setval((lint)val_ - x.val_ + md);
    }
    constexpr ModInt operator*(const ModInt &x) const {
        return ModInt()._setval((lint)val_ * x.val_ % md);
    }
    constexpr ModInt operator/(const ModInt &x) const {
        return ModInt()._setval((lint)val_ * x.inv().val() % md);
    }
    constexpr ModInt operator-() const { return ModInt()._setval(md - val_); }
    constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
    constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
    constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
    constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
    friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt(a) + x; }
    friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt(a) - x; }
    friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt(a) * x; }
    friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt(a) / x; }
    constexpr bool operator==(const ModInt &x) const { return val_ == x.val_; }
    constexpr bool operator!=(const ModInt &x) const { return val_ != x.val_; }
    constexpr bool operator<(const ModInt &x) const {
        return val_ < x.val_;
    } // To use std::map<ModInt, T>
    friend std::istream &operator>>(std::istream &is, ModInt &x) {
        lint t;
        return is >> t, x = ModInt(t), is;
    }
    constexpr friend std::ostream &operator<<(std::ostream &os, const ModInt &x) {
        return os << x.val_;
    }

    constexpr ModInt pow(lint n) const {
        ModInt ans = 1, tmp = *this;
        while (n) {
            if (n & 1) ans *= tmp;
            tmp *= tmp, n >>= 1;
        }
        return ans;
    }

    static constexpr int cache_limit = std::min(md, 1 << 21);
    static std::vector<ModInt> facs, facinvs, invs;

    constexpr static void _precalculation(int N) {
        const int l0 = facs.size();
        if (N > md) N = md;
        if (N <= l0) return;
        facs.resize(N), facinvs.resize(N), invs.resize(N);
        for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;
        facinvs[N - 1] = facs.back().pow(md - 2);
        for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);
        for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];
    }

    constexpr ModInt inv() const {
        if (this->val_ < cache_limit) {
            if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0};
            while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
            return invs[this->val_];
        } else {
            return this->pow(md - 2);
        }
    }
    constexpr ModInt fac() const {
        while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
        return facs[this->val_];
    }
    constexpr ModInt facinv() const {
        while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
        return facinvs[this->val_];
    }
    constexpr ModInt doublefac() const {
        lint k = (this->val_ + 1) / 2;
        return (this->val_ & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac())
                                : ModInt(k).fac() * ModInt(2).pow(k);
    }

    constexpr ModInt nCr(int r) const {
        if (r < 0 or this->val_ < r) return ModInt(0);
        return this->fac() * (*this - r).facinv() * ModInt(r).facinv();
    }

    constexpr ModInt nPr(int r) const {
        if (r < 0 or this->val_ < r) return ModInt(0);
        return this->fac() * (*this - r).facinv();
    }

    static ModInt binom(int n, int r) {
        static long long bruteforce_times = 0;

        if (r < 0 or n < r) return ModInt(0);
        if (n <= bruteforce_times or n < (int)facs.size()) return ModInt(n).nCr(r);

        r = std::min(r, n - r);

        ModInt ret = ModInt(r).facinv();
        for (int i = 0; i < r; ++i) ret *= n - i;
        bruteforce_times += r;

        return ret;
    }

    // Multinomial coefficient, (k_1 + k_2 + ... + k_m)! / (k_1! k_2! ... k_m!)
    // Complexity: O(sum(ks))
    template <class Vec> static ModInt multinomial(const Vec &ks) {
        ModInt ret{1};
        int sum = 0;
        for (int k : ks) {
            assert(k >= 0);
            ret *= ModInt(k).facinv(), sum += k;
        }
        return ret * ModInt(sum).fac();
    }

    // Catalan number, C_n = binom(2n, n) / (n + 1)
    // C_0 = 1, C_1 = 1, C_2 = 2, C_3 = 5, C_4 = 14, ...
    // https://oeis.org/A000108
    // Complexity: O(n)
    static ModInt catalan(int n) {
        if (n < 0) return ModInt(0);
        return ModInt(n * 2).fac() * ModInt(n + 1).facinv() * ModInt(n).facinv();
    }

