#line 2 "library/template/template.hpp"
#include <bits/stdc++.h>
using namespace std;

#line 2 "library/template/macro.hpp"
#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b) - 1; i >= (a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())
#define YN(b) cout << ((b) ? "YES" : "NO") << "\n";
#define Yn(b) cout << ((b) ? "Yes" : "No") << "\n";
#define yn(b) cout << ((b) ? "yes" : "no") << "\n";
#line 6 "library/template/template.hpp"

#line 2 "library/template/util.hpp"
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <class T>
using priority_queue_asc = priority_queue<T, vector<T>, greater<T>>;

template <class T, class S = T>
S SUM(const vector<T>& a) {
  return accumulate(ALL(a), S(0));
}
template <class T1, class T2>
inline bool chmin(T1& a, T2 b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2>
inline bool chmax(T1& a, T2 b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2>
inline bool chmin_opt(optional<T1>& a, T2 b) {
  if (!a || a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T1, class T2>
inline bool chmax_opt(optional<T1>& a, T2 b) {
  if (!a || a < b) {
    a = b;
    return true;
  }
  return false;
}

template <class T>
int popcnt(T x) {
  return __builtin_popcountll(x);
}
template <class T>
int topbit(T x) {
  return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <class T>
int lowbit(T x) {
  return (x == 0 ? -1 : __builtin_ctzll(x));
}
#line 8 "library/template/template.hpp"

#line 2 "library/template/inout.hpp"
struct Fast {
  Fast() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(15);
  }
} fast;

ostream& operator<<(ostream& os, __uint128_t x) {
  char buf[40];
  size_t k = 0;
  while (x > 0) buf[k++] = (char)(x % 10 + '0'), x /= 10;
  if (k == 0) buf[k++] = '0';
  while (k) os << buf[--k];
  return os;
}
ostream& operator<<(ostream& os, __int128_t x) {
  return x < 0 ? (os << '-' << (__uint128_t)(-x)) : (os << (__uint128_t)x);
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a);
template <class T1, class T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
  return is >> p.first >> p.second;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
  return os << p.first << " " << p.second;
}
template <class T>
istream& operator>>(istream& is, vector<T>& a) {
  for (auto& v : a) is >> v;
  return is;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& a) {
  for (auto it = a.begin(); it != a.end();) {
    os << *it;
    if (++it != a.end()) os << " ";
  }
  return os;
}
template <class T, size_t N>
ostream& operator<<(ostream& os, const array<T, N>& a) {
  for (auto it = a.begin(); it != a.end();) {
    os << *it;
    if (++it != a.end()) os << " ";
  }
  return os;
}
template <class T>
ostream& operator<<(ostream& os, const set<T>& st) {
  os << "{";
  for (auto it = st.begin(); it != st.end();) {
    os << *it;
    if (++it != st.end()) os << ",";
  }
  os << "}";
  return os;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2>& mp) {
  os << "{";
  for (auto it = mp.begin(); it != mp.end();) {
    os << it->first << ":" << it->second;
    if (++it != mp.end()) os << ",";
  }
  os << "}";
  return os;
}

void in() {}
template <typename T, class... U>
void in(T& t, U&... u) {
  cin >> t;
  in(u...);
}
template <class... T>
void in_zip(int n, T&... t) {
  assert(n >= 0 && ((size(t) >= static_cast<size_t>(n)) && ...));
  for (int i = 0; i < n; i++) in(t[i]...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T& t, const U&... u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}
template <class T, class U>
void out_opt(const optional<T>& opt, const U& fallback, ostream& os = cout) {
  if (opt.has_value())
    os << opt.value();
  else
    os << fallback;
  os << "\n";
}
template <class T, class U>
void out_opt(const vector<optional<T>>& vec, const U& fallback, ostream& os = cout) {
  for (auto it = vec.begin(); it != vec.end();) {
    if ((*it).has_value())
      os << (*it).value();
    else
      os << fallback;
    if (++it != vec.end()) os << " ";
  }
  os << "\n";
}

