// https://github.com/yosupo06/library-checker-problems/blob/4fcedb6dcaf1b768b2de93324d6bfa395a5b05e6/enumerative_combinatorics/factorial/sol/correct.cpp
#include <cstdio>
#include <vector>
#include <cassert>
#include <array>

using namespace std;

using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using u128 = unsigned __int128;

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))

#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }

template <typename mint>
mint inv(int n) {
  static const int mod = mint::get_mod();
  static vector<mint> dat = {0, 1};
  assert(0 <= n);
  if (n >= mod) n %= mod;
  while (len(dat) <= n) {
    int k = len(dat);
    int q = (mod + k - 1) / k;
    dat.eb(dat[k * q - mod] * mint::raw(q));
  }
  return dat[n];
}

template <typename mint>
mint fact(int n) {
  static const int mod = mint::get_mod();
  assert(0 <= n && n < mod);
  static vector<mint> dat = {1, 1};
  while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * mint::raw(len(dat)));
  return dat[n];
}

template <typename mint>
mint fact_inv(int n) {
  static vector<mint> dat = {1, 1};
  if (n < 0) return mint(0);
  while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * inv<mint>(len(dat)));
  return dat[n];
}

template <class mint, class... Ts>
mint fact_invs(Ts... xs) {
  return (mint(1) * ... * fact_inv<mint>(xs));
}

template <int mod>
struct modint {
  static constexpr u32 umod = u32(mod);
  static_assert(umod < u32(1) << 31);
  u32 val;

  static modint raw(u32 v) {
    modint x;
    x.val = v;
    return x;
  }
  constexpr modint() : val(0) {}
  constexpr modint(u32 x) : val(x % umod) {}
  constexpr modint(u64 x) : val(x % umod) {}
  constexpr modint(int x) : val((x %= mod) < 0 ? x + mod : x){};
  constexpr modint(ll x) : val((x %= mod) < 0 ? x + mod : x){};
  bool operator<(const modint &other) const { return val < other.val; }
  modint &operator+=(const modint &p) {
    if ((val += p.val) >= umod) val -= umod;
    return *this;
  }
  modint &operator-=(const modint &p) {
    if ((val += umod - p.val) >= umod) val -= umod;
    return *this;
  }
  modint &operator*=(const modint &p) {
    val = u64(val) * p.val % umod;
    return *this;
  }
  modint &operator/=(const modint &p) {
    *this *= p.inverse();
    return *this;
  }
  modint operator-() const { return modint::raw(val ? mod - val : u32(0)); }
  modint operator+(const modint &p) const { return modint(*this) += p; }
  modint operator-(const modint &p) const { return modint(*this) -= p; }
  modint operator*(const modint &p) const { return modint(*this) *= p; }
  modint operator/(const modint &p) const { return modint(*this) /= p; }
  bool operator==(const modint &p) const { return val == p.val; }
  bool operator!=(const modint &p) const { return val != p.val; }
  modint inverse() const {
    int a = val, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b), swap(u -= t * v, v);
    }
    return modint(u);
  }
  modint pow(ll n) const {
    assert(n >= 0);
    modint ret(1), mul(val);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  static constexpr int get_mod() { return mod; }
  // (n, r), r は 1 の 2^n 乗根
  static constexpr pair<int, int> ntt_info() {
    if (mod == 167772161) return {25, 17};
    if (mod == 469762049) return {26, 30};
    if (mod == 754974721) return {24, 362};
    if (mod == 880803841) return {23, 211};
    if (mod == 943718401) return {22, 663003469};
    if (mod == 998244353) return {23, 31};
    if (mod == 1045430273) return {20, 363};
    if (mod == 1051721729) return {20, 330};
    if (mod == 1053818881) return {20, 2789};
    return {-1, -1};
  }
  static constexpr bool can_ntt() { return ntt_info().fi != -1; }
};

using modint998 = modint<998244353>;

