// BEGIN: main.cpp
#line 1 "main.cpp"
// BEGIN: my_template.hpp
#line 1 "my_template.hpp"
#if defined(USE_PCH)
#include <my_template_compiled.hpp>
#else
#if defined(__GNUC__)
#include <bits/allocator.h>
#pragma GCC optimize("Ofast,unroll-loops")
// 環境によってはコンパイル成功かつ実行時エラー
#pragma GCC target("avx2,popcnt")
#endif
#include <bits/stdc++.h>
#include <cassert>

using namespace std;

using ll = long long;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class>
constexpr bool dependent_false = false;

template <class T>
constexpr T infty = [] {
  static_assert(dependent_false<T>, "infty<T> is not defined");
  return T{};
}();
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
template <>
constexpr double infty<double> = numeric_limits<double>::infinity();
template <>
constexpr long double infty<long double> =
    numeric_limits<long double>::infinity();

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>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using pq_max = priority_queue<T>;
template <class T>
using pq_min = priority_queue<T, vector<T>, greater<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 vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#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 = ll(a) - 1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = ll(a) - 1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = ll(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 all(x) (x).begin(), (x).end()
#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

#define stoi stoll

// require y > 0
template <typename T>
T floor(T x, T y) {
  return x / y - (x % y < 0);
}

// require y > 0
template <typename T>
T ceil(T x, T y) {
  return (x / y) + (x % y > 0);
}

// require y > 0
template <typename T>
T bmod(T x, T y) {
  T r = x % y;
  return (r < 0 ? r + y : r);
}

// require y > 0
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = x / y, r = x % y;
  if (r < 0) --q, r += y;
  return {q, r};
}

constexpr auto TEN = [] {
  array<u64, 20> A{};
  A[0] = 1;
  for (int i = 1; i < 20; ++i) A[i] = 10 * A[i - 1];
  return A;
}();

template <typename T, typename U>
T SUM(const U& A) {
  return std::accumulate(A.begin(), A.end(), T{});
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
template <class C, class T>
inline long long LB(const C& c, const T& x) {
  return lower_bound(c.begin(), c.end(), x) - c.begin();
}
template <class C, class T>
inline long long UB(const C& c, const T& x) {
  return upper_bound(c.begin(), c.end(), x) - c.begin();
}
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end())

template <typename T>
T POP(deque<T>& que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <class T, class Container, class Compare>
T POP(priority_queue<T, Container, Compare>& que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T>& que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (1) {
    ll x = midpoint(ok, ng);
    if (x == ok || x == ng) break;
    (check(x) ? ok : ng) = x;
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = midpoint(ok, ng);
    (check(x) ? ok : ng) = x;
  }
  return midpoint(ok, ng);
}

template <class T, class S>
inline bool chmax(T& a, const S& b) {
  T c = max<T>(a, b);
  bool changed = (c != a);
  a = c;
  return changed;
}
template <class T, class S>
inline bool chmin(T& a, const S& b) {
  T c = min<T>(a, b);
  bool changed = (c != a);
  a = c;
  return changed;
}

// ? は -1
vc<int> s_to_vi(const string& S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vc<T> cumsum(const vc<U>& A, int off = 1) {
  int N = A.size();
  vc<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vc<int> argsort(const vc<T>& A) {
  vc<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T>& A, const vc<int>& I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}

template <typename T, typename... Vectors>
void concat(vc<T>& first, const Vectors&... others) {
  first.reserve(first.size() + (others.size() + ... + 0));
  (first.insert(first.end(), others.begin(), others.end()), ...);
}

// i128
template <class T, enable_if_t<is_same_v<T, i128>, int> = 0>
constexpr i128 abs(T x) {
  return x < 0 ? -x : x;
}

constexpr i128 gcd(i128 a, i128 b) {
  while (b != 0) {
    i128 c = a % b;
    a = b, b = c;
  }
  return abs(a);
}
#endif
// END: my_template.hpp
#line 2 "main.cpp"
// BEGIN: other/io2.hpp
#line 1 "other/io2.hpp"
#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(...)           \
  long double __VA_ARGS__; \
  IN(__VA_ARGS__)

#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)

void read(int& a) { cin >> a; }
void read(long long& a) { cin >> a; }
void read(char& a) { cin >> a; }
void read(double& a) { cin >> a; }
void read(long double& a) { cin >> a; }
void read(string& a) { cin >> a; }
template <class T, class S>
void read(pair<T, S>& p) {
  read(p.first), read(p.second);
}
template <class T>
void read(vector<T>& a) {
  for (auto& i : a) read(i);
}
template <class T>
void read(T& a) {
  cin >> a;
}
void IN() {}
template <class Head, class... Tail>
void IN(Head& head, Tail&... tail) {
  read(head);
  IN(tail...);
}

template <typename T, typename U>
ostream& operator<<(ostream& os, const pair<T, U>& A) {
  os << A.fi << " " << A.se;
  return os;
}

template <typename T>
ostream& operator<<(ostream& os, const vector<T>& A) {
  for (size_t i = 0; i < A.size(); i++) {
    if (i) os << " ";
    os << A[i];
  }
  return os;
}

class CoutInitializer {
 public:
  CoutInitializer() { std::cout << std::fixed << std::setprecision(15); }
};
static CoutInitializer cout_initializer;

void print() {
  cout << "\n";
  cout.flush();
}

template <class Head, class... Tail>
void print(Head&& head, Tail&&... tail) {
  cout << head;
  if (sizeof...(Tail)) cout << " ";
  print(forward<Tail>(tail)...);
}

#if defined(LOCAL)
template <class... Ts>
inline void _show_pack(const char* func, int line, const char* names,
                       Ts&&... args) {
  // [DEBUG] solve:123 のように先頭に出す
  cout << "[DEBUG " << func << ':' << line << "] ";

  const char* p = names;
  bool first = true;

  auto next_token = [&]() -> std::pair<const char*, const char*> {
    while (*p == ' ' || *p == ',') ++p;
    const char* l = p;
    while (*p && *p != ',') ++p;
    const char* r = p;
    return {l, r};
  };

  (
      [&] {
        auto [l, r] = next_token();
        while (r > l && r[-1] == ' ') --r;
        if (!first) cout << ' ';
        first = false;
        std::string name(l, r);
        cout << name << " = " << args;
      }(),
      ...);
  print();
}

#define SHOW(...) _show_pack(__func__, __LINE__, #__VA_ARGS__, __VA_ARGS__)
#else
#define SHOW(...)
#endif

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
// END: other/io2.hpp
#line 3 "main.cpp"

// BEGIN: poly/fps_pow.hpp
#line 1 "poly/fps_pow.hpp"
// BEGIN: poly/count_terms.hpp
#line 1 "poly/count_terms.hpp"
template <typename mint>
int count_terms(const vc<mint>& f) {
  int t = 0;
  FOR(i, len(f)) if (f[i] != mint(0))++ t;
  return t;
}  // END: poly/count_terms.hpp
#line 3 "poly/fps_pow.hpp"
// BEGIN: poly/fps_exp.hpp
#line 1 "poly/fps_exp.hpp"
// BEGIN: poly/convolution.hpp
#line 1 "poly/convolution.hpp"

// BEGIN: mod/modint.hpp
#line 1 "mod/modint.hpp"
// BEGIN: mod/modint_common.hpp
#line 1 "mod/modint_common.hpp"

// BEGIN: other/bit.hpp
#line 1 "other/bit.hpp"