namespace IO {
template <class T, class... U>
T read(U&&... u) {
  T t = T(forward<U>(u)...);
  in(t);
  return t;
}
namespace Graph {
vector<vector<int>> unweighted(int n, int m, bool directed = false, int offset = 1) {
  vector<vector<int>> g(n);
  for (int i = 0; i < m; i++) {
    int u, v;
    cin >> u >> v;
    u -= offset, v -= offset;
    g[u].push_back(v);
    if (!directed) g[v].push_back(u);
  }
  return g;
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, int m, bool directed = false, int offset = 1) {
  vector<vector<pair<int, T>>> g(n);
  for (int i = 0; i < m; i++) {
    int u, v;
    T w;
    cin >> u >> v >> w;
    u -= offset, v -= offset;
    g[u].push_back({v, w});
    if (!directed) g[v].push_back({u, w});
  }
  return g;
}
}  // namespace Graph
namespace Tree {
vector<vector<int>> unweighted(int n, bool directed = false, int offset = 1) {
  return Graph::unweighted(n, n - 1, directed, offset);
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, bool directed = false, int offset = 1) {
  return Graph::weighted<T>(n, n - 1, directed, offset);
}
vector<vector<int>> rooted(int n, bool to_root = true, bool to_leaf = true, int offset = 1) {
  vector<vector<int>> g(n);
  for (int i = 1; i < n; i++) {
    int p;
    cin >> p;
    p -= offset;
    if (to_root) g[i].push_back(p);
    if (to_leaf) g[p].push_back(i);
  }
  return g;
}
}  // namespace Tree
}  // namespace IO
#line 10 "library/template/template.hpp"

#line 2 "library/template/debug.hpp"
#ifdef LOCAL
#define debug 1
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define debug 0
#define show(...) true
#endif
template <class T>
void _show(int, T) {
  cerr << '\n';
}
template <class T1, class T2, class... T3>
void _show(int i, const T1& a, const T2& b, const T3&... c) {
  for (; a[i] != ',' && a[i] != '\0'; i++) cerr << a[i];
  cerr << ":" << b << " ";
  _show(i + 1, a, c...);
}
#line 2 "main.cpp"

#line 2 "library/math/util.hpp"