template <class T>
vc<vc<T>> matrix_mul(const vc<vc<T>> &A, const vc<vc<T>> &B, int N1 = -1,
                     int N2 = -1, int N3 = -1) {
  if (N1 == -1) { N1 = len(A), N2 = len(B), N3 = len(B[0]); }
  vv(u32, b, N3, N2);
  FOR(i, N2) FOR(j, N3) b[j][i] = B[i][j].val;
  vv(T, C, N1, N3);

  if ((T::get_mod() < (1 << 30)) && N2 <= 16) {
    FOR(i, N1) FOR(j, N3) {
      u64 sm = 0;
      FOR(m, N2) sm += u64(A[i][m].val) * b[j][m];
      C[i][j] = sm;
    }
  } else {
    FOR(i, N1) FOR(j, N3) {
      u128 sm = 0;
      FOR(m, N2) sm += u64(A[i][m].val) * b[j][m];
      C[i][j] = T::raw(sm % (T::get_mod()));
    }
  }
  return C;
}

template <class T>
struct Monoid_Mul {
  using value_type = T;
  using X = T;
  static constexpr X op(const X &x, const X &y) noexcept { return x * y; }
  static constexpr X inverse(const X &x) noexcept { return X(1) / x; }
  static constexpr X unit() { return X(1); }
  static constexpr bool commute = true;
};

template <class Monoid>
struct Sliding_Window_Aggregation {
  using X = typename Monoid::value_type;
  using value_type = X;
  int sz = 0;
  vc<X> dat;
  vc<X> cum_l;
  X cum_r;

  Sliding_Window_Aggregation()
      : cum_l({Monoid::unit()}), cum_r(Monoid::unit()) {}

  int size() { return sz; }

  void push(X x) {
    ++sz;
    cum_r = Monoid::op(cum_r, x);
    dat.eb(x);
  }

  void pop() {
    --sz;
    cum_l.pop_back();
    if (len(cum_l) == 0) {
      cum_l = {Monoid::unit()};
      cum_r = Monoid::unit();
      while (len(dat) > 1) {
        cum_l.eb(Monoid::op(dat.back(), cum_l.back()));
        dat.pop_back();
      }
      dat.pop_back();
    }
  }

  X lprod() { return cum_l.back(); }
  X rprod() { return cum_r; }

  X prod() { return Monoid::op(cum_l.back(), cum_r); }
};

// long でも大丈夫
// (val * x - 1) が mod の倍数になるようにする
// 特に mod=0 なら x=0 が満たす
ll mod_inv(ll val, ll mod) {
  assert(mod >= 0);
  if (mod == 0) return 0;
  val %= mod;
  if (val < 0) val += mod;
  ll a = val, b = mod, u = 1, v = 0, t;
  while (b > 0) {
    t = a / b;
    swap(a -= t * b, b), swap(u -= t * v, v);
  }
  if (u < 0) u += mod;
  return u;
}

constexpr u32 mod_pow_constexpr(u64 a, u64 n, u32 mod) {
  a %= mod;
  u64 res = 1;
  FOR(32) {
    if (n & 1) res = res * a % mod;
    a = a * a % mod, n /= 2;
  }
  return res;
}

template <typename T, u32 p0, u32 p1, u32 p2>
T CRT3(u64 a0, u64 a1, u64 a2) {
  static_assert(p0 < p1 && p1 < p2);
  static constexpr u64 x0_1 = mod_pow_constexpr(p0, p1 - 2, p1);
  static constexpr u64 x01_2 = mod_pow_constexpr(u64(p0) * p1 % p2, p2 - 2, p2);
  u64 c = (a1 - a0 + p1) * x0_1 % p1;
  u64 a = a0 + c * p0;
  c = (a2 - a % p2 + p2) * x01_2 % p2;
  return T(a) + T(c) * T(p0) * T(p1);
}