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_sgn(int x) { return (__builtin_parity(unsigned(x)) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
// (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)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T kth_bit(int k) {
  return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
  return x >> k & 1;
}

template <typename UINT>
struct all_bit {
  UINT s;
  all_bit(UINT s) : s(s) {}
  struct iter {
    UINT s;
    int operator*() const { return lowbit(s); }
    void operator++() { s &= s - 1; }
    bool operator!=(nullptr_t) const { return s; }
  };
  iter begin() const { return {s}; }
  nullptr_t end() const { return nullptr; }
};

template <typename UINT>
struct all_subset {
  UINT s;
  all_subset(UINT s) : s(s) {}
  struct iter {
    UINT s, t;
    bool done = false;
    UINT operator*() const { return t; }
    void operator++() {
      done = (t == 0);
      t = (t - 1) & s;
    }
    bool operator!=(nullptr_t) const { return !done; }
  };
  iter begin() const { return {s, s}; }
  nullptr_t end() const { return nullptr; }
};

constexpr u64 full_mask(int n) {
  return n == 64 ? -1ULL : (1ULL << n) - 1;
}  // END: other/bit.hpp
#line 4 "mod/modint_common.hpp"

struct has_mod_impl {
  template <class T>
  static auto check(T&& x) -> decltype(x.get_mod(), std::true_type{});
  template <class T>
  static auto check(...) -> std::false_type;
};

template <class T>
class has_mod : public decltype(has_mod_impl::check<T>(std::declval<T>())) {};

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};
  if (len(dat) <= n) {
    int now = len(dat);
    int m = min(mod, 1 << (topbit(n) + 1));
    dat.resize(m);
    FOR(i, now, m) dat[i] = dat[i - 1] * mint::raw(i);
  }
  return dat[n];
}

template <typename mint>
mint fact_inv(int n) {
  static const int mod = mint::get_mod();
  static vector<mint> dat = {1, 1};
  if (n < 0) return mint(0);
  if (len(dat) <= n) {
    int now = len(dat);
    int m = min(mod, 1 << (topbit(n) + 1));
    dat.resize(m);
    dat[m - 1] = fact<mint>(m - 1).inverse();
    FOR_R(i, now, m - 1) dat[i] = dat[i + 1] * mint::raw(i + 1);
  }
  return dat[n];
}

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

template <typename mint>
mint inv(int n) {
  static const int mod = mint::get_mod();
  assert(1 <= n && n < mod);
  return fact<mint>(n - 1) * fact_inv<mint>(n);
}

template <>
double inv<double>(int n) {
  assert(n != 0);
  return 1.0 / n;
}

template <typename mint, class Head, class... Tail>
mint multinomial(Head&& head, Tail&&... tail) {
  return fact<mint>(head) * fact_invs<mint>(std::forward<Tail>(tail)...);
}

template <typename mint>
mint C_dense(int n, int k) {
  assert(n >= 0);
  if (k < 0 || n < k) return 0;
  static vvc<mint> C;
  static int H = 0, W = 0;
  auto calc = [&](int i, int j) -> mint {
    if (i == 0) return (j == 0 ? mint(1) : mint(0));
    return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);
  };
  if (W <= k) {
    FOR(i, H) {
      C[i].resize(k + 1);
      FOR(j, W, k + 1) { C[i][j] = calc(i, j); }
    }
    W = k + 1;
  }
  if (H <= n) {
    C.resize(n + 1);
    FOR(i, H, n + 1) {
      C[i].resize(W);
      FOR(j, W) { C[i][j] = calc(i, j); }
    }
    H = n + 1;
  }
  return C[n][k];
}

template <typename mint, bool large = false, bool dense = false>
mint C(ll n, ll k) {
  assert(n >= 0);
  if (k < 0 || n < k) return 0;
  if constexpr (dense) return C_dense<mint>(n, k);
  if constexpr (!large) return multinomial<mint>(n, k, n - k);
  k = min(k, n - k);
  mint x(1);
  FOR(i, k) x *= mint(n - i);
  return x * fact_inv<mint>(k);
}

template <typename mint, bool large = false>
mint C_inv(ll n, ll k) {
  assert(n >= 0);
  assert(0 <= k && k <= n);
  if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);
  return mint(1) / C<mint, 1>(n, k);
}

// [x^d](1-x)^{-n}
template <typename mint, bool large = false, bool dense = false>
mint C_negative(ll n, ll d) {
  assert(n >= 0);
  if (d < 0) return mint(0);
  if (n == 0) {
    return (d == 0 ? mint(1) : mint(0));
  }
  return C<mint, large, dense>(n + d - 1, d);
}  // END: mod/modint_common.hpp
#line 3 "mod/modint.hpp"

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(u128 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){};
  constexpr modint(i128 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 {
    if (n < 0) return inverse().pow(-n);
    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 == 120586241) return {20, 74066978};
    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 == 1004535809) return {21, 582313106};
    if (mod == 1012924417) return {21, 368093570};
    if (mod == 1224736769) return {24, 1191450770};
    if (mod == 2013265921) return {27, 244035102};
    return {-1, -1};
  }
  static constexpr bool can_ntt() { return ntt_info().fi != -1; }
};

#ifdef FASTIO
template <int mod>
void rd(modint<mod>& x) {
  fastio::rd(x.val);
  x.val %= mod;
  // assert(0 <= x.val && x.val < mod);
}
template <int mod>
void wt(modint<mod> x) {
  fastio::wt(x.val);
}
#endif

using modint107 = modint<1000000007>;
using modint998 = modint<998244353>;
// END: mod/modint.hpp
#line 4 "poly/convolution.hpp"
// BEGIN: mod/mod_inv.hpp
#line 1 "mod/mod_inv.hpp"

// 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) {
  if (mod == 0) return 0;
  mod = abs(mod);
  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;
}
// END: mod/mod_inv.hpp
#line 5 "poly/convolution.hpp"
// BEGIN: mod/crt3.hpp
#line 1 "mod/crt3.hpp"

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>
T CRT2(u64 a0, u64 a1) {
  static_assert(p0 < p1);
  static constexpr u64 x0_1 = mod_pow_constexpr(p0, p1 - 2, p1);
  u64 c = (a1 - a0 + p1) * x0_1 % p1;
  return a0 + c * p0;
}

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 x1 = mod_pow_constexpr(p0, p1 - 2, p1);
  static constexpr u64 x2 = mod_pow_constexpr(u64(p0) * p1 % p2, p2 - 2, p2);
  static constexpr u64 p01 = u64(p0) * p1;
  u64 c = (a1 - a0 + p1) * x1 % p1;
  u64 ans_1 = a0 + c * p0;
  c = (a2 - ans_1 % p2 + p2) * x2 % p2;
  return T(ans_1) + T(c) * T(p01);
}

template <typename T, u32 p0, u32 p1, u32 p2, u32 p3>
T CRT4(u64 a0, u64 a1, u64 a2, u64 a3) {
  static_assert(p0 < p1 && p1 < p2 && p2 < p3);
  static constexpr u64 x1 = mod_pow_constexpr(p0, p1 - 2, p1);
  static constexpr u64 x2 = mod_pow_constexpr(u64(p0) * p1 % p2, p2 - 2, p2);
  static constexpr u64 x3 =
      mod_pow_constexpr(u64(p0) * p1 % p3 * p2 % p3, p3 - 2, p3);
  static constexpr u64 p01 = u64(p0) * p1;
  u64 c = (a1 - a0 + p1) * x1 % p1;
  u64 ans_1 = a0 + c * p0;
  c = (a2 - ans_1 % p2 + p2) * x2 % p2;
  u128 ans_2 = ans_1 + c * static_cast<u128>(p01);
  c = (a3 - ans_2 % p3 + p3) * x3 % p3;
  return T(ans_2) + T(c) * T(p01) * T(p2);
}

template <typename T, u32 p0, u32 p1, u32 p2, u32 p3, u32 p4>
T CRT5(u64 a0, u64 a1, u64 a2, u64 a3, u64 a4) {
  static_assert(p0 < p1 && p1 < p2 && p2 < p3 && p3 < p4);
  static constexpr u64 x1 = mod_pow_constexpr(p0, p1 - 2, p1);
  static constexpr u64 x2 = mod_pow_constexpr(u64(p0) * p1 % p2, p2 - 2, p2);
  static constexpr u64 x3 =
      mod_pow_constexpr(u64(p0) * p1 % p3 * p2 % p3, p3 - 2, p3);
  static constexpr u64 x4 =
      mod_pow_constexpr(u64(p0) * p1 % p4 * p2 % p4 * p3 % p4, p4 - 2, p4);
  static constexpr u64 p01 = u64(p0) * p1;
  static constexpr u64 p23 = u64(p2) * p3;
  u64 c = (a1 - a0 + p1) * x1 % p1;
  u64 ans_1 = a0 + c * p0;
  c = (a2 - ans_1 % p2 + p2) * x2 % p2;
  u128 ans_2 = ans_1 + c * static_cast<u128>(p01);
  c = static_cast<u64>(a3 - ans_2 % p3 + p3) * x3 % p3;
  u128 ans_3 = ans_2 + static_cast<u128>(c * p2) * p01;
  c = static_cast<u64>(a4 - ans_3 % p4 + p4) * x4 % p4;
  return T(ans_3) + T(c) * T(p01) * T(p23);
}
// END: mod/crt3.hpp
#line 6 "poly/convolution.hpp"
// BEGIN: poly/convolution_naive.hpp
#line 1 "poly/convolution_naive.hpp"