namespace Math {
template <class T>
T safe_mod(T a, T b) {
  assert(b != 0);
  if (b < 0) a = -a, b = -b;
  a %= b;
  return a >= 0 ? a : a + b;
}
template <class T>
T floor(T a, T b) {
  assert(b != 0);
  if (b < 0) a = -a, b = -b;
  return a >= 0 ? a / b : (a + 1) / b - 1;
}
template <class T>
T ceil(T a, T b) {
  assert(b != 0);
  if (b < 0) a = -a, b = -b;
  return a > 0 ? (a - 1) / b + 1 : a / b;
}
long long isqrt(long long n) {
  if (n <= 0) return 0;
  long long x = sqrt(n);
  while ((__int128)(x + 1) * (x + 1) <= n) x++;
  while ((__int128)x * x > n) x--;
  return x;
}
long long floor_root(long long n, int k) {
  assert(n >= 0);
  if (n == 0) return 0;
  assert(k >= 1);
  if (k == 1) return n;
  if (k > 64) return 1;
  long long x = round(pow((long double)n, 1.0L / k));
  auto check = [&](long long a) {
    if (a <= 0) return true;
    __int128_t p = 1;
    for (int i = 0; i < k; ++i)
      if ((p *= a) > n) return false;
    return true;
  };
  while (check(x + 1)) x++;
  while (!check(x)) x--;
  return x;
}
unsigned long long floor_root_unsigned(unsigned long long n, int k) {
  assert(k >= 1);
  if (n <= 1 || k == 1) return n;
  if (k >= 64) return 1;
  int bits = (64 + k - 1) / k;
  unsigned long long ok = 1, ng = min(n, 1ULL << bits);
  auto check = [&](unsigned long long a) {
    __uint128_t p = 1;
    for (int i = 0; i < k; i++) {
      p *= a;
      if (p > n) return false;
    }
    return true;
  };
  while (ok + 1 < ng) {
    unsigned long long mid = ok + (ng - ok) / 2;
    (check(mid) ? ok : ng) = mid;
  }
  return ok;
}
// return g=gcd(a,b)
// a*x+b*y=g
// - b!=0 -> 0<=x<|b|/g
// - b=0  -> ax=g
template <class T>
T ext_gcd(T a, T b, T& x, T& y) {
  T a0 = a, b0 = b;
  bool sgn_a = a < 0, sgn_b = b < 0;
  if (sgn_a) a = -a;
  if (sgn_b) b = -b;
  if (b == 0) {
    x = sgn_a ? -1 : 1;
    y = 0;
    return a;
  }
  T x00 = 1, x01 = 0, x10 = 0, x11 = 1;
  while (b != 0) {
    T q = a / b, r = a - b * q;
    x00 -= q * x01;
    x10 -= q * x11;
    swap(x00, x01);
    swap(x10, x11);
    a = b, b = r;
  }
  x = x00, y = x10;
  if (sgn_a) x = -x;
  if (sgn_b) y = -y;
  if (b0 != 0) {
    a0 /= a, b0 /= a;
    if (b0 < 0) a0 = -a0, b0 = -b0;
    T q = x >= 0 ? x / b0 : (x + 1) / b0 - 1;
    x -= b0 * q;
    y += a0 * q;
  }
  return a;
}
constexpr long long inv_mod(long long x, long long m) {
  x %= m;
  if (x < 0) x += m;
  long long a = m, b = x;
  long long y0 = 0, y1 = 1;
  while (b > 0) {
    long long q = a / b;
    swap(a -= q * b, b);
    swap(y0 -= q * y1, y1);
  }
  if (y0 < 0) y0 += m / a;
  return y0;
}
long long pow_mod(long long x, long long n, long long m) {
  if (m == 1) return 0;
  x = (x % m + m) % m;
  long long y = 1;
  while (n) {
    if (n & 1) y = y * x % m;
    x = x * x % m;
    n >>= 1;
  }
  return y;
}
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 = x % m;
  if (y >= m) y += m;
  while (n) {
    if (n & 1) r = (r * y) % _m;
    y = (y * y) % _m;
    n >>= 1;
  }
  return r;
}
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);
};  // namespace Math
#line 3 "library/modint/modint.hpp"

template <unsigned int m = 998244353>
struct ModInt {
  using mint = ModInt;
  static constexpr unsigned int get_mod() { return m; }
  static mint raw(int v) {
    mint x;
    x._v = v;
    return x;
  }
  ModInt() : _v(0) {}
  ModInt(int64_t v) {
    long long x = (long long)(v % (long long)(umod()));
    if (x < 0) x += umod();
    _v = (unsigned int)(x);
  }
  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 *= rhs.inv(); }
  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 (is_prime) {
      assert(_v);
      return pow(umod() - 2);
    } else {
      auto inv = Math::inv_mod(_v, umod());
      return raw(inv);
    }
  }
  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; }
  friend istream& operator>>(istream& is, mint& x) {
    int64_t v;
    is >> v;
    x = mint(v);
    return is;
  }
  friend ostream& operator<<(ostream& os, const mint& x) { return os << x.val(); }

 private:
  unsigned int _v;
  static constexpr unsigned int umod() { return m; }
  static constexpr bool is_prime = Math::is_prime<m>;
};
using ModInt998244353 = ModInt<998244353>;
using ModInt1000000007 = ModInt<1000000007>;
#line 4 "main.cpp"
using mint = ModInt998244353;
#line 2 "library/fps/fps-ntt-friendly.hpp"