template <class T>
vc<T> convolution_naive(const vc<T> &a, const vc<T> &b) {
  int n = int(a.size()), m = int(b.size());
  if (n > m) return convolution_naive<T>(b, a);
  if (n == 0) return {};
  vc<T> ans(n + m - 1);
  if (n <= 16 && (T::get_mod() < (1 << 30))) {
    for (int k = 0; k < n + m - 1; ++k) {
      int s = max(0, k - m + 1);
      int t = min(n, k + 1);
      u64 sm = 0;
      for (int i = s; i < t; ++i) { sm += u64(a[i].val) * (b[k - i].val); }
      ans[k] = sm;
    }
  } else {
    for (int k = 0; k < n + m - 1; ++k) {
      int s = max(0, k - m + 1);
      int t = min(n, k + 1);
      u128 sm = 0;
      for (int i = s; i < t; ++i) { sm += u64(a[i].val) * (b[k - i].val); }
      ans[k] = T::raw(sm % T::get_mod());
    }
  }
  return ans;
}

template <typename T>
vc<T> convolution_karatsuba(const vc<T> &f, const vc<T> &g) {
  const int thresh = 30;
  if (min(len(f), len(g)) <= thresh) return convolution_naive(f, g);
  int n = max(len(f), len(g));
  int m = (n + 1) / 2;
  vc<T> f1, f2, g1, g2;
  if (len(f) < m) f1 = f;
  if (len(f) >= m) f1 = {f.begin(), f.begin() + m};
  if (len(f) >= m) f2 = {f.begin() + m, f.end()};
  if (len(g) < m) g1 = g;
  if (len(g) >= m) g1 = {g.begin(), g.begin() + m};
  if (len(g) >= m) g2 = {g.begin() + m, g.end()};
  vc<T> a = convolution_karatsuba(f1, g1);
  vc<T> b = convolution_karatsuba(f2, g2);
  FOR(i, len(f2)) f1[i] += f2[i];
  FOR(i, len(g2)) g1[i] += g2[i];
  vc<T> c = convolution_karatsuba(f1, g1);
  vc<T> F(len(f) + len(g) - 1);
  assert(2 * m + len(b) <= len(F));
  FOR(i, len(a)) F[i] += a[i], c[i] -= a[i];
  FOR(i, len(b)) F[2 * m + i] += b[i], c[i] -= b[i];
  if (c.back() == T(0)) c.pop_back();
  FOR(i, len(c)) if (c[i] != T(0)) F[m + i] += c[i];
  return F;
}

template <class mint>
void ntt(vector<mint> &a, bool inverse) {
  assert(mint::can_ntt());
  const int rank2 = mint::ntt_info().fi;
  const int mod = mint::get_mod();
  static array<mint, 30> root, iroot;
  static array<mint, 30> rate2, irate2;
  static array<mint, 30> rate3, irate3;

  static bool prepared = 0;
  if (!prepared) {
    prepared = 1;
    root[rank2] = mint::ntt_info().se;
    iroot[rank2] = mint(1) / root[rank2];
    FOR_R(i, rank2) {
      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];
    }
    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];
    }
  }