template <class T, typename enable_if<!has_mod<T>::value>::type* = nullptr>
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 {};
  vector<T> ans(n + m - 1);
  FOR(i, n) FOR(j, m) ans[i + j] += a[i] * b[j];
  return ans;
}

template <class T, typename enable_if<has_mod<T>::value>::type* = nullptr>
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;
}
// END: poly/convolution_naive.hpp
#line 7 "poly/convolution.hpp"
// BEGIN: poly/convolution_karatsuba.hpp
#line 1 "poly/convolution_karatsuba.hpp"
#line 2 "poly/convolution_karatsuba.hpp"

// 任意の環でできる
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 = ceil(n, 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;
}  // END: poly/convolution_karatsuba.hpp
#line 8 "poly/convolution.hpp"
// BEGIN: poly/ntt.hpp
#line 1 "poly/ntt.hpp"
#line 3 "poly/ntt.hpp"

template <class mint>
void ntt(vector<mint>& a, bool inverse) {
  assert(mint::can_ntt());
  const int rank2 = mint::ntt_info().fi;
  const u32 mod = mint::get_mod();
  static array<mint, 30> root, iroot;
  static array<mint, 30> rate2, irate2;
  static array<mint, 30> rate3, irate3;

  assert(rank2 != -1 && len(a) <= (1 << max(0, rank2)));

  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;
      }
    }
  }
}
// END: poly/ntt.hpp
#line 9 "poly/convolution.hpp"

template <class mint>
vector<mint> convolution_ntt(vector<mint> a, vector<mint> b) {
  assert(mint::can_ntt());
  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>
vector<mint> convolution_garner(const vector<mint>& a, const vector<mint>& b) {
  int n = len(a), m = len(b);
  if (!n || !m) return {};
  static constexpr int p0 = 167772161;
  static constexpr int p1 = 469762049;
  static constexpr int p2 = 754974721;
  using mint0 = modint<p0>;
  using mint1 = modint<p1>;
  using mint2 = modint<p2>;
  vc<mint0> a0(n), b0(m);
  vc<mint1> a1(n), b1(m);
  vc<mint2> a2(n), b2(m);
  FOR(i, n) a0[i] = a[i].val, a1[i] = a[i].val, a2[i] = a[i].val;
  FOR(i, m) b0[i] = b[i].val, b1[i] = b[i].val, b2[i] = b[i].val;
  auto c0 = convolution_ntt<mint0>(a0, b0);
  auto c1 = convolution_ntt<mint1>(a1, b1);
  auto c2 = convolution_ntt<mint2>(a2, b2);
  vc<mint> c(len(c0));
  FOR(i, n + m - 1) {
    c[i] = CRT3<mint, p0, p1, p2>(c0[i].val, c1[i].val, c2[i].val);
  }
  return c;
}

vector<ll> convolution(vector<ll> a, vector<ll> b) {
  int n = len(a), m = len(b);
  if (!n || !m) return {};
  if (min(n, m) <= 2500) return convolution_naive(a, b);

  ll mi_a = MIN(a), mi_b = MIN(b);
  for (auto& x : a) x -= mi_a;
  for (auto& x : b) x -= mi_b;
  assert(MAX(a) * MAX(b) <= 1e18);

  auto Ac = cumsum<ll>(a), Bc = cumsum<ll>(b);
  vi res(n + m - 1);
  for (int k = 0; k < n + m - 1; ++k) {
    int s = max(0, k - m + 1);
    int t = min(n, k + 1);
    res[k] += (t - s) * mi_a * mi_b;
    res[k] += mi_a * (Bc[k - s + 1] - Bc[k - t + 1]);
    res[k] += mi_b * (Ac[t] - Ac[s]);
  }

  static constexpr u32 MOD1 = 1004535809;
  static constexpr u32 MOD2 = 1012924417;
  using mint1 = modint<MOD1>;
  using mint2 = modint<MOD2>;

  vc<mint1> a1(n), b1(m);
  vc<mint2> a2(n), b2(m);
  FOR(i, n) a1[i] = a[i], a2[i] = a[i];
  FOR(i, m) b1[i] = b[i], b2[i] = b[i];

  auto c1 = convolution_ntt<mint1>(a1, b1);
  auto c2 = convolution_ntt<mint2>(a2, b2);

  FOR(i, n + m - 1) { res[i] += CRT2<u64, MOD1, MOD2>(c1[i].val, c2[i].val); }
  return res;
}

template <typename mint>
vc<mint> convolution(const vc<mint>& a, const vc<mint>& b) {
  if (mint::get_mod() == 2) {
    vc<modint998> aa, bb;
    for (auto& x : a) aa.eb(x.val);
    for (auto& x : b) bb.eb(x.val);
    aa = convolution<modint998>(aa, bb);
    vc<mint> ANS(len(aa));
    FOR(i, len(aa)) ANS[i] = aa[i].val & 1;
    return ANS;
  }
  int n = len(a), m = len(b);
  if (!n || !m) return {};
  if (mint::can_ntt()) {
    if (min(n, m) <= 50) return convolution_karatsuba<mint>(a, b);
    return convolution_ntt(a, b);
  }
  if (min(n, m) <= 200) return convolution_karatsuba<mint>(a, b);
  return convolution_garner(a, b);
}  // END: poly/convolution.hpp
#line 3 "poly/fps_exp.hpp"
// BEGIN: poly/integrate.hpp
#line 1 "poly/integrate.hpp"

// 不定積分：integrate(f)
// 定積分：integrate(f, L, R)
template <typename mint>
vc<mint> integrate(const vc<mint>& f) {
  vc<mint> g(len(f) + 1);
  FOR3(i, 1, len(g)) g[i] = f[i - 1] * inv<mint>(i);
  return g;
}

// 不定積分：integrate(f)
// 定積分：integrate(f, L, R)
template <typename mint>
mint integrate(const vc<mint>& f, mint L, mint R) {
  mint I = 0;
  mint pow_L = 1, pow_R = 1;
  FOR(i, len(f)) {
    pow_L *= L, pow_R *= R;
    I += inv<mint>(i + 1) * f[i] * (pow_R - pow_L);
  }
  return I;
}  // END: poly/integrate.hpp
#line 4 "poly/fps_exp.hpp"
// BEGIN: poly/differentiate.hpp
#line 1 "poly/differentiate.hpp"

template <typename mint>
vc<mint> differentiate(const vc<mint>& f) {
  if (len(f) <= 1) return {};
  vc<mint> g(len(f) - 1);
  FOR(i, len(g)) g[i] = f[i + 1] * mint(i + 1);
  return g;
}  // END: poly/differentiate.hpp
#line 5 "poly/fps_exp.hpp"
#line 6 "poly/fps_exp.hpp"

template <typename mint>
vc<mint> fps_exp_sparse(vc<mint>& f) {
  if (len(f) == 0) return {mint(1)};
  assert(f[0] == 0);
  int N = len(f);
  // df を持たせる
  vc<pair<int, mint>> dat;
  FOR(i, 1, N) if (f[i] != mint(0)) dat.eb(i - 1, mint(i) * f[i]);
  vc<mint> F(N);
  F[0] = 1;
  FOR(n, 1, N) {
    mint rhs = 0;
    for (auto&& [k, fk] : dat) {
      if (k > n - 1) break;
      rhs += fk * F[n - 1 - k];
    }
    F[n] = rhs * inv<mint>(n);
  }
  return F;
}