#line 2 "library/fft/ntt.hpp"

template <class mint>
struct NTT {
  static constexpr unsigned int mod = mint::get_mod();
  static constexpr unsigned long long pow_constexpr(unsigned long long x, unsigned long long n, unsigned long long m) {
    unsigned long long y = 1;
    while (n) {
      if (n & 1) y = y * x % m;
      x = x * x % m;
      n >>= 1;
    }
    return y;
  }
  static constexpr unsigned int get_g() {
    unsigned long long x = 2;
    while (pow_constexpr(x, (mod - 1) >> 1, mod) == 1) x += 1;
    return x;
  }
  static constexpr unsigned int g = get_g();
  static constexpr int rank2 = __builtin_ctzll(mod - 1);
  array<mint, rank2 + 1> root;
  array<mint, rank2 + 1> iroot;
  array<mint, max(0, rank2 - 2 + 1)> rate2;
  array<mint, max(0, rank2 - 2 + 1)> irate2;
  array<mint, max(0, rank2 - 3 + 1)> rate3;
  array<mint, max(0, rank2 - 3 + 1)> irate3;

  NTT() {
    root[rank2] = mint(g).pow((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];
      }
    }
  }
  void ntt(vector<mint>& a) {
    int n = int(a.size());
    int h = __builtin_ctzll((unsigned int)n);
    assert(h <= rank2);
    a.resize(1 << h);
    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 *= rate2[__builtin_ctzll(~(unsigned int)(s))];
        }
        len++;
      } else {
        // 4-base
        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++) {
            auto mod2 = 1ULL * mint::get_mod() * mint::get_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 *= rate3[__builtin_ctzll(~(unsigned int)(s))];
        }
        len += 2;
      }
    }
  }
  void intt(vector<mint>& a) {
    int n = int(a.size());
    int h = __builtin_ctzll((unsigned int)n);
    assert(h <= rank2);
    a.resize(1 << h);

    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::get_mod() + l.val() - r.val()) * irot.val();
          }
          if (s + 1 != (1 << (len - 1))) irot *= irate2[__builtin_ctzll(~(unsigned int)(s))];
        }
        len--;
      } else {
        // 4-base
        int p = 1 << (h - len);
        mint irot = 1, iimag = 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::get_mod() + a2 - a3) * iimag.val()).val();
            a[i + offset] = a0 + a1 + a2 + a3;
            a[i + offset + 1 * p] = (a0 + (mint::get_mod() - a1) + a2na3iimag) * irot.val();
            a[i + offset + 2 * p] = (a0 + a1 + (mint::get_mod() - a2) + (mint::get_mod() - a3)) * irot2.val();
            a[i + offset + 3 * p] = (a0 + (mint::get_mod() - a1) + (mint::get_mod() - a2na3iimag)) * irot3.val();
          }
          if (s + 1 != (1 << (len - 2))) irot *= irate3[__builtin_ctzll(~(unsigned int)(s))];
        }
        len -= 2;
      }
    }
    mint e = mint(n).inv();
    for (auto& x : a) x *= e;
  }
  vector<mint> multiply(const vector<mint>& a, const vector<mint>& b) {
    if (a.empty() || b.empty()) return vector<mint>();
    int n = a.size(), m = b.size();
    int sz = n + m - 1;
    if (n <= 30 || m <= 30) {
      if (n > 30) return multiply(b, a);
      vector<mint> res(sz);
      for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++) res[i + j] += a[i] * b[j];
      return res;
    }
    int sz1 = 1;
    while (sz1 < sz) sz1 <<= 1;
    vector<mint> res(sz1);
    for (int i = 0; i < n; i++) res[i] = a[i];
    ntt(res);
    if (a == b)
      for (int i = 0; i < sz1; i++) res[i] *= res[i];
    else {
      vector<mint> c(sz1);
      for (int i = 0; i < m; i++) c[i] = b[i];
      ntt(c);
      for (int i = 0; i < sz1; i++) res[i] *= c[i];
    }
    intt(res);
    res.resize(sz);
    return res;
  }
  // c[i]=sum[j]a[j]b[i+j]
  vector<mint> middle_product(const vector<mint>& a, const vector<mint>& b) {
    if (b.empty() || a.size() > b.size()) return {};
    int n = a.size(), m = b.size();
    int sz = m - n + 1;
    if (n <= 30 || sz <= 30) {
      vector<mint> res(sz);
      for (int i = 0; i < sz; i++)
        for (int j = 0; j < n; j++) res[i] += a[j] * b[i + j];
      return res;
    }
    int sz1 = 1;
    while (sz1 < m) sz1 <<= 1;
    vector<mint> res(sz1), b2(sz1);
    reverse_copy(a.begin(), a.end(), res.begin());
    copy(b.begin(), b.end(), b2.begin());
    ntt(res);
    ntt(b2);
    for (int i = 0; i < res.size(); i++) res[i] *= b2[i];
    intt(res);
    res.resize(m);
    res.erase(res.begin(), res.begin() + n - 1);
    return res;
  }
  void ntt_doubling(vector<mint>& a) {
    int n = (int)a.size();
    auto b = a;
    intt(b);
    mint r = 1, zeta = mint(g).pow((mint::get_mod() - 1) / (n << 1));
    for (int i = 0; i < n; i++) b[i] *= r, r *= zeta;
    ntt(b);
    copy(b.begin(), b.end(), back_inserter(a));
  }
};
/**
 * @brief NTT (数論変換)
 * @docs docs/fft/ntt.md
 */
#line 2 "library/fps/formal-power-series.hpp"