  int n = int(a.size());
  int h = topbit(n);
  assert(n == 1 << h);
  if (!inverse) {
    int len = 0;
    while (len < h) {
      if (h - len == 1) {
        int p = 1 << (h - len - 1);
        mint rot = 1;
        FOR(s, 1 << len) {
          int offset = s << (h - len);
          FOR(i, p) {
            auto l = a[i + offset];
            auto r = a[i + offset + p] * rot;
            a[i + offset] = l + r;
            a[i + offset + p] = l - r;
          }
          rot *= rate2[topbit(~s & -~s)];
        }
        len++;
      } else {
        int p = 1 << (h - len - 2);
        mint rot = 1, imag = 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++) {
            u64 mod2 = u64(mod) * mod;
            u64 a0 = a[i + offset].val;
            u64 a1 = u64(a[i + offset + p].val) * rot.val;
            u64 a2 = u64(a[i + offset + 2 * p].val) * rot2.val;
            u64 a3 = u64(a[i + offset + 3 * p].val) * rot3.val;
            u64 a1na3imag = (a1 + mod2 - a3) % mod * imag.val;
            u64 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);
          }
          rot *= rate3[topbit(~s & -~s)];
        }
        len += 2;
      }
    }
  } else {
    mint coef = mint(1) / mint(len(a));
    FOR(i, len(a)) a[i] *= coef;
    int len = h;
    while (len) {
      if (len == 1) {
        int p = 1 << (h - len);
        mint irot = 1;
        FOR(s, 1 << (len - 1)) {
          int offset = s << (h - len + 1);
          FOR(i, p) {
            u64 l = a[i + offset].val;
            u64 r = a[i + offset + p].val;
            a[i + offset] = l + r;
            a[i + offset + p] = (mod + l - r) * irot.val;
          }
          irot *= irate2[topbit(~s & -~s)];
        }
        len--;
      } else {
        int p = 1 << (h - len);
        mint irot = 1, iimag = iroot[2];
        FOR(s, (1 << (len - 2))) {
          mint irot2 = irot * irot;
          mint irot3 = irot2 * irot;
          int offset = s << (h - len + 2);
          for (int i = 0; i < p; i++) {
            u64 a0 = a[i + offset + 0 * p].val;
            u64 a1 = a[i + offset + 1 * p].val;
            u64 a2 = a[i + offset + 2 * p].val;
            u64 a3 = a[i + offset + 3 * p].val;
            u64 x = (mod + a2 - a3) * iimag.val % mod;
            a[i + offset] = a0 + a1 + a2 + a3;
            a[i + offset + 1 * p] = (a0 + mod - a1 + x) * irot.val;
            a[i + offset + 2 * p] = (a0 + a1 + 2 * mod - a2 - a3) * irot2.val;
            a[i + offset + 3 * p] = (a0 + 2 * mod - a1 - x) * irot3.val;
          }
          irot *= irate3[topbit(~s & -~s)];
        }
        len -= 2;
      }
    }
  }
}

template <class mint>
vector<mint> convolution_ntt(vector<mint> a, vector<mint> b) {
  if (a.empty() || b.empty()) return {};
  int n = int(a.size()), m = int(b.size());
  int sz = 1;
  while (sz < n + m - 1) sz *= 2;

  // sz = 2^k のときの高速化。分割統治的なやつで損しまくるので。
  if ((n + m - 3) <= sz / 2) {
    auto a_last = a.back(), b_last = b.back();
    a.pop_back(), b.pop_back();
    auto c = convolution(a, b);
    c.resize(n + m - 1);
    c[n + m - 2] = a_last * b_last;
    FOR(i, len(a)) c[i + len(b)] += a[i] * b_last;
    FOR(i, len(b)) c[i + len(a)] += b[i] * a_last;
    return c;
  }

  a.resize(sz), b.resize(sz);
  bool same = a == b;
  ntt(a, 0);
  if (same) {
    b = a;
  } else {
    ntt(b, 0);
  }
  FOR(i, sz) a[i] *= b[i];
  ntt(a, 1);
  a.resize(n + m - 1);
  return a;
}

template <typename mint>
vc<mint> convolution(const vc<mint> &a, const vc<mint> &b) {
  int n = len(a), m = len(b);
  if (!n || !m) return {};
  if (min(n, m) <= 50) return convolution_karatsuba<mint>(a, b);
  return convolution_ntt(a, b);
}

// Input: f(0), ..., f(n-1) and c. Return: f(c)
template <typename T>
T lagrange_interpolate_iota(vc<T> &f, T c) {
  int n = len(f);
  if (int(c.val) < n) return f[c.val];
  auto a = f;
  FOR(i, n) {
    a[i] = a[i] * fact_inv<T>(i) * fact_inv<T>(n - 1 - i);
    if ((n - 1 - i) & 1) a[i] = -a[i];
  }
  vc<T> lp(n + 1), rp(n + 1);
  lp[0] = rp[n] = 1;
  FOR(i, n) lp[i + 1] = lp[i] * (c - i);
  FOR_R(i, n) rp[i] = rp[i + 1] * (c - i);
  T ANS = 0;
  FOR(i, n) ANS += a[i] * lp[i] * rp[i + 1];
  return ANS;
}