template <typename mint>
vc<mint> fps_exp_dense(vc<mint>& h) {
  const int n = len(h);
  assert(n > 0 && h[0] == mint(0));
  if (mint::can_ntt()) {
    vc<mint>& f = h;
    vc<mint> b = {1, (1 < n ? f[1] : 0)};
    vc<mint> c = {1}, z1, z2 = {1, 1};
    while (len(b) < n) {
      int m = len(b);
      auto y = b;
      y.resize(2 * m);
      ntt(y, 0);
      z1 = z2;
      vc<mint> z(m);
      FOR(i, m) z[i] = y[i] * z1[i];
      ntt(z, 1);
      FOR(i, m / 2) z[i] = 0;
      ntt(z, 0);
      FOR(i, m) z[i] *= -z1[i];
      ntt(z, 1);
      c.insert(c.end(), z.begin() + m / 2, z.end());
      z2 = c;
      z2.resize(2 * m);
      ntt(z2, 0);

      vc<mint> x(f.begin(), f.begin() + m);
      FOR(i, len(x) - 1) x[i] = x[i + 1] * mint(i + 1);
      x.back() = 0;
      ntt(x, 0);
      FOR(i, m) x[i] *= y[i];
      ntt(x, 1);

      FOR(i, m - 1) x[i] -= b[i + 1] * mint(i + 1);

      x.resize(m + m);
      FOR(i, m - 1) x[m + i] = x[i], x[i] = 0;
      ntt(x, 0);
      FOR(i, m + m) x[i] *= z2[i];
      ntt(x, 1);
      FOR_R(i, len(x) - 1) x[i + 1] = x[i] * inv<mint>(i + 1);
      x[0] = 0;

      FOR3(i, m, min(n, m + m)) x[i] += f[i];
      FOR(i, m) x[i] = 0;
      ntt(x, 0);
      FOR(i, m + m) x[i] *= y[i];
      ntt(x, 1);
      b.insert(b.end(), x.begin() + m, x.end());
    }
    b.resize(n);
    return b;
  }

  const int L = len(h);
  assert(L > 0 && h[0] == mint(0));
  int LOG = 0;
  while (1 << LOG < L) ++LOG;
  h.resize(1 << LOG);
  auto dh = differentiate(h);
  vc<mint> f = {1}, g = {1};
  int m = 1;

  vc<mint> p;

  FOR(LOG) {
    p = convolution(f, g);
    p.resize(m);
    p = convolution(p, g);
    p.resize(m);
    g.resize(m);
    FOR(i, m) g[i] += g[i] - p[i];
    p = {dh.begin(), dh.begin() + m - 1};
    p = convolution(f, p);
    p.resize(m + m - 1);
    FOR(i, m + m - 1) p[i] = -p[i];
    FOR(i, m - 1) p[i] += mint(i + 1) * f[i + 1];
    p = convolution(p, g);

    p.resize(m + m - 1);
    FOR(i, m - 1) p[i] += dh[i];
    p = integrate(p);
    FOR(i, m + m) p[i] = h[i] - p[i];
    p[0] += mint(1);
    f = convolution(f, p);
    f.resize(m + m);
    m += m;
  }
  f.resize(L);
  return f;
}

template <typename mint>
vc<mint> fps_exp(vc<mint>& f) {
  int n = count_terms(f);
  int t = (mint::can_ntt() ? 320 : 3000);
  return (n <= t ? fps_exp_sparse<mint>(f) : fps_exp_dense<mint>(f));
}
// END: poly/fps_exp.hpp
#line 4 "poly/fps_pow.hpp"
// BEGIN: poly/fps_log.hpp
#line 1 "poly/fps_log.hpp"

// BEGIN: poly/fps_inv.hpp
#line 1 "poly/fps_inv.hpp"
#line 3 "poly/fps_inv.hpp"
#line 4 "poly/fps_inv.hpp"

template <typename mint>
vc<mint> fps_inv_sparse(const vc<mint>& f) {
  int N = len(f);
  vc<pair<int, mint>> dat;
  FOR(i, 1, N) if (f[i] != mint(0)) dat.eb(i, f[i]);
  vc<mint> g(N);
  mint g0 = mint(1) / f[0];
  g[0] = g0;
  FOR(n, 1, N) {
    mint rhs = 0;
    for (auto&& [k, fk] : dat) {
      if (k > n) break;
      rhs -= fk * g[n - k];
    }
    g[n] = rhs * g0;
  }
  return g;
}

template <typename mint>
vc<mint> fps_inv_dense_ntt(const vc<mint>& F) {
  vc<mint> G = {mint(1) / F[0]};
  ll N = len(F), n = 1;
  G.reserve(N);
  while (n < N) {
    vc<mint> f(2 * n), g(2 * n);
    FOR(i, min(N, 2 * n)) f[i] = F[i];
    FOR(i, n) g[i] = G[i];
    ntt(f, false), ntt(g, false);
    FOR(i, 2 * n) f[i] *= g[i];
    ntt(f, true);
    FOR(i, n) f[i] = 0;
    ntt(f, false);
    FOR(i, 2 * n) f[i] *= g[i];
    ntt(f, true);
    FOR(i, n, min(N, 2 * n)) G.eb(-f[i]);
    n *= 2;
  }
  return G;
}

template <typename mint>
vc<mint> fps_inv_dense(const vc<mint>& F) {
  if (mint::can_ntt()) return fps_inv_dense_ntt(F);
  const int N = len(F);
  vc<mint> R = {mint(1) / F[0]};
  vc<mint> p;
  int m = 1;
  while (m < N) {
    p = convolution(R, R);
    p.resize(m + m);
    vc<mint> f = {F.begin(), F.begin() + min(m + m, N)};
    p = convolution(p, f);
    R.resize(m + m);
    FOR(i, m + m) R[i] = R[i] + R[i] - p[i];
    m += m;
  }
  R.resize(N);
  return R;
}

template <typename mint>
vc<mint> fps_inv(const vc<mint>& f) {
  assert(f[0] != mint(0));
  int n = count_terms(f);
  int t = (mint::can_ntt() ? 160 : 820);
  return (n <= t ? fps_inv_sparse<mint>(f) : fps_inv_dense<mint>(f));
}
// END: poly/fps_inv.hpp
#line 4 "poly/fps_log.hpp"
#line 5 "poly/fps_log.hpp"

template <typename mint>
vc<mint> fps_log_dense(const vc<mint>& f) {
  assert(f[0] == mint(1));
  ll N = len(f);
  vc<mint> df = f;
  FOR(i, N) df[i] *= mint(i);
  df.erase(df.begin());
  auto f_inv = fps_inv(f);
  auto g = convolution(df, f_inv);
  g.resize(N - 1);
  g.insert(g.begin(), 0);
  FOR(i, 1, N) g[i] *= inv<mint>(i);
  return g;
}

template <typename mint>
vc<mint> fps_log_sparse(const vc<mint>& f) {
  int N = f.size();
  vc<pair<int, mint>> dat;
  FOR(i, 1, N) if (f[i] != mint(0)) dat.eb(i, f[i]);
  vc<mint> F(N);
  vc<mint> g(N - 1);
  for (int n = 0; n < N - 1; ++n) {
    mint rhs = mint(n + 1) * f[n + 1];
    for (auto&& [i, fi] : dat) {
      if (i > n) break;
      rhs -= fi * g[n - i];
    }
    g[n] = rhs;
    F[n + 1] = rhs * inv<mint>(n + 1);
  }
  return F;
}

template <typename mint>
vc<mint> fps_log(const vc<mint>& f) {
  assert(f[0] == mint(1));
  int n = count_terms(f);
  int t = (mint::can_ntt() ? 200 : 1200);
  return (n <= t ? fps_log_sparse<mint>(f) : fps_log_dense<mint>(f));
}
// END: poly/fps_log.hpp
#line 5 "poly/fps_pow.hpp"