    ModInt sqrt() const {
        if (val_ == 0) return 0;
        if (md == 2) return val_;
        if (pow((md - 1) / 2) != 1) return 0;
        ModInt b = 1;
        while (b.pow((md - 1) / 2) == 1) b += 1;
        int e = 0, m = md - 1;
        while (m % 2 == 0) m >>= 1, e++;
        ModInt x = pow((m - 1) / 2), y = (*this) * x * x;
        x *= (*this);
        ModInt z = b.pow(m);
        while (y != 1) {
            int j = 0;
            ModInt t = y;
            while (t != 1) j++, t *= t;
            z = z.pow(1LL << (e - j - 1));
            x *= z, z *= z, y *= z;
            e = j;
        }
        return ModInt(std::min(x.val_, md - x.val_));
    }
};
template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};

using mint = ModInt<998244353>;

// Integer convolution for arbitrary mod
// with NTT (and Garner's algorithm) for ModInt / ModIntRuntime class.
// We skip Garner's algorithm if `skip_garner` is true or mod is in `nttprimes`.
// input: a (size: n), b (size: m)
// return: vector (size: n + m - 1)
template <typename MODINT>
std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner);

constexpr int nttprimes[3] = {998244353, 167772161, 469762049};

// Integer FFT (Fast Fourier Transform) for ModInt class
// (Also known as Number Theoretic Transform, NTT)
// is_inverse: inverse transform
// ** Input size must be 2^n **
template <typename MODINT> void ntt(std::vector<MODINT> &a, bool is_inverse = false) {
    int n = a.size();
    if (n == 1) return;
    static const int mod = MODINT::mod();
    static const MODINT root = MODINT::get_primitive_root();
    assert(__builtin_popcount(n) == 1 and (mod - 1) % n == 0);

    static std::vector<MODINT> w{1}, iw{1};
    for (int m = w.size(); m < n / 2; m *= 2) {
        MODINT dw = root.pow((mod - 1) / (4 * m)), dwinv = 1 / dw;
        w.resize(m * 2), iw.resize(m * 2);
        for (int i = 0; i < m; i++) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * dwinv;
    }

    if (!is_inverse) {
        for (int m = n; m >>= 1;) {
            for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
                for (int i = s; i < s + m; i++) {
                    MODINT x = a[i], y = a[i + m] * w[k];
                    a[i] = x + y, a[i + m] = x - y;
                }
            }
        }
    } else {
        for (int m = 1; m < n; m *= 2) {
            for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
                for (int i = s; i < s + m; i++) {
                    MODINT x = a[i], y = a[i + m];
                    a[i] = x + y, a[i + m] = (x - y) * iw[k];
                }
            }
        }
        int n_inv = MODINT(n).inv().val();
        for (auto &v : a) v *= n_inv;
    }
}
template <int MOD>
std::vector<ModInt<MOD>> nttconv_(const std::vector<int> &a, const std::vector<int> &b) {
    int sz = a.size();
    assert(a.size() == b.size() and __builtin_popcount(sz) == 1);
    std::vector<ModInt<MOD>> ap(sz), bp(sz);
    for (int i = 0; i < sz; i++) ap[i] = a[i], bp[i] = b[i];
    ntt(ap, false);
    if (a == b)
        bp = ap;
    else
        ntt(bp, false);
    for (int i = 0; i < sz; i++) ap[i] *= bp[i];
    ntt(ap, true);
    return ap;
}
long long garner_ntt_(int r0, int r1, int r2, int mod) {
    using mint2 = ModInt<nttprimes[2]>;
    static const long long m01 = 1LL * nttprimes[0] * nttprimes[1];
    static const long long m0_inv_m1 = ModInt<nttprimes[1]>(nttprimes[0]).inv().val();
    static const long long m01_inv_m2 = mint2(m01).inv().val();