template <class mint>
struct FormalPowerSeries : vector<mint> {
  using vector<mint>::vector;
  using FPS = FormalPowerSeries;
  FormalPowerSeries(const vector<mint>& r) : vector<mint>(r) {}
  FormalPowerSeries(vector<mint>&& r) : vector<mint>(std::move(r)) {}
  FPS& operator=(const vector<mint>& r) {
    vector<mint>::operator=(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 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.at(g.size() - 1).inv();
      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) {
    assert(sz >= 0);
    if ((int)this->size() <= sz)
      this->clear();
    else
      this->erase(this->begin(), this->begin() + sz);
    return *this;
  }
  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) {
    assert(sz >= 0);
    this->insert(this->begin(), sz, mint(0));
    return *this;
  }
  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_ntt();
  FPS& operator*=(const FPS& r);
  FPS middle_product(const FPS& r) const;
  void ntt();
  void intt();
  void ntt_doubling();
  static int ntt_root();
  FPS inv(int deg = -1) const;
  FPS exp(int deg = -1) const;
};
template <typename mint>
void* FormalPowerSeries<mint>::ntt_ptr = nullptr;
#line 5 "library/fps/fps-ntt-friendly.hpp"

template <class mint>
void FormalPowerSeries<mint>::set_ntt() {
  if (!ntt_ptr) ntt_ptr = new NTT<mint>;
}
template <class mint>
FormalPowerSeries<mint>& FormalPowerSeries<mint>::operator*=(const FormalPowerSeries<mint>& r) {
  if (this->empty() || r.empty()) {
    this->clear();
    return *this;
  }
  set_ntt();
  auto ret = static_cast<NTT<mint>*>(ntt_ptr)->multiply(*this, r);
  return *this = FormalPowerSeries<mint>(ret.begin(), ret.end());
}
template <class mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::middle_product(const FormalPowerSeries<mint>& r) const {
  set_ntt();
  auto ret = static_cast<NTT<mint>*>(ntt_ptr)->middle_product(*this, r);
  return FormalPowerSeries<mint>(ret.begin(), ret.end());
}
template <class mint>
void FormalPowerSeries<mint>::ntt() {
  set_ntt();
  static_cast<NTT<mint>*>(ntt_ptr)->ntt(*this);
}
template <class mint>
void FormalPowerSeries<mint>::intt() {
  set_ntt();
  static_cast<NTT<mint>*>(ntt_ptr)->intt(*this);
}
template <class mint>
void FormalPowerSeries<mint>::ntt_doubling() {
  set_ntt();
  static_cast<NTT<mint>*>(ntt_ptr)->ntt_doubling(*this);
}
template <typename mint>
int FormalPowerSeries<mint>::ntt_root() {
  set_ntt();
  return static_cast<NTT<mint>*>(ntt_ptr)->g;
}
template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::inv(int deg) const {
  assert((*this)[0] != mint(0));
  if (deg == -1) deg = (*this).size();
  FPS ret{mint(1) / (*this)[0]};
  for (int i = 1; i < deg; i <<= 1)
    ret = (ret + ret - ret * ret * (*this).pre(i << 1)).pre(i << 1);
  return ret.pre(deg);
}
template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::exp(int deg) const {
  assert((*this)[0] == mint(0));
  if (deg == -1) deg = (*this).size();
  FPS ret{mint(1)};
  for (int i = 1; i < deg; i <<= 1)
    ret = (ret * ((*this).pre(i << 1) - ret.log(i << 1) + 1)).pre(i << 1);
  return ret.pre(deg);
}
#line 6 "main.cpp"
using fps = FormalPowerSeries<mint>;
#line 2 "library/modint/factorial.hpp"