// fps の k 乗を求める。k >= 0 の前提である。
// 定数項が 1 で、k が mint の場合には、fps_pow_1 を使うこと。
// ・dense な場合： log, exp を使う O(NlogN)
// ・sparse な場合： O(NK)
template <typename mint>
vc<mint> fps_pow(const vc<mint>& f, ll k) {
  assert(0 <= k);
  int n = len(f);
  if (k == 0) {
    vc<mint> g(n);
    g[0] = mint(1);
    return g;
  }
  int d = n;
  FOR_R(i, n) if (f[i] != 0) d = i;
  // d * k >= n
  if (d >= ceil<ll>(n, k)) {
    vc<mint> g(n);
    return g;
  }
  ll off = d * k;
  mint c = f[d];
  mint c_inv = mint(1) / mint(c);
  vc<mint> g(n - off);
  FOR(i, n - off) g[i] = f[d + i] * c_inv;
  g = fps_pow_1(g, mint(k));
  vc<mint> h(n);
  c = c.pow(k);
  FOR(i, len(g)) h[off + i] = g[i] * c;
  return h;
}

template <typename mint>
vc<mint> fps_pow_1_sparse(const vc<mint>& f, mint K) {
  int N = len(f);
  assert(N == 0 || f[0] == mint(1));
  vc<pair<int, mint>> dat;
  FOR(i, 1, N) if (f[i] != mint(0)) dat.eb(i, f[i]);
  vc<mint> g(N);
  g[0] = 1;
  FOR(n, N - 1) {
    mint& x = g[n + 1];
    for (auto&& [d, cf] : dat) {
      if (d > n + 1) break;
      mint t = cf * g[n - d + 1];
      x += t * (K * mint(d) - mint(n - d + 1));
    }
    x *= inv<mint>(n + 1);
  }
  return g;
}

template <typename mint>
vc<mint> fps_pow_1_dense(const vc<mint>& f, mint K) {
  assert(f[0] == mint(1));
  auto log_f = fps_log(f);
  FOR(i, len(f)) log_f[i] *= K;
  return fps_exp_dense(log_f);
}

template <typename mint>
vc<mint> fps_pow_1(const vc<mint>& f, mint K) {
  int n = count_terms(f);
  int t = (mint::can_ntt() ? 100 : 1300);
  return (n <= t ? fps_pow_1_sparse(f, K) : fps_pow_1_dense(f, K));
}
// END: poly/fps_pow.hpp
#line 5 "main.cpp"
// BEGIN: poly/composition.hpp
#line 1 "poly/composition.hpp"

#line 4 "poly/composition.hpp"
// BEGIN: poly/poly_taylor_shift.hpp
#line 1 "poly/poly_taylor_shift.hpp"

// BEGIN: mod/powertable.hpp
#line 1 "mod/powertable.hpp"
// BEGIN: nt/primetable.hpp
#line 1 "nt/primetable.hpp"

template <typename T = int>
vc<T> primetable(int LIM) {
  ++LIM;
  const int S = 32768;
  static int done = 2;
  static vc<T> primes = {2}, sieve(S + 1);

  if (done < LIM) {
    done = LIM;

    primes = {2}, sieve.assign(S + 1, 0);
    const int R = LIM / 2;
    primes.reserve(int(LIM / log(LIM) * 1.1));
    vc<pair<int, int>> cp;
    for (int i = 3; i <= S; i += 2) {
      if (!sieve[i]) {
        cp.eb(i, i * i / 2);
        for (int j = i * i; j <= S; j += 2 * i) sieve[j] = 1;
      }
    }
    for (int L = 1; L <= R; L += S) {
      array<bool, S> block{};
      for (auto& [p, idx] : cp)
        for (int i = idx; i < S + L; idx = (i += p)) block[i - L] = 1;
      FOR(i, min(S, R - L)) if (!block[i]) primes.eb((L + i) * 2 + 1);
    }
  }
  int k = LB(primes, LIM + 1);
  return {primes.begin(), primes.begin() + k};
}
// END: nt/primetable.hpp
#line 3 "mod/powertable.hpp"

// a^0, ..., a^N
template <typename mint>
vc<mint> powertable_1(mint a, ll N) {
  // table of a^i
  vc<mint> f(N + 1, 1);
  FOR(i, N) f[i + 1] = a * f[i];
  return f;
}

// 0^e, ..., N^e
template <typename mint>
vc<mint> powertable_2(ll e, ll N) {
  auto primes = primetable(N);
  vc<mint> f(N + 1, 1);
  f[0] = mint(0).pow(e);
  for (auto&& p : primes) {
    if (p > N) break;
    mint xp = mint(p).pow(e);
    ll pp = p;
    while (pp <= N) {
      ll i = pp;
      while (i <= N) {
        f[i] *= xp;
        i += pp;
      }
      pp *= p;
    }
  }
  return f;
}
// END: mod/powertable.hpp
#line 4 "poly/poly_taylor_shift.hpp"
#line 5 "poly/poly_taylor_shift.hpp"

// f(x) -> f(x+c)
template <typename mint>
vc<mint> poly_taylor_shift(vc<mint> f, mint c) {
  if (c == mint(0)) return f;
  ll N = len(f);
  FOR(i, N) f[i] *= fact<mint>(i);
  auto b = powertable_1<mint>(c, N);
  FOR(i, N) b[i] *= fact_inv<mint>(i);
  reverse(all(f));
  f = convolution(f, b);
  f.resize(N);
  reverse(all(f));
  FOR(i, N) f[i] *= fact_inv<mint>(i);
  return f;
}
// END: poly/poly_taylor_shift.hpp
#line 5 "poly/composition.hpp"
// BEGIN: poly/transposed_ntt.hpp
#line 1 "poly/transposed_ntt.hpp"

template <class mint>
void transposed_ntt(vector<mint>& a, bool inverse) {
  assert(mint::can_ntt());
  const int rank2 = mint::ntt_info().fi;
  const u32 mod = mint::get_mod();
  static array<mint, 30> root, iroot;
  static array<mint, 30> rate2, irate2;
  static array<mint, 30> rate3, irate3;

  assert(rank2 != -1 && len(a) <= (1 << max(0, rank2)));

  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 = h;
    while (len > 0) {
      if (len == 1) {
        int p = 1 << (h - len);
        mint rot = 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) * rot.val;
          }
          rot *= rate2[topbit(~s & -~s)];
        }
        len--;
      } else {
        int p = 1 << (h - len);
        mint rot = 1, imag = root[2];
        FOR(s, (1 << (len - 2))) {
          int offset = s << (h - len + 2);
          mint rot2 = rot * rot;
          mint rot3 = rot2 * rot;
          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) * imag.val % mod;
            a[i + offset] = a0 + a1 + a2 + a3;
            a[i + offset + 1 * p] = (a0 + mod - a1 + x) * rot.val;
            a[i + offset + 2 * p] = (a0 + a1 + 2 * mod - a2 - a3) * rot2.val;
            a[i + offset + 3 * p] = (a0 + 2 * mod - a1 - x) * rot3.val;
          }
          rot *= rate3[topbit(~s & -~s)];
        }
        len -= 2;
      }
    }
  } else {
    mint coef = mint(1) / mint(len(a));
    FOR(i, len(a)) a[i] *= coef;
    int len = 0;
    while (len < h) {
      if (len == h - 1) {
        int p = 1 << (h - len - 1);
        mint irot = 1;
        FOR(s, 1 << len) {
          int offset = s << (h - len);
          FOR(i, p) {
            auto l = a[i + offset];
            auto r = a[i + offset + p] * irot;
            a[i + offset] = l + r;
            a[i + offset + p] = l - r;
          }
          irot *= irate2[topbit(~s & -~s)];
        }
        len++;
      } else {
        int p = 1 << (h - len - 2);
        mint irot = 1, iimag = iroot[2];
        for (int s = 0; s < (1 << len); s++) {
          mint irot2 = irot * irot;
          mint irot3 = irot2 * irot;
          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) * irot.val;
            u64 a2 = u64(a[i + offset + 2 * p].val) * irot2.val;
            u64 a3 = u64(a[i + offset + 3 * p].val) * irot3.val;
            u64 a1na3imag = (a1 + mod2 - a3) % mod * iimag.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);
          }
          irot *= irate3[topbit(~s & -~s)];
        }
        len += 2;
      }
    }
  }
}
// END: poly/transposed_ntt.hpp
#line 6 "poly/composition.hpp"