    int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1];
    auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * m01_inv_m2;
    return (r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val()) % mod;
}
template <typename MODINT>
std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner) {
    if (a.empty() or b.empty()) return {};
    int sz = 1, n = a.size(), m = b.size();
    while (sz < n + m) sz <<= 1;
    if (sz <= 16) {
        std::vector<MODINT> ret(n + m - 1);
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) ret[i + j] += a[i] * b[j];
        }
        return ret;
    }
    int mod = MODINT::mod();
    if (skip_garner or
        std::find(std::begin(nttprimes), std::end(nttprimes), mod) != std::end(nttprimes)) {
        a.resize(sz), b.resize(sz);
        if (a == b) {
            ntt(a, false);
            b = a;
        } else {
            ntt(a, false), ntt(b, false);
        }
        for (int i = 0; i < sz; i++) a[i] *= b[i];
        ntt(a, true);
        a.resize(n + m - 1);
    } else {
        std::vector<int> ai(sz), bi(sz);
        for (int i = 0; i < n; i++) ai[i] = a[i].val();
        for (int i = 0; i < m; i++) bi[i] = b[i].val();
        auto ntt0 = nttconv_<nttprimes[0]>(ai, bi);
        auto ntt1 = nttconv_<nttprimes[1]>(ai, bi);
        auto ntt2 = nttconv_<nttprimes[2]>(ai, bi);
        a.resize(n + m - 1);
        for (int i = 0; i < n + m - 1; i++)
            a[i] = garner_ntt_(ntt0[i].val(), ntt1[i].val(), ntt2[i].val(), mod);
    }
    return a;
}

template <typename MODINT>
std::vector<MODINT> nttconv(const std::vector<MODINT> &a, const std::vector<MODINT> &b) {
    return nttconv<MODINT>(a, b, false);
}


// Formal Power Series (形式的冪級数) based on ModInt<mod> / ModIntRuntime
// Reference: https://ei1333.github.io/luzhiled/snippets/math/formal-power-series.html
template <typename T> struct FormalPowerSeries : std::vector<T> {
    using std::vector<T>::vector;
    using P = FormalPowerSeries;

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

    P operator+(const P &r) const { return P(*this) += r; }
    P operator+(const T &v) const { return P(*this) += v; }
    P operator-(const P &r) const { return P(*this) -= r; }
    P operator-(const T &v) const { return P(*this) -= v; }
    P operator*(const P &r) const { return P(*this) *= r; }
    P operator*(const T &v) const { return P(*this) *= v; }
    P operator/(const P &r) const { return P(*this) /= r; }
    P operator/(const T &v) const { return P(*this) /= v; }
    P operator%(const P &r) const { return P(*this) %= r; }

    P &operator+=(const P &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;
    }
    P &operator+=(const T &v) {
        if (this->empty()) this->resize(1);
        (*this)[0] += v;
        return *this;
    }
    P &operator-=(const P &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;
    }
    P &operator-=(const T &v) {
        if (this->empty()) this->resize(1);
        (*this)[0] -= v;
        return *this;
    }
    P &operator*=(const T &v) {
        for (auto &x : (*this)) x *= v;
        return *this;
    }
    P &operator*=(const P &r) {
        if (this->empty() || r.empty())
            this->clear();
        else {
            auto ret = nttconv(*this, r);
            *this = P(ret.begin(), ret.end());
        }
        return *this;
    }
    P &operator%=(const P &r) {
        *this -= *this / r * r;
        return *this;
    }
    P operator-() const {
        P ret = *this;
        for (auto &v : ret) v = -v;
        return ret;
    }
    P &operator/=(const T &v) {
        assert(v != T(0));
        for (auto &x : (*this)) x /= v;
        return *this;
    }
    P &operator/=(const P &r) {
        if (this->size() < r.size()) {
            this->clear();
            return *this;
        }
        int n = (int)this->size() - r.size() + 1;
        return *this = (reversed().pre(n) * r.reversed().inv(n)).pre(n).reversed(n);
    }
    P pre(int sz) const {
        P ret(this->begin(), this->begin() + std::min((int)this->size(), sz));
        return ret;
    }
    P operator>>(int sz) const {
        if ((int)this->size() <= sz) return {};
        return P(this->begin() + sz, this->end());
    }
    P operator<<(int sz) const {
        if (this->empty()) return {};
        P ret(*this);
        ret.insert(ret.begin(), sz, T(0));
        return ret;
    }

    P reversed(int sz = -1) const {
        assert(sz >= -1);
        P ret(*this);
        if (sz != -1) ret.resize(sz, T());
        std::reverse(ret.begin(), ret.end());
        return ret;
    }