template <class mint>
struct Factorial {
  static void reserve(int n) {
    inv(n);
    fact(n);
    fact_inv(n);
  }
  static mint inv(int n) {
    static long long mod = mint::get_mod();
    static vector<mint> buf({0, 1});
    assert(n != 0);
    if (mod != mint::get_mod()) {
      mod = mint::get_mod();
      buf = vector<mint>({0, 1});
    }
    while ((int)buf.capacity() <= n) buf.reserve(buf.capacity() * 2);
    while ((int)buf.size() <= n) {
      long long k = buf.size(), q = (mod + k - 1) / k;
      buf.push_back(q * buf[k * q - mod]);
    }
    return buf[n];
  }
  static mint fact(int n) {
    static long long mod = mint::get_mod();
    static vector<mint> buf({1, 1});
    assert(n >= 0);
    if (mod != mint::get_mod()) {
      mod = mint::get_mod();
      buf = vector<mint>({1, 1});
    }
    while ((int)buf.capacity() <= n) buf.reserve(buf.capacity() * 2);
    while ((int)buf.size() <= n) {
      long long k = buf.size();
      buf.push_back(buf.back() * k);
    }
    return buf[n];
  }
  static mint fact_inv(int n) {
    static long long mod = mint::get_mod();
    static vector<mint> buf({1, 1});
    assert(n >= 0);
    if (mod != mint::get_mod()) {
      mod = mint::get_mod();
      buf = vector<mint>({1, 1});
    }
    if ((int)buf.size() <= n) inv(n);
    while ((int)buf.capacity() <= n) buf.reserve(buf.capacity() * 2);
    while ((int)buf.size() <= n) {
      long long k = buf.size();
      buf.push_back(buf.back() * inv(k));
    }
    return buf[n];
  }
  static mint binom(int n, int r) {
    if (r < 0 || r > n) return 0;
    return fact(n) * fact_inv(r) * fact_inv(n - r);
  }
  static mint binom_naive(int n, int r) {
    if (r < 0 || r > n) return 0;
    mint res = fact_inv(r);
    for (int i = 0; i < r; i++) res *= n - i;
    return res;
  }
  static mint multinom(const vector<int>& r) {
    int n = 0;
    for (auto& x : r) {
      if (x < 0) return 0;
      n += x;
    }
    mint res = fact(n);
    for (auto& x : r) res *= fact_inv(x);
    return res;
  }
  static mint P(int n, int r) {
    if (r < 0 || r > n) return 0;
    return fact(n) * fact_inv(n - r);
  }
  // partition n items to r groups (allow empty group)
  static mint H(int n, int r) {
    if (n < 0 || r < 0) return 0;
    return r == 0 ? 1 : binom(n + r - 1, r);
  }
};
/**
 * @brief 階乗, 二項係数
 */
#line 4 "library/fps/taylor-shift.hpp"