template <typename mint>
vc<mint> composition_old(vc<mint>& Q, vc<mint>& P) {
  int n = len(P);
  assert(len(P) == len(Q));
  int k = 1;
  while (k * k < n) ++k;
  // compute powers of P
  vv(mint, pow1, k + 1);
  pow1[0] = {1};
  pow1[1] = P;
  FOR3(i, 2, k + 1) {
    pow1[i] = convolution(pow1[i - 1], pow1[1]);
    pow1[i].resize(n);
  }
  vv(mint, pow2, k + 1);
  pow2[0] = {1};
  pow2[1] = pow1[k];
  FOR3(i, 2, k + 1) {
    pow2[i] = convolution(pow2[i - 1], pow2[1]);
    pow2[i].resize(n);
  }
  vc<mint> ANS(n);
  FOR(i, k + 1) {
    vc<mint> f(n);
    FOR(j, k) {
      if (k * i + j < len(Q)) {
        mint coef = Q[k * i + j];
        FOR(d, len(pow1[j])) f[d] += pow1[j][d] * coef;
      }
    }
    f = convolution(f, pow2[i]);
    f.resize(n);
    FOR(d, n) ANS[d] += f[d];
  }
  return ANS;
}

// f(g(x)), O(Nlog^2N)
template <typename mint>
vc<mint> composition_0_ntt(vc<mint> f, vc<mint> g) {
  assert(len(f) == len(g));
  if (f.empty()) return {};

  int n0 = len(f);
  int n = 1;
  while (n < len(f)) n *= 2;
  f.resize(n), g.resize(n);

  vc<mint> W(n);
  {
    // bit reverse order
    vc<int> btr(n);
    int log = topbit(n);
    FOR(i, n) { btr[i] = (btr[i >> 1] >> 1) + ((i & 1) << (log - 1)); }
    int t = mint::ntt_info().fi;
    mint r = mint::ntt_info().se;
    mint dw = r.inverse().pow((1 << t) / (2 * n));
    mint w = 1;
    for (auto& i : btr) {
      W[i] = w, w *= dw;
    }
  }

  auto rec = [&](auto& rec, int n, int k, vc<mint>& Q) -> vc<mint> {
    if (n == 1) {
      reverse(all(f));
      transposed_ntt(f, 1);
      mint c = mint(1) / mint(k);
      for (auto& x : f) x *= c;
      vc<mint> p(4 * k);
      FOR(i, k) p[2 * i] = f[i];
      return p;
    }
    auto doubling_y = [&](vc<mint>& A, int l, int r, bool t) -> void {
      mint z = W[k / 2].inverse();
      vc<mint> f(k);
      if (!t) {
        FOR(i, l, r) {
          FOR(j, k) f[j] = A[2 * n * j + i];
          ntt(f, 1);
          mint r = 1;
          FOR(j, 1, k) r *= z, f[j] *= r;
          ntt(f, 0);
          FOR(j, k) A[2 * n * (k + j) + i] = f[j];
        }
      } else {
        FOR(i, l, r) {
          FOR(j, k) f[j] = A[2 * n * (k + j) + i];
          transposed_ntt(f, 0);
          mint r = 1;
          FOR(j, 1, k) r *= z, f[j] *= r;
          transposed_ntt(f, 1);
          FOR(j, k) A[2 * n * j + i] += f[j];
        }
      }
    };

    auto FFT_x = [&](vc<mint>& A, int l, int r, bool t) -> void {
      vc<mint> f(2 * n);
      if (!t) {
        FOR(j, l, r) {
          move(A.begin() + 2 * n * j, A.begin() + 2 * n * (j + 1), f.begin());
          ntt(f, 0);
          move(all(f), A.begin() + 2 * n * j);
        }
      } else {
        FOR(j, l, r) {
          move(A.begin() + 2 * n * j, A.begin() + 2 * n * (j + 1), f.begin());
          transposed_ntt(f, 0);
          move(all(f), A.begin() + 2 * n * j);
        }
      }
    };

    if (n <= k) doubling_y(Q, 1, n, 0), FFT_x(Q, 0, 2 * k, 0);
    if (n > k) FFT_x(Q, 0, k, 0), doubling_y(Q, 0, 2 * n, 0);

    FOR(i, 2 * n * k) Q[i] += 1;
    FOR(i, 2 * n * k, 4 * n * k) Q[i] -= 1;

    vc<mint> nxt_Q(4 * n * k);
    vc<mint> F(2 * n), G(2 * n), f(n), g(n);
    FOR(j, 2 * k) {
      move(Q.begin() + 2 * n * j, Q.begin() + 2 * n * j + 2 * n, G.begin());
      FOR(i, n) { g[i] = G[2 * i] * G[2 * i + 1]; }
      ntt(g, 1);
      move(g.begin(), g.begin() + n / 2, nxt_Q.begin() + n * j);
    }
    FOR(j, 4 * k) nxt_Q[n * j] = 0;

    vc<mint> p = rec(rec, n / 2, k * 2, nxt_Q);
    FOR_R(j, 2 * k) {
      move(p.begin() + n * j, p.begin() + n * j + n / 2, f.begin());
      move(Q.begin() + 2 * n * j, Q.begin() + 2 * n * j + 2 * n, G.begin());
      fill(f.begin() + n / 2, f.end(), mint(0));
      transposed_ntt(f, 1);
      FOR(i, n) {
        f[i] *= W[i];
        F[2 * i] = G[2 * i + 1] * f[i], F[2 * i + 1] = -G[2 * i] * f[i];
      }
      move(F.begin(), F.end(), p.begin() + 2 * n * j);
    }
    if (n <= k) FFT_x(p, 0, 2 * k, 1), doubling_y(p, 0, n, 1);
    if (n > k) doubling_y(p, 0, 2 * n, 1), FFT_x(p, 0, k, 1);
    return p;
  };

  vc<mint> Q(4 * n);
  FOR(i, n) Q[i] = -g[i];

  vc<mint> p = rec(rec, n, 1, Q);
  p.resize(n);
  reverse(all(p));
  p.resize(n0);
  return p;
}

template <typename mint>
vc<mint> composition_0_garner(vc<mint> f, vc<mint> g) {
  constexpr u32 ps[] = {167772161, 469762049, 754974721};
  using mint0 = modint<ps[0]>;
  using mint1 = modint<ps[1]>;
  using mint2 = modint<ps[2]>;

  auto rec = [&](auto& rec, int n, int k, vc<mint> Q) -> vc<mint> {
    if (n == 1) {
      vc<mint> p(2 * k);
      reverse(all(f));
      FOR(i, k) p[2 * i] = f[i];
      return p;
    }
    vc<mint0> Q0(4 * n * k), R0(4 * n * k), p0(4 * n * k);
    vc<mint1> Q1(4 * n * k), R1(4 * n * k), p1(4 * n * k);
    vc<mint2> Q2(4 * n * k), R2(4 * n * k), p2(4 * n * k);
    FOR(i, 2 * n * k) {
      Q0[i] = Q[i].val, R0[i] = (i % 2 == 0 ? Q[i].val : (-Q[i]).val);
      Q1[i] = Q[i].val, R1[i] = (i % 2 == 0 ? Q[i].val : (-Q[i]).val);
      Q2[i] = Q[i].val, R2[i] = (i % 2 == 0 ? Q[i].val : (-Q[i]).val);
    }
    ntt(Q0, 0), ntt(Q1, 0), ntt(Q2, 0), ntt(R0, 0), ntt(R1, 0), ntt(R2, 0);
    FOR(i, 4 * n * k) Q0[i] *= R0[i], Q1[i] *= R1[i], Q2[i] *= R2[i];
    ntt(Q0, 1), ntt(Q1, 1), ntt(Q2, 1);
    vc<mint> QQ(4 * n * k);
    FOR(i, 4 * n * k) {
      QQ[i] = CRT3<mint, ps[0], ps[1], ps[2]>(Q0[i].val, Q1[i].val, Q2[i].val);
    }
    FOR(i, 0, 2 * n * k, 2) { QQ[2 * n * k + i] += Q[i] + Q[i]; }
    vc<mint> nxt_Q(2 * n * k);
    FOR(j, 2 * k) FOR(i, n / 2) {
      nxt_Q[n * j + i] = QQ[(2 * n) * j + (2 * i + 0)];
    }