    P differential() const { // formal derivative (differential) of f.p.s.
        const int n = (int)this->size();
        P ret(std::max(0, n - 1));
        for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);
        return ret;
    }

    P integral() const {
        const int n = (int)this->size();
        P ret(n + 1);
        ret[0] = T(0);
        for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1);
        return ret;
    }

    /**
     * @brief f(x)g(x) = 1 (mod x^deg)
     *
     * @param deg
     * @return P ret.size() == deg
     */
    P inv(int deg) const {
        assert(deg >= -1);
        if (deg == 0) return {};

        assert(this->size() and this->at(0) != T()); // Requirement: F(0) != 0
        const int n = this->size();
        if (deg == -1) deg = n;

        P ret({T(1) / this->at(0)});
        for (int i = 1; i < deg; i <<= 1) {
            auto h = (pre(i << 1) * ret).pre(i << 1) >> i;
            auto tmp = (-h * ret).pre(i);
            ret.insert(ret.end(), tmp.cbegin(), tmp.cend());
            ret.resize(i << 1);
        }
        return ret.pre(deg);
    }

    P log(int len = -1) const {
        assert(len >= -1);
        if (len == 0) return {};

        assert(this->size() and ((*this)[0]) == T(1)); // Requirement: F(0) = 1

        const int n = (int)this->size();
        if (len == 0) return {};
        if (len == -1) len = n;
        return (this->differential() * this->inv(len)).pre(len - 1).integral();
    }

    P sqrt(int deg = -1) const {
        assert(deg >= -1);
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        if (this->empty()) return {};
        if ((*this)[0] == T(0)) {
            for (int i = 1; i < n; i++)
                if ((*this)[i] != T(0)) {
                    if ((i & 1) or deg - i / 2 <= 0) return {};
                    return (*this >> i).sqrt(deg - i / 2) << (i / 2);
                }
            return {};
        }
        T sqrtf0 = (*this)[0].sqrt();
        if (sqrtf0 == T(0)) return {};

        P y = (*this) / (*this)[0], ret({T(1)});
        T inv2 = T(1) / T(2);
        for (int i = 1; i < deg; i <<= 1) ret = (ret + y.pre(i << 1) * ret.inv(i << 1)) * inv2;
        return ret.pre(deg) * sqrtf0;
    }

    P exp(int deg = -1) const {
        assert(deg >= -1);
        assert(this->empty() or ((*this)[0]) == T(0)); // Requirement: F(0) = 0
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        P ret({T(1)});
        for (int i = 1; i < deg; i <<= 1) {
            ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1);
        }
        return ret.pre(deg);
    }

    P pow(long long k, int deg = -1) const {
        assert(deg >= -1);
        const int n = (int)this->size();
        if (deg == -1) deg = n;

        if (k == 0) {
            P ret(deg);
            if (deg >= 1) ret[0] = T(1);
            ret.shrink();
            return ret;
        }

        for (int i = 0; i < n; i++) {
            if ((*this)[i] != T(0)) {
                T rev = T(1) / (*this)[i];
                P C = (*this) * rev, D(n - i);
                for (int j = i; j < n; j++) D[j - i] = C.coeff(j);
                D = (D.log(deg) * T(k)).exp(deg) * (*this)[i].pow(k);
                if (__int128(k) * i > deg) return {};
                P E(deg);
                long long S = i * k;
                for (int j = 0; j + S < deg and j < (int)D.size(); j++) E[j + S] = D[j];
                E.shrink();
                return E;
            }
        }
        return *this;
    }

    // Calculate f(X + c) from f(X), O(NlogN)
    P shift(T c) const {
        const int n = (int)this->size();
        P ret = *this;
        for (int i = 0; i < n; i++) ret[i] *= T(i).fac();
        std::reverse(ret.begin(), ret.end());
        P exp_cx(n, 1);
        for (int i = 1; i < n; i++) exp_cx[i] = exp_cx[i - 1] * c * T(i).inv();
        ret = ret * exp_cx;
        ret.resize(n);
        std::reverse(ret.begin(), ret.end());
        for (int i = 0; i < n; i++) ret[i] *= T(i).facinv();
        return ret;
    }

