#line 1 "test.cpp"
//#pragma GCC target("avx2")
//#pragma GCC optimize("O3")
//#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#include <debug.hpp>
#define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#define debug(...) (static_cast<void>(0))
#endif
using ll = long long;
using ld = long double;
using pll = pair<ll,ll>;
using pii = pair<int,int>;
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 vpii = vector<pii>;
using vpll = vector<pll>;
using vs = vector<string>;
template<class T> using pq = priority_queue<T,vector<T>,greater<T>>;
#define overload4(_1, _2, _3, _4, name, ...) name
#define overload3(a,b,c,name,...) name
#define rep1(n) for (ll UNUSED_NUMBER = 0; UNUSED_NUMBER < (n); ++UNUSED_NUMBER)
#define rep2(i, n) for (ll i = 0; i < (n); ++i)
#define rep3(i, a, b) for (ll i = (a); i < (b); ++i)
#define rep4(i, a, b, c) for (ll i = (a); i < (b); i += (c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(n) for(ll i = (n) - 1;i >= 0;i--)
#define rrep2(i,n) for(ll i = (n) - 1;i >= 0;i--)
#define rrep3(i,a,b) for(ll i = (b) - 1;i >= (a);i--)
#define rrep4(i,a,b,c) for(ll i = (a) + ((b)-(a)-1) / (c) * (c);i >= (a);i -= c)
#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define all1(i) begin(i),end(i)
#define all2(i,a) begin(i),begin(i)+a
#define all3(i,a,b) begin(i)+a,begin(i)+b
#define all(...) overload3(__VA_ARGS__, all3, all2, all1)(__VA_ARGS__)
#define sum(...) accumulate(all(__VA_ARGS__),0LL)
template<class T> bool chmin(T &a, const T &b){ if(a > b){ a = b; return 1; } else return 0; }
template<class T> bool chmax(T &a, const T &b){ if(a < b){ a = b; return 1; } else return 0; }
template<class T> auto min(const T& a){ return *min_element(all(a)); }
template<class T> auto max(const T& a){ return *max_element(all(a)); }
template<class... Ts> void in(Ts&... t);
#define INT(...) int __VA_ARGS__; in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__; in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__; in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__; in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__; in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__; in(__VA_ARGS__)
#define VEC(type, name, size) vector<type> name(size); in(name)
#define VV(type, name, h, w) vector<vector<type>> name(h, vector<type>(w)); in(name)
ll intpow(ll a, ll b){ ll ans = 1; while(b){if(b & 1) ans *= a; a *= a; b /= 2;} return ans;}
ll modpow(ll a, ll b, ll p){ ll ans = 1; a %= p;while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; }
ll GCD(ll a,ll b) { if(a == 0 || b == 0) return a + b; if(a % b == 0) return b; else return GCD(b,a%b);}
ll LCM(ll a,ll b) { if(a == 0) return b; if(b == 0) return a;return a / GCD(a,b) * b;}
namespace IO{
#define VOID(a) decltype(void(a))
struct setting{ setting(){cin.tie(nullptr); ios::sync_with_stdio(false);fixed(cout); cout.precision(12);}} setting;
template<int I> struct P : P<I-1>{};
template<> struct P<0>{};
template<class T> void i(T& t){ i(t, P<3>{}); }
void i(vector<bool>::reference t, P<3>){ int a; i(a); t = a; }
template<class T> auto i(T& t, P<2>) -> VOID(cin >> t){ cin >> t; }
template<class T> auto i(T& t, P<1>) -> VOID(begin(t)){ for(auto&& x : t) i(x); }
template<class T, size_t... idx> void ituple(T& t, index_sequence<idx...>){
    in(get<idx>(t)...);}
template<class T> auto i(T& t, P<0>) -> VOID(tuple_size<T>{}){
    ituple(t, make_index_sequence<tuple_size<T>::value>{});}
#undef VOID
}
#define unpack(a) (void)initializer_list<int>{(a, 0)...}
template<class... Ts> void in(Ts&... t){ unpack(IO :: i(t)); }
#undef unpack
//constexpr int mod = 1000000007;
constexpr int mod = 998244353;
static const double PI = 3.1415926535897932;
template <class F> struct REC {
    F f;
    REC(F &&f_) : f(forward<F>(f_)) {}
    template <class... Args> auto operator()(Args &&...args) const { return f(*this, forward<Args>(args)...); }};
#line 2 "library/modint/LazyMontgomeryModint.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(r * mod == 1);
    static_assert(mod < (1 << 30));
    static_assert((mod & 1) == 1);
    u32 a;
    constexpr LazyMontgomeryModInt() : a(0) {}
    constexpr LazyMontgomeryModInt(const int64_t &b)
      : a(reduce(u64(b % mod + mod) * n2)){};