// f(x+a)
template <class mint>
FormalPowerSeries<mint> TaylorShift(FormalPowerSeries<mint> f, mint a) {
  using fps = FormalPowerSeries<mint>;
  if (f.size() <= 1) return f;
  int n = f.size();
  using fact = Factorial<mint>;
  fact::reserve(n);
  for (int i = 0; i < n; i++) f[i] *= fact::fact(i);
  reverse(f.begin(), f.end());
  fps g(n, mint(1));
  for (int i = 1; i < n; i++) g[i] = g[i - 1] * a * fact::inv(i);
  f = (f * g).pre(n);
  reverse(f.begin(), f.end());
  for (int i = 0; i < n; i++) f[i] *= fact::fact_inv(i);
  return f;
}
/**
 * @brief Taylor Shift
 * @docs docs/fps/taylor-shift.md
 */
#line 4 "library/fps/composition.hpp"

template <class mint>
FormalPowerSeries<mint> Composition(FormalPowerSeries<mint> f, FormalPowerSeries<mint> g, int n = -1) {
  if (n == -1) n = f.size();
  assert(n >= 0);
  if (n == 0 || f.size() == 0) return FormalPowerSeries<mint>(n);

  f = TaylorShift(f, g[0]);
  int k = 1;
  while (k < f.size()) k <<= 1;
  int l = 1, m = 2 * k * l;
  int log = __builtin_ctz((unsigned int)m);

  mint wi = mint(FormalPowerSeries<mint>::ntt_root()).inv().pow((mint::get_mod() - 1) >> (log + 1));
  vector<int> rev(m);
  for (int i = 0; i < rev.size(); i++) rev[i] = (rev[i / 2] / 2) | ((i & 1) << (log - 1));
  vector<mint> pow(m, 1);
  for (int i = 1; i < m; i++) pow[rev[i]] = pow[rev[i - 1]] * wi;

  mint inv2 = mint(2).inv();
  FormalPowerSeries<mint> P(m), Q(m);
  for (int i = 1; i < g.size() && i < k; i++) Q[i] = -g[i];
  auto rec = [&](auto rec, int k, int l, FormalPowerSeries<mint> Q) {
    if (k <= 1) {
      for (int i = 0; i < l && i < f.size(); i++) P[(l - 1 - i) * 2] = f[i];
      return;
    }
    Q.resize(2 * m), Q.ntt();
    FormalPowerSeries<mint> Q1(m);
    for (int i = 0; i < m; i++) {
      mint b = (i >> (log - 1)) == 0 ? 1 : -1;
      int j = i << 1;
      Q1[i] = Q[j] * Q[j ^ 1] + (Q[j] + Q[j ^ 1]) * b;
    }
    Q1.intt();
    k >>= 1, l <<= 1;
    for (int i = k; i < k * 2; i++)
      for (int j = 0; j < l; j++)
        Q1[i + j * k * 2] = 0;
    rec(rec, k, l, Q1);
    for (int i = k; i < k * 2; i++)
      for (int j = 0; j < l; j++)
        P[i + j * k * 2] = 0;
    P.resize(m);
    reverse(P.begin() + 1, P.end());
    P.ntt(), P.resize(2 * m);
    for (int i = m - 1; i >= 0; i--) {
      mint b = (i >> (log - 1)) == 0 ? 1 : -1;
      P[2 * i + 1] = -(Q[2 * i] + b) * pow[i] * P[i];
      P[2 * i] = (Q[2 * i + 1] + b) * pow[i] * P[i];
    }
    P.intt();
    reverse(P.begin() + 1, P.end());
  };
  rec(rec, k, l, Q);

  P.resize(k);
  P = P.rev();
  P.resize(n);
  return P;
}
/**
 * @brief FPS 合成
 * @docs docs/fps/composition.md
 */
#line 8 "main.cpp"

void solve() {
  int n, m;
  in(n, m);
  fps f(n), g(n), h(n);
  in(f, g, h);

  auto ans = Composition(h, g * f[1].pow(m));
  out(ans);
}

int main() {
  int T = 1;
  // in(T);
  while (T--) solve();
}