// Input: f(0), ..., f(n-1) and c, m
// Return: f(c), f(c+1), ..., f(c+m-1)
// Complexity: M(n, n + m)
template <typename mint>
vc<mint> lagrange_interpolate_iota(vc<mint> &f, mint c, int m) {
  if (m <= 60) {
    vc<mint> ANS(m);
    FOR(i, m) ANS[i] = lagrange_interpolate_iota(f, c + mint(i));
    return ANS;
  }
  ll n = len(f);
  auto a = f;
  FOR(i, n) {
    a[i] = a[i] * fact_inv<mint>(i) * fact_inv<mint>(n - 1 - i);
    if ((n - 1 - i) & 1) a[i] = -a[i];
  }
  // x = c, c+1, ... に対して a0/x + a1/(x-1) + ... を求めておく
  vc<mint> b(n + m - 1);
  FOR(i, n + m - 1) b[i] = mint(1) / (c + mint(i - n + 1));
  a = convolution(a, b);

  Sliding_Window_Aggregation<Monoid_Mul<mint>> swag;
  vc<mint> ANS(m);
  ll L = 0, R = 0;
  FOR(i, m) {
    while (L < i) { swag.pop(), ++L; }
    while (R - L < n) { swag.push(c + mint((R++) - n + 1)); }
    auto coef = swag.prod();
    if (coef == 0) {
      ANS[i] = f[(c + i).val];
    } else {
      ANS[i] = a[i + n - 1] * coef;
    }
  }
  return ANS;
}

template <typename T>
vc<vc<T>> prefix_product_of_poly_matrix(vc<vc<vc<T>>> &A, ll k) {
  int n = len(A);

  using MAT = vc<vc<T>>;
  auto shift = [&](vc<MAT> &G, T x) -> vc<MAT> {
    int d = len(G);
    vvv(T, H, d, n, n);
    FOR(i, n) FOR(j, n) {
      vc<T> g(d);
      FOR(l, d) g[l] = G[l][i][j];
      auto h = lagrange_interpolate_iota(g, x, d);
      FOR(l, d) H[l][i][j] = h[l];
    }
    return H;
  };

  auto evaluate = [&](vc<T> &f, T x) -> T {
    T res = 0;
    T p = 1;
    FOR(i, len(f)) {
      res += f[i] * p;
      p *= x;
    }
    return res;
  };

  ll deg = 1;
  FOR(i, n) FOR(j, n) deg = max(deg, len(A[i][j]) - 1);

  vc<MAT> G(deg + 1);
  ll v = 1;
  while (deg * v * v < k) v *= 2;
  T iv = T(1) / T(v);

  FOR(i, len(G)) {
    T x = T(v) * T(i);
    vv(T, mat, n, n);
    FOR(j, n) FOR(k, n) mat[j][k] = evaluate(A[j][k], x);
    G[i] = mat;
  }

  for (ll w = 1; w != v; w *= 2) {
    T W = w;
    auto G1 = shift(G, W * iv);
    auto G2 = shift(G, (W * T(deg) * T(v) + T(v)) * iv);
    auto G3 = shift(G, (W * T(deg) * T(v) + T(v) + W) * iv);
    FOR(i, w * deg + 1) {
      G[i] = matrix_mul(G1[i], G[i]);
      G2[i] = matrix_mul(G3[i], G2[i]);
    }
    copy(G2.begin(), G2.end() - 1, back_inserter(G));
  }

  vv(T, res, n, n);
  FOR(i, n) res[i][i] = 1;
  ll i = 0;
  while (i + v <= k) res = matrix_mul(G[i / v], res), i += v;
  while (i < k) {
    vv(T, mat, n, n);
    FOR(j, n) FOR(k, n) mat[j][k] = evaluate(A[j][k], i);
    res = matrix_mul(mat, res);
    ++i;
  }
  return res;
}

template <typename T>
T prefix_product_of_poly(vc<T> &f, ll k) {
  vc<vc<vc<T>>> A(1);
  A[0].resize(1);
  A[0][0] = f;
  auto res = prefix_product_of_poly_matrix(A, k);
  return res[0][0];
}

using mint = modint998;

mint fact(const int n) {
  vc<mint> f = {1, 1};
  return prefix_product_of_poly(f, n);
}

// https://ferin-tech.hatenablog.com/entry/2018/01/17/010829
#define __USE_MINGW_ANSI_STDIO 0
#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
#define int ll
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef pair<int, int> PII;