    static constexpr u32 reduce(const u64 &b) {
        return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
    }
    constexpr mint &operator+=(const mint &b) {
        if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
        return *this;
    }
    constexpr mint &operator-=(const mint &b) {
        if (i32(a -= b.a) < 0) a += 2 * mod;
        return *this;
    }
    constexpr mint &operator*=(const mint &b) {
        a = reduce(u64(a) * b.a);
        return *this;
    }
    constexpr mint &operator/=(const mint &b) {
        *this *= b.inverse();
        return *this;
    }
    constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
    constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
    constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
    constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
    constexpr bool operator==(const mint &b) const {
        return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
    }
    constexpr bool operator!=(const mint &b) const {
        return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
    }
    constexpr mint operator-() const { return mint() - mint(*this); }
    constexpr mint pow(u64 n) const {
        mint ret(1), mul(*this);
        while (n > 0) {
        if (n & 1) ret *= mul;
        mul *= mul;
        n >>= 1;
        }
        return ret;
    }
    constexpr mint inverse() const { return pow(mod - 2); }
    friend ostream &operator<<(ostream &os, const mint &b) {
        return os << b.get();
    }
    friend istream &operator>>(istream &is, mint &b) {
        int64_t t;
        is >> t;
        b = LazyMontgomeryModInt<mod>(t);
        return (is);
    }
    constexpr u32 get() const {
        u32 ret = reduce(a);
        return ret >= mod ? ret - mod : ret;
    }
    static constexpr u32 get_mod() { return mod; }
};
#line 86 "test.cpp"
using mint = LazyMontgomeryModInt<mod>;
using vm = vector<mint>;
using vvm = vector<vm>;
using vvvm = vector<vvm>;
#line 2 "library/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) {
            {
                int j0 = 0,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;
                }
            }
            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) {
            {
                int j0 = 0,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 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;
                }
            }
            mint ww = one,xx = one * dy[2],yy = one;
            u <<= 2;
            for(int jh = 4;jh < u;) {
                ww = xx * xx,yy = xx * imag;
                int j0 = jh * v;
                int je = j0 + v;
                int j2 = je + v;
                for(;j0 < je;++j0,++j2) {
                    mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];
                    mint t0p1 = t0 + t1, t2p3 = t2 + t3;
                    mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
                    a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;
                    a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;       
                }
                xx *= dy[__builtin_ctzll(jh += 4)];
            }
            u >>= 4;
            v <<= 2;
        }
        if(k & 1) {
            u = 1 << (k - 1);
            for(int j = 0;j < u;++j) {
                mint ajv = a[j] - a[j+u];
                a[j] += a[j+u];
                a[j+u] = ajv;
            }
        }
    }
    void ntt(vector<mint> &a) {
        if((int)a.size() <= 1) return;
        fft4(a,__builtin_ctz(a.size()));
    }
    void intt(vector<mint> &a) {
        if((int)a.size() <= 1) return;
        ifft4(a,__builtin_ctz(a.size()));
        mint iv = mint(a.size()).inverse();
        for(auto &x:a) x *= iv;
    }
    vector<mint> multiply(const vector<mint> &a,const vector<mint> &b) {
        int l = a.size() + b.size() - 1;
        if(min<int>(a.size(),b.size()) <= 40) {
            vector<mint> s(l);
            for(int i = 0;i < (int)a.size();++i) for(int j = 0;j < (int)b.size();++j) s[i+j] += a[i] * b[j];
            return s;
        }
        int k = 2, M = 4;
        while(M < l) M <<= 1, ++k;
        //setwy(k);
        vector<mint> s(M), t(M);
        for(int i = 0;i < (int)a.size();++i) s[i] = a[i];
        for(int i = 0;i < (int)b.size();++i) t[i] = b[i];
        fft4(s,k);
        fft4(t,k);
        for(int i = 0;i < M;++i) s[i] *= t[i];
        ifft4(s,k);
        s.resize(l);
        mint invm = mint(M).inverse();
        for(int i = 0;i < l;++i) s[i] *= invm;
        return s;
    }
    void ntt_doubling(vector<mint> &a) {
        int M = (int)a.size();
        auto b = a;
        intt(b);
        mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));
        for(int i = 0;i < M;++i) b[i] *= r,r *= zeta;
        ntt(b);
        copy(begin(b),end(b),back_inserter(a));
    }
};
#line 91 "test.cpp"
#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;
  }