    T coeff(int i) const {
        if ((int)this->size() <= i or i < 0) return T(0);
        return (*this)[i];
    }

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

vector<mint> bernoulli_number_test(int N) {
    FormalPowerSeries<mint> x({0, 1});
    FormalPowerSeries<mint> b = ((x.exp(N + 3) - 1) >> 1).inv(N + 1);
    vector<mint> ret;
    for (int i = 0; i <= N; i++) ret.push_back(b.coeff(i) * mint(i).fac());

    if (N > 2) ret.at(1) = mint(2).inv();
    return ret;
}

#include <cassert>
#include <fstream>
#include <vector>

// 結合法則が成立する要素の列について連続部分列の積を前計算を利用し高速に求める
template <class S, S (*op)(S, S), S (*e)(), S (*getter)(long long), int Bucket> struct product_embedding {
    std::vector<S> pre_; // pre_[i] = S[i * Bucket] * ... * S[(i + 1) * Bucket - 1]

    product_embedding(std::vector<S> pre) : pre_(pre) {}

    S prod(long long l, long long r) { // S[l] * ... * S[r - 1]
        assert(0 <= l);
        assert(l <= r);
        assert(r <= (long long)Bucket * (long long)pre_.size());

        if (r - l <= Bucket) {
            S ret = e();
            while (l < r) ret = op(ret, getter(l++));
            return ret;
        }

        long long lb = (l + Bucket - 1) / Bucket, rb = r / Bucket;
        S ret = e();
        for (long long i = l; i < lb * Bucket; ++i) ret = op(ret, getter(i));
        for (int i = lb; i < rb; ++i) ret = op(ret, pre_[i]);
        for (long long i = rb * Bucket; i < r; ++i) ret = op(ret, getter(i));
        return ret;
    }

    static void prerun(std::string filename, long long upper_lim) {
        std::ofstream ofs(filename);

        long long cur = 0;
        long long num_bucket = (upper_lim + Bucket - 1) / Bucket;

        ofs << "({";
        while (num_bucket--) {
            S p = e();
            for (int t = 0; t < Bucket; ++t) { p = op(p, getter(cur++)); }
            ofs << p;
            if (num_bucket) ofs << ",";
        }
        ofs << "});";
    }
};
using S = int;
constexpr S md = 998244353;
S op(S l, S r) { return (long long)l * r % md; }
S e() { return 1; }
S getter(long long i) { return i + 1 >= md ? (i + 1) % md : i + 1; }
using PE = product_embedding<S, op, e, getter, 500000>;