#define IN(a, b, x) (a<=x&&x<b)
#define PB push_back

const ll LLINF = (1LL<<60);
const int INF = (1LL<<30);
const int MOD = 1000000007;

template <typename T> T &chmin(T &a, const T &b) { return a = min(a, b); }
template <typename T> T &chmax(T &a, const T &b) { return a = max(a, b); }
template<class S,class T>
ostream &operator <<(ostream& out,const pair<S,T>& a){
  out<<'('<<a.first<<','<<a.second<<')';
  return out;
}

int dx[] = {0, 1, 0, -1}, dy[] = {1, 0, -1, 0};

// ax + by = gcd(a, b) となる {x, y, gcd(a, b)} を返す
// O(log(min(a, b)))
ll extgcd(ll a, ll b, ll &x, ll &y) {
  ll g = a; x = 1, y = 0;
  if(b != 0) g = extgcd(b, a%b, y, x), y -= (a/b) * x;
  return g;
}

// a^-1 mod n を返す　存在しなければ-1
// O(log(n))
ll inv(ll a, ll n) {
  ll s, t;
  extgcd(a, n, s, t);
  return (n+s) % n;
}

// 二分累乗法 x^e % mod O(log(e))
ll binpow(ll x, ll e, ll mod) {
  ll a = 1, p = x;
  while(e > 0) {
    if(e%2 == 0) {p = (p*p) % mod; e /= 2;}
    else {a = (a*p) % mod; e--;}
  }
  return a % mod;
}

// x = a1 mod m1, x2 = a2 mod m2 を解く オーバーフローには注意
// O(log(min(m1, m2)))
pair<ll, ll> crt(ll a1, ll a2, ll m1, ll m2) {
  auto normal = [](ll x, ll m) { return x>=-x ? x%m : m-(-x)%m; };
  auto modmul = [&normal](ll a, ll b, ll m) { return normal(a, m)*normal(b, m)%m; };
  ll k1, k2;
  ll g = extgcd(m1, m2, k1, k2);
  if(normal(a1, g) != normal(a2, g)) return {-1, -1};
  ll l = m1 / g * m2;
  ll x = a1 + modmul(modmul((a2-a1)/g, k1, l), m1, l);
  return {x, l};
}

pair<ll, ll> crt(vector<ll> a, vector<ll> m) {
  ll mod = 1, ans = 0;
  int n = a.size();
  for (int i = 0; i < n; ++i) {
    tie(ans, mod) = crt(ans, a[i], mod, m[i]);
    if(ans == -1) return {-1, -1};
  }
  return {ans, mod};
}

ll C(ll n, ll r, ll p, ll q) {
  if(n < 0 || r < 0 || r > n) return 0;
  // pr = p^q
  int pr = 1;
  for (int i = 0; i < q; ++i) pr *= p;

  ll z = n-r;
  int e0 = 0;
  for(ll u=n/p;u;u/=p) e0 += u;
  for(ll u=r/p;u;u/=p) e0 -= u;
  for(ll u=z/p;u;u/=p) e0 -= u;
  int em = 0;
  for(ll u=n/pr;u;u/=p) em += u;
  for(ll u=r/pr;u;u/=p) em -= u;
  for(ll u=z/pr;u;u/=p) em -= u;

  ll ret = 1;
  while(n > 0) {
    const mint tmp = fact(n%pr) / fact(r%pr) / fact(z%pr);
    ret = ret * ll{tmp.val} % pr;
    n /= p; r /= p; z /= p;
  }
  (ret *= binpow(p, e0, pr)) %= pr;
  if(!(p==2 && q >= 3) && em%2) ret = (pr-ret) % pr;
  return ret;
}

ll func(ll n, ll r, ll mod) {
  ll x = mod;
  vector<ll> a, m;
  a.PB(C(n, r, mod, 1));
  m.PB(mod);

  return crt(a, m).first;
}


signed main() {
  int n, m; cin >> n >> m;
  cout << func(n, m, 998244353) << '\n';
  return 0;
}