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

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

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

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

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

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

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

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

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

/**
 * @brief 多項式/形式的冪級数ライブラリ
 * @docs docs/fps/formal-power-series.md
 */
#line 2 "modulo/binomial.hpp"

template <typename T>
struct Binomial {
  vector<T> f, g, h;
  Binomial(int MAX = 0) {
    assert(T::get_mod() != 0 && "Binomial<mint>()");
    f.resize(1, T{1});
    g.resize(1, T{1});
    h.resize(1, T{1});
    while (MAX >= (int)f.size()) extend();
  }

  void extend() {
    int n = f.size();
    int m = n * 2;
    f.resize(m);
    g.resize(m);
    h.resize(m);
    for (int i = n; i < m; i++) f[i] = f[i - 1] * T(i);
    g[m - 1] = f[m - 1].inverse();
    h[m - 1] = g[m - 1] * f[m - 2];
    for (int i = m - 2; i >= n; i--) {
      g[i] = g[i + 1] * T(i + 1);
      h[i] = g[i] * f[i - 1];
    }
  }

  T fac(int i) {
    if (i < 0) return T(0);
    while (i >= (int)f.size()) extend();
    return f[i];
  }

  T finv(int i) {
    if (i < 0) return T(0);
    while (i >= (int)g.size()) extend();
    return g[i];
  }

  T inv(int i) {
    if (i < 0) return -inv(-i);
    while (i >= (int)h.size()) extend();
    return h[i];
  }

  T C(int n, int r) {
    if (n < 0 || n < r || r < 0) return T(0);
    return fac(n) * finv(n - r) * finv(r);
  }

  inline T operator()(int n, int r) { return C(n, r); }

  template <typename I>
  T multinomial(const vector<I>& r) {
    static_assert(is_integral<I>::value == true);
    int n = 0;
    for (auto& x : r) {
      if (x < 0) return T(0);
      n += x;
    }
    T res = fac(n);
    for (auto& x : r) res *= finv(x);
    return res;
  }

  template <typename I>
  T operator()(const vector<I>& r) {
    return multinomial(r);
  }

  T C_naive(int n, int r) {
    if (n < 0 || n < r || r < 0) return T(0);
    T ret = T(1);
    r = min(r, n - r);
    for (int i = 1; i <= r; ++i) ret *= inv(i) * (n--);
    return ret;
  }

  T P(int n, int r) {
    if (n < 0 || n < r || r < 0) return T(0);
    return fac(n) * finv(n - r);
  }

  T H(int n, int r) {
    if (n < 0 || r < 0) return T(0);
    return r == 0 ? 1 : C(n + r - 1, r);
  }
};
#line 4 "fps/taylor-shift.hpp"