    vc<mint> nxt_p = rec(rec, n / 2, k * 2, nxt_Q);
    vc<mint> pq(4 * n * k);
    FOR(j, 2 * k) FOR(i, n / 2) {
      pq[(2 * n) * j + (2 * i + 1)] += nxt_p[n * j + i];
    }

    vc<mint> p(2 * n * k);
    FOR(i, 2 * n * k) { p[i] += pq[2 * n * k + i]; }
    FOR(i, 4 * n * k) {
      p0[i] += pq[i].val, p1[i] += pq[i].val, p2[i] += pq[i].val;
    }
    transposed_ntt(p0, 1), transposed_ntt(p1, 1), transposed_ntt(p2, 1);
    FOR(i, 4 * n * k) p0[i] *= R0[i], p1[i] *= R1[i], p2[i] *= R2[i];
    transposed_ntt(p0, 0), transposed_ntt(p1, 0), transposed_ntt(p2, 0);
    FOR(i, 2 * n * k) {
      p[i] += CRT3<mint, ps[0], ps[1], ps[2]>(p0[i].val, p1[i].val, p2[i].val);
    }
    return p;
  };
  assert(len(f) == len(g));
  int n = 1;
  while (n < len(f)) n *= 2;
  int out_len = len(f);
  f.resize(n), g.resize(n);
  int k = 1;
  vc<mint> Q(2 * n);
  FOR(i, n) Q[i] = -g[i];
  vc<mint> p = rec(rec, n, k, Q);

  vc<mint> output(n);
  FOR(i, n) output[i] = p[i];
  reverse(all(output));
  output.resize(out_len);
  return output;
}

template <typename mint>
vc<mint> composition(vc<mint> f, vc<mint> g) {
  assert(len(f) == len(g));
  if (f.empty()) return {};
  // [x^0]g=0 に帰着しておく
  if (g[0] != mint(0)) {
    f = poly_taylor_shift<mint>(f, g[0]);
    g[0] = 0;
  }
  if (mint::can_ntt()) {
    return composition_0_ntt(f, g);
  }
  return composition_0_garner(f, g);
}
// END: poly/composition.hpp
#line 6 "main.cpp"
// BEGIN: poly/compositional_inverse.hpp
#line 1 "poly/compositional_inverse.hpp"
#line 2 "poly/compositional_inverse.hpp"
// #include "poly/composition.hpp"
// BEGIN: poly/fps_div.hpp
#line 1 "poly/fps_div.hpp"

#line 4 "poly/fps_div.hpp"
#line 5 "poly/fps_div.hpp"

// f/g. f の長さで出力される.
template <typename mint, bool SPARSE = false>
vc<mint> fps_div(vc<mint> f, vc<mint> g) {
  if (SPARSE || count_terms(g) < 200) return fps_div_sparse(f, g);
  int n = len(f);
  g.resize(n);
  g = fps_inv<mint>(g);
  f = convolution(f, g);
  f.resize(n);
  return f;
}

// f/g ただし g は sparse
template <typename mint>
vc<mint> fps_div_sparse(vc<mint> f, vc<mint>& g) {
  if (g[0] != mint(1)) {
    mint cf = g[0].inverse();
    for (auto&& x : f) x *= cf;
    for (auto&& x : g) x *= cf;
  }

  vc<pair<int, mint>> dat;
  FOR(i, 1, len(g)) if (g[i] != mint(0)) dat.eb(i, -g[i]);
  FOR(i, len(f)) {
    for (auto&& [j, x] : dat) {
      if (i >= j) f[i] += x * f[i - j];
    }
  }
  return f;
}  // END: poly/fps_div.hpp
#line 4 "poly/compositional_inverse.hpp"
#line 5 "poly/compositional_inverse.hpp"
// BEGIN: poly/power_projection.hpp
#line 1 "poly/power_projection.hpp"

#line 4 "poly/power_projection.hpp"

template <typename mint>
vc<mint> power_projection_0_ntt(vc<mint> wt, vc<mint> f, int m) {
  assert(len(f) == len(wt) && f[0] == mint(0));

  int n = 1;
  while (n < len(f)) n *= 2;

  for (auto& x : f) x = -x;
  f.resize(n), wt.resize(n);
  reverse(all(wt));
  vc<mint>&P = wt, &Q = f;
  P.resize(4 * n), Q.resize(4 * n);

  vc<mint> W(n);
  {
    // bit reverse order
    vc<int> btr(n);
    int log = topbit(n);
    FOR(i, n) { btr[i] = (btr[i >> 1] >> 1) + ((i & 1) << (log - 1)); }
    int t = mint::ntt_info().fi;
    mint r = mint::ntt_info().se;
    mint dw = r.inverse().pow((1 << t) / (2 * n));
    mint w = 1;
    for (auto& i : btr) {
      W[i] = w, w *= dw;
    }
  }

  int k = 1;
  while (n > 1) {
    /*
    FFT step
    04.. -> 048c
    15.. -> 159d
    .... -> 26ae
    .... -> 37bf
    */

    auto doubling_y = [&](vc<mint>& A, int l, int r) -> void {
      mint z = W[k / 2].inverse();
      vc<mint> f(k);
      FOR(i, l, r) {
        FOR(j, k) f[j] = A[2 * n * j + i];
        ntt(f, 1);
        mint r = 1;
        FOR(j, 1, k) r *= z, f[j] *= r;
        ntt(f, 0);
        FOR(j, k) A[2 * n * (k + j) + i] = f[j];
      }
    };

    auto FFT_x = [&](vc<mint>& A, int l, int r) -> void {
      vc<mint> f(2 * n);
      FOR(j, l, r) {
        move(A.begin() + 2 * n * j, A.begin() + 2 * n * (j + 1), f.begin());
        ntt(f, 0);
        move(all(f), A.begin() + 2 * n * j);
      }
    };

    if (n <= k) {
      doubling_y(P, 0, n), doubling_y(Q, 1, n);
      FFT_x(P, 0, 2 * k), FFT_x(Q, 0, 2 * k);
    } else {
      FFT_x(P, 0, k), FFT_x(Q, 0, k);
      doubling_y(P, 0, 2 * n), doubling_y(Q, 0, 2 * n);
    }
    FOR(i, 2 * n * k) Q[i] += 1;
    FOR(i, 2 * n * k, 4 * n * k) Q[i] -= 1;