int main() {
    PE pe({832944090,704684917,615706648,847294252,88352218,907186201,691150420,913840185,615963223,855364605,119871024,260484657,859947701,746803828,757605891,90252390,303168424,458692733,447902118,519044747,337902171,527262360,806954223,278433728,371945574,802657446,33796109,479029221,13074962,263679799,637034850,968665616,191551499,17396452,627009992,772903324,570222470,206900285,819076745,27672112,241549436,692501166,560987504,452030081,798290073,486395423,289596666,373492135,488937237,104582136,702664424,722130811,867669096,953433936,525925834,547831392,810191792,259515457,646462939,87520491,45130800,872439232,854509412,546905493,416913780,370009844,215906029,270663392,633518868,353660403,9557444,137174105,113142527,530062995,558370997,969283332,686746504,389907830,185278447,2425097,216737352,899793077,357571905,270870373,314893045,911840177,444906080,381832665,401470410,692839732,98864994,541679223,616224683,267140709,104124053,511029824,635050637,706453173,285939194,200357740,510478137,185885637,397669445,443607993,554478339,46750669,139176254,538999618,459494109,733260799,617176936,512018697,746780475,667740900,537479303,86146177,662071180,518101865,134794267,754404967,955634140,820294170,889803075,352952586,848590919,563568811,795071441,695639765,262777923,924356134,335545297,709511822,241813913,923488656,693947185,996767921,229966252,669350019,990409291,615776680,665912266,234328009,79764676,457436288,761000715,581509788,882807186,500352747,445576519,424358603,329380611,766526824,392121440,484087487,945403082,661078349,361486608,418779645,2047908,790121293,717319608,181370889,246321649,264130035,593914025,501011429,888792043,726043686,543471483,558121411,25320611,380791470,864178613,322869975,75052465,671375132,934470063,681356552,731820230,540562934,246250337,898548852,501435722,645211462,984306599,603512249,10173564,103142919,483320083,77477420,504125401,871282714,893685842,442026845,172237327,462737473,305280106,236641044,130159734,127411991,450000803,748338626,662543565,468110724,132498639,291021318,545257818,551546108,701726537,313606148,297564719,382416160,67102615,279512928,78638017,448448905,756688280,593997502,312588959,290832776,129707390,624650235,557355897,238261927,121925590,362083384,234875527,425833339,480539233,106030094,172218364,952925093,635704320,635763376,943293808,664757555,535325704,160913233,342146476,610171684,349280028,532241258,647283895,785956119,487557452,875742751,329524131,939160764,470188386,727473676,865816474,153612065,285604631,606994152,96707086,146082330,131276205,694526979,795908785,574669965,68297241,310263879,981026205,682536036,382231137,475872984,295877903,451223167,876264010,708776818,696873077,23468719,6656113,772393476,648660683,452073171,702772465,655566941,660259716,845914532,171812887,170722369,429075375,638795268,129509320,470723034,681826522,61667818,426797734,717004532,416360058,225664875,290024229,918559157,188631059,422932338,759185298,513413011,796306384,267387829,520944657,522529672,489563204,732763088,169165050,917393532,645351691,829660260,34801306,400284161,79943282,940469822,870134687,32915287,179372351,117987380,534980592,472079946,120654283,369256017,12840367,220843777,987347928,531915924,454678057,473647442,908234924,93612215,354346483,244447478,902987399,374480738,391608870,16717414,383590348,562466602,287498834,548484934,223919319,105791239,733705025,653133119,920458406,926100928,541250239,917374201,476441488,876170735,210115868,257550453,88859392,208330688,28766939,559304604,617055733,384236027,920029552,297649547,582781732,162607781,925103418,10535319,494631007,113663680,982682735,28164542,847728321,667610886,341090839,935561939,179913956,177548070,765619720,268917887,747391931,808473081,414391352,396867630,268971031,577589482,844186883,899701547,926976231,742075664,382014807,123049443,78097534,240479098,960060331,597901213,358197202,944743545,794008581,796488938,122198933,532051694,855497454,212107682,550619009,655108052,980800940,322905946,641588402,571533601,240943570,902228965,394730555,880954325,30654933,831081844,365432633,129673244,943766468,243363382,892539880,481048296,299162179,692900032,323398505,996843507,597243714,458077362,191032769,405281429,969138036,931305831,572728483,402096153,376617212,165408216,868339148,748866282,592619490,669915230,613204348,472216681,23106973,308027574,128618720,887545879,377040748,406795107,60356254,374078096,560583986,13507308,37108919,390026819,103131865,893733906,425718096,503242327,546689046,896034414,322730412,830016747,233676778,755669800,333658230,900914110,557355351,659554106,824580104,610352358,842181708,697570971,457633454,859557456,436699936,228365152,487929223,318447092,36520112,676609456,869218838,945078316,358762590,115086076,487078887,105140302,414903418,369303270,723079185,781996045,35010079,332207777,980330188,346113692,875293652,394264892,452282275,683269960,646642323,765688763,496251030,162639942,768347695,76245924,379013965,431439069,740925481,127244598,72274088,159283742,715440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    int N, K;
    cin >> N >> K;
    dbg(make_tuple(N, K));

    const auto ber = bernoulli_number_test(K + 2);

    auto sum = [&](int p, int n) {
        mint ret = 0;
        REP(r, p + 1) {
            ret += mint(p + 1).nCr(r)  * ber.at(r) * mint(n).pow(p - r + 1);
        }
        return ret / mint(p + 1);
    };

    mint ret = sum(K, N) * N - sum(K + 1, N);

    lint fac = 0;
    if (N - 1 <= 998244352) fac = pe.prod(0, N - 1);

    cout << ret * 2 * fac << '\n';
}