// calculate F(x + a)
template <typename mint>
FormalPowerSeries<mint> TaylorShift(FormalPowerSeries<mint> f, mint a,
                                    Binomial<mint>& C) {
  using fps = FormalPowerSeries<mint>;
  int N = f.size();
  for (int i = 0; i < N; i++) f[i] *= C.fac(i);
  reverse(begin(f), end(f));
  fps g(N, mint(1));
  for (int i = 1; i < N; i++) g[i] = g[i - 1] * a * C.inv(i);
  f = (f * g).pre(N);
  reverse(begin(f), end(f));
  for (int i = 0; i < N; i++) f[i] *= C.finv(i);
  return f;
}
template<typename mint>
void FormalPowerSeries<mint>::set_fft() {
    if(!ntt_ptr) ntt_ptr = new NTT<mint>;
}
template<typename mint>
FormalPowerSeries<mint> &FormalPowerSeries<mint>::operator*=(const FormalPowerSeries<mint> &r){
    if(this->empty() || r.empty()) {
        this->clear();
        return *this;
    } 
    set_fft();
    auto ret = static_cast<NTT<mint>*>(ntt_ptr)->multiply(*this,r);
    return *this = FormalPowerSeries<mint>(ret.begin(),ret.end());
}
template<typename mint>
void FormalPowerSeries<mint>::ntt() {
    set_fft();
    static_cast<NTT<mint>*>(ntt_ptr)->ntt(*this);
}
template<typename mint>
void FormalPowerSeries<mint>::intt() {
    set_fft();
    static_cast<NTT<mint>*>(ntt_ptr)->intt(*this);
}
template<typename mint>
void FormalPowerSeries<mint>::ntt_doubling() {
    set_fft();
    static_cast<NTT<mint>*>(ntt_ptr)->ntt_doubling(*this);
}
template<typename mint>
int FormalPowerSeries<mint>::ntt_pr() {
    set_fft();
    return static_cast<NTT<mint>*>(ntt_pr)->pr;
}
template<typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::inv(int deg) const {
    assert((*this)[0] != mint(0));
    if(deg == -1) deg = (int)this->size();
    FormalPowerSeries<mint> res(deg);
    res[0] = {mint(1)/(*this)[0]};
    for(int d = 1;d < deg;d <<= 1) {
        FormalPowerSeries<mint> f(2*d),g(2*d); 
        for(int j = 0;j < min((int)this->size(),2*d);j++) f[j] = (*this)[j];
        for(int j = 0;j < d;j++) g[j] = res[j];
        f.ntt();
        g.ntt();
        for(int j = 0;j < 2 * d;j++) f[j] *= g[j];
        f.intt();
        for(int j = 0;j < d;j++) f[j] = 0;
        f.ntt();
        for(int j = 0;j < 2 * d;j++) f[j] *= g[j];
        f.intt();
        for(int j = d;j < min(2 * d,deg);j++) res[j] = -f[j];
    }
    return res.pre(deg);
}
template<typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::exp(int deg) const {
    using fps = FormalPowerSeries<mint>;
    assert((*this).size() == 0 || (*this)[0] == mint(0));
    if(deg == -1) deg = this->size();
    fps inv;
    inv.reserve(deg + 1);
    inv.push_back(mint(0));
    inv.push_back(mint(1));
    auto inplace_integral = [&](fps &F) -> void {
        const int n = (int)F.size();
        auto MOD = mint::get_mod();
        while((int)inv.size() <= n) {
            int i = inv.size();
            inv.push_back((-inv[MOD%i]) * (MOD/i));
        }
        F.insert(begin(F),mint(0));
        for(int i = 1;i <= n;i++) F[i] *= inv[i];
    };
    auto inplace_diff = [](fps &F) -> void {
        if(F.empty()) return;
        F.erase(begin(F));
        mint coeff = 1,one = 1;
        for(int i = 0;i < (int)F.size();i++) {
            F[i] *= coeff;
            coeff += one;
        }
    };
    fps b{1,1 < (int)this->size() ? (*this)[1]:0},c{1},z1,z2{1,1};
    for(int m = 2;m < deg;m *= 2) {
        auto y = b;
        y.resize(2*m);
        y.ntt();
        z1 = z2;
        fps z(m);
        for(int i = 0;i < m;++i) z[i] = y[i] * z1[i];
        z.intt();
        fill(begin(z),begin(z)+m/2,mint(0));
        z.ntt();
        for(int i = 0;i < m;++i) z[i] *= -z1[i];
        z.intt();
        c.insert(end(c),begin(z)+m/2,end(z));
        z2 = c;
        z2.resize(2*m);
        z2.ntt();
        fps x(begin(*this),begin(*this)+min<int>(this->size(),m));
        x.resize(m);
        inplace_diff(x);
        x.push_back(mint(0));
        x.ntt();
        for(int i = 0;i < m;++i) x[i] *= y[i];
        x.intt();
        x -= b.diff();
        x.resize(2*m);
        for(int i = 0;i < m - 1;++i) x[m+i] = x[i],x[i] = mint(0);
        x.ntt();
        for(int i = 0;i < 2 * m;++i) x[i] *= z2[i];
        x.intt();
        x.pop_back();
        inplace_integral(x);
        for(int i = m;i < min<int>(this->size(),2*m);++i) x[i] += (*this)[i];
        fill(begin(x),begin(x)+m,mint(0));
        x.ntt();
        for(int i = 0;i < 2 * m;++i) x[i] *= y[i];
        x.intt();
        b.insert(end(b),begin(x)+m,end(x));
    }
    return fps{begin(b),begin(b)+deg};
}
/**
 * @brief 平行移動
 * @docs docs/fps/fps-taylor-shift.md
 */
#line 5 "fps/fps-famous-series.hpp"