    /*
    048c -> 0248????
    159d -> ....????
    26ae
    37bf
    */
    vc<mint> F(2 * n), G(2 * n), f(n), g(n);
    FOR(j, 2 * k) {
      move(P.begin() + 2 * n * j, P.begin() + 2 * n * j + 2 * n, F.begin());
      move(Q.begin() + 2 * n * j, Q.begin() + 2 * n * j + 2 * n, G.begin());
      FOR(i, n) {
        f[i] = W[i] * (F[2 * i] * G[2 * i + 1] - F[2 * i + 1] * G[2 * i]);
        g[i] = G[2 * i] * G[2 * i + 1];
      }
      ntt(f, 1), ntt(g, 1);
      fill(f.begin() + n / 2, f.end(), mint(0));
      fill(g.begin() + n / 2, g.end(), mint(0));
      move(all(f), P.begin() + n * j);
      move(all(g), Q.begin() + n * j);
    }
    fill(P.begin() + 2 * n * k, P.end(), mint(0));
    fill(Q.begin() + 2 * n * k, Q.end(), mint(0));
    FOR(j, 4 * k) Q[n * j] = 0;
    n /= 2, k *= 2;
  }
  FOR(i, k) P[i] = P[2 * i];
  P.resize(k);
  mint c = mint(1) / mint(k);
  for (auto& x : P) x *= c;
  ntt(P, 1);
  reverse(all(P));
  P.resize(m + 1);
  return P;
}
// \sum_j[x^j]f^i を i=0,1,...,m
template <typename mint>
vc<mint> power_projection(vc<mint> wt, vc<mint> f, int m) {
  assert(len(f) == len(wt));
  if (f.empty()) {
    return vc<mint>(m + 1, mint(0));
  }
  if (f[0] != mint(0)) {
    mint c = f[0];
    f[0] = 0;
    vc<mint> A = power_projection(wt, f, m);
    FOR(p, m + 1) A[p] *= fact_inv<mint>(p);
    vc<mint> B(m + 1);
    mint pow = 1;
    FOR(q, m + 1) B[q] = pow * fact_inv<mint>(q), pow *= c;
    A = convolution<mint>(A, B);
    A.resize(m + 1);
    FOR(i, m + 1) A[i] *= fact<mint>(i);
    return A;
  }
  return power_projection_0_ntt(wt, f, m);
}
// END: poly/power_projection.hpp
#line 6 "poly/compositional_inverse.hpp"

// O(N^2)
// template <typename mint>
// vc<mint> compositional_inverse_old(const vc<mint>& F) {
//   const int N = len(F);
//   if (N == 0) return {};
//   assert(F[0] == mint(0));
//   if (N == 1) return F;
//   assert(F[0] == mint(0) && F[1] != mint(0));
//   vc<mint> DF = differentiate(F);

//   vc<mint> G(2);
//   G[1] = mint(1) / F[1];
//   while (len(G) < N) {
//     // G:= G(x)-(F(G(x))-x)/DF(G(x))
//     int n = len(G);
//     vc<mint> G1, G2;
//     {
//       vc<mint> FF(2 * n), GG(2 * n), DFF(n);
//       FOR(i, min<int>(len(F), 2 * n)) FF[i] = F[i];
//       FOR(i, min<int>(len(DF), n)) DFF[i] = DF[i];
//       FOR(i, n) GG[i] = G[i];
//       G1 = composition(FF, GG);
//       G2 = composition(DFF, G);
//     }
//     G1 = {G1.begin() + n, G1.end()};
//     G1 = fps_div(G1, G2);
//     G.resize(2 * n);
//     FOR(i, n) G[n + i] -= G1[i];
//   }
//   G.resize(N);
//   return G;
// }

template <typename mint>
vc<mint> compositional_inverse(vc<mint> f) {
  const int n = len(f) - 1;
  if (n == -1) return {};
  assert(f[0] == mint(0));
  if (n == 0) return f;
  assert(f[1] != mint(0));
  mint c = f[1];
  mint ic = c.inverse();
  for (auto& x : f) x *= ic;
  vc<mint> wt(n + 1);
  wt[n] = 1;

  vc<mint> A = power_projection<mint>(wt, f, n);
  vc<mint> g(n);
  FOR(i, 1, n + 1) g[n - i] = mint(n) * A[i] * inv<mint>(i);
  g = fps_pow_1<mint>(g, -inv<mint>(n));
  g.insert(g.begin(), 0);

  mint pow = 1;
  FOR(i, len(g)) g[i] *= pow, pow *= ic;
  return g;
}

// G->F(G), G->DF(G) を与える
// len(G) まで求める. len(F) まで求めてもいいよ.
// 計算量は合成とだいたい同等
template <typename mint, typename F1, typename F2>
vc<mint> compositional_inverse(const vc<mint>& F, F1 comp_F, F2 comp_DF) {
  const int N = len(F);
  assert(N <= 0 || F[0] == mint(0));
  assert(N <= 1 || F[1] != mint(0));

  vc<mint> G(2);
  G[1] = mint(1) / F[1];
  while (len(G) < N) {
    int n = len(G);
    // G:= G(x)-(F(G(x))-x)/DF(G(x))
    vc<mint> G2 = comp_DF(G);
    G.resize(2 * n);
    vc<mint> G1 = comp_F(G);
    G1 = {G1.begin() + n, G1.end()};
    G1 = fps_div(G1, G2);
    FOR(i, n) G[n + i] -= G1[i];
  }
  G.resize(N);
  return G;
}
// END: poly/compositional_inverse.hpp
#line 7 "main.cpp"
// BEGIN: random/base.hpp
#line 1 "random/base.hpp"

u64 RNG_64() {
  static u64 x_ =
      u64(chrono::duration_cast<chrono::nanoseconds>(
              chrono::high_resolution_clock::now().time_since_epoch())
              .count()) *
      10150724397891781847ULL;
  x_ ^= x_ << 7;
  return x_ ^= x_ >> 9;
}

u64 RNG(u64 lim) { return RNG_64() % lim; }

ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); }
// END: random/base.hpp
#line 8 "main.cpp"

using mint = modint998;

/*
とりあえず分割統治 log^3 にはなっている
これを実装するかあ

n,S(x),T(x) given
Find P(x) such that:
S(x)P(F(x))-aP(x)=T(x) mod x^2n

初期問題から見て低次のところだけは
[x^0]P(x)=0
[x^1]P(x)=1
ということにする

yukicoder オンライン実行
N=100000: 5097ms
www
*/

void solve() {
  LL(N);
  vc<mint> F(N);
  FOR(i, N) read(F[i].val);
  mint a = F[1];

  vc<mint> ANS(N);

  auto dfs = [&](auto& dfs, int L, int R, vc<mint> T) -> void {
    if (R == L + 1) {
      if (L == 1) {
        ANS[1] = 1;
        return;
      }
      mint s = a.pow(L);
      ANS[L] = T[0] / (s - a);
      return;
    }
    int M = (L + R) / 2;
    int n = R - L;
    dfs(dfs, L, M, T);
    int m = M - L;
    /*
    P(x) := A(x)+x^mB(x)
    S(x)F(x)^mB(F(x)) + S(x)A(F(x)) - a[A(x) + x^mB(x)] = T(x) mod x^n
    A given
    S(x)F(x)^mB(F(x)) - ax^mB(x) = T(x) - S(x)A(F(x)) + aA(x) mod x^n

    x^m で割る

    nxt_S(x)B(F(x)) - aB(x) = [T(x) - S(x)A(F(x)) + aA(x)]/x^m mod x^{n-m}
    */
    // vc<mint> nxt_S(n - m);
    // {
    //   FOR(i, n - m) nxt_S[i] = F[1 + i];
    //   nxt_S = fps_pow<mint>(nxt_S, m);
    //   vc<mint> tmp(n - m);
    //   FOR(i, n - m) tmp[i] = S[i];
    //   nxt_S = convolution<mint>(nxt_S, tmp);
    // }
    // T から引いていく
    vc<mint> A(n);
    FOR(i, m) A[i] = ANS[L + i];
    FOR(i, n) T[i] += a * A[i];
    vc<mint> f(n);
    FOR(i, n) f[i] = F[i];
    vc<mint> g(m);
    A = composition<mint>(A, f);
    // S(x)=(F(x)/x)^L
    vc<mint> S(n);
    FOR(i, n) S[i] = F[1 + i];
    S = fps_pow<mint>(S, L);
    A = convolution<mint>(S, A);
    A.resize(n);
    FOR(i, n) T[i] -= A[i];
    FOR(i, m) assert(T[i] == 0);
    T = {T.begin() + m, T.begin() + n};
    dfs(dfs, M, R, T);
  };
  vc<mint> T(N);
  T[0] = 0;
  dfs(dfs, 0, N, T);

  // print(ANS);

  vc<mint> G = ANS;
  vc<mint> H = compositional_inverse<mint>(G);
  vc<int> out;
  for (auto& x : G) out.eb(x.val);
  print(out);
  out.clear();
  for (auto& x : H) out.eb(x.val);
  print(out);
}

signed main() { solve(); }
// END: main.cpp