template <typename mint>
FormalPowerSeries<mint> Stirling1st(int N, Binomial<mint> &C) {
  using fps = FormalPowerSeries<mint>;
  if (N <= 0) return fps{1};
  int lg = 31 - __builtin_clz(N);
  fps f = {0, 1};
  for (int i = lg - 1; i >= 0; i--) {
    int n = N >> i;
    f *= TaylorShift(f, mint(n >> 1), C);
    if (n & 1) f = (f << 1) + f * (n - 1);
  }
  return f;
}

template <typename mint>
FormalPowerSeries<mint> Stirling2nd(int N, Binomial<mint> &C) {
  using fps = FormalPowerSeries<mint>;
  fps f(N + 1), g(N + 1);
  for (int i = 0; i <= N; i++) {
    f[i] = mint(i).pow(N) * C.finv(i);
    g[i] = (i & 1) ? -C.finv(i) : C.finv(i);
  }
  return (f * g).pre(N + 1);
}

template <typename mint>
FormalPowerSeries<mint> BernoulliEGF(int N, Binomial<mint> &C) {
  using fps = FormalPowerSeries<mint>;
  fps f(N + 1);
  for (int i = 0; i <= N; i++) f[i] = C.finv(i + 1);
  return f.inv(N + 1);
}

template <typename mint>
FormalPowerSeries<mint> Partition(int N, Binomial<mint> &C) {
  using fps = FormalPowerSeries<mint>;
  fps f(N + 1);
  f[0] = 1;
  for (int k = 1; k <= N; k++) {
    long long k1 = 1LL * k * (3 * k + 1) / 2;
    long long k2 = 1LL * k * (3 * k - 1) / 2;
    if (k2 > N) break;
    if (k1 <= N) f[k1] += ((k & 1) ? -1 : 1);
    if (k2 <= N) f[k2] += ((k & 1) ? -1 : 1);
  }
  return f.inv();
}

template <typename mint>
vector<mint> Montmort(int N) {
  if (N <= 1) return {0};
  if (N == 2) return {0, 1};
  vector<mint> f(N);
  f[0] = 0, f[1] = 1;
  mint coeff = 2, one = 1;
  for (int i = 2; i < N; i++) {
    f[i] = (f[i - 1] + f[i - 2]) * coeff;
    coeff += one;
  }
  return f;
};

/**
 * @brief 有名な数列
 */
Binomial<mint> C;
int main() {
    INT(n);
    mint ans;
    auto s1 = Stirling1st<mint>(n,C);
    rep(i,1,n+1) ans += s1[i] * i * i * i;
    cout << ans << '\n';
}