#line 1 "No_40_\u591a\u9805\u5f0f\u306e\u5272\u308a\u7b97.cpp"
#define YRSD
#line 2 "YRS/all.hpp"

#line 2 "YRS/aa/head.hpp"

#include <iostream>
#include <algorithm>

#include <array>
#include <bitset>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <string>
#include <tuple>

#include <bit>
#include <chrono>
#include <functional>
#include <iomanip>
#include <utility>
#include <type_traits>
#include <cassert>
#include <cctype>
#include <cmath>
#include <cstring>
#include <ctime>
#include <limits>
#include <ranges>
#include <concepts>

#define TE template <typename T>
#define TES template <typename T, typename ...S>
#define Z auto
#define ep emplace_back
#define eb emplace
#define fi first
#define se second
#define all(x) (x).begin(), (x).end()

#define OV4(a, b, c, d, e, ...) e
#define FOR1(a) for (int _ = 0; _ < (a); ++_)
#define FOR2(i, a) for (int i = 0; i < (a); ++i)
#define FOR3(i, a, b) for (int i = (a); i < (b); ++i)
#define FOR4(i, a, b, c) for (int i = (a); i < (b); i += (c))
#define FOR(...) OV4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR1_R(a) for (int _ = (a) - 1; _ >= 0; --_)
#define FOR2_R(i, a) for (int i = (a) - 1; i >= 0; --i)
#define FOR3_R(i, a, b) for (int i = (b) - 1; i >= (a); --i)
#define FOR4_R(i, a, b, c) for (int i = (b) - 1; i >= (a); i -= (c))
#define FOR_R(...) OV4(__VA_ARGS__, FOR4_R, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define FOR_subset(t, s) for (int t = (s); t > -1; t = (t == 0 ? -1 : (t - 1) & s))

#define sort ranges::sort

using namespace std;

TE using vc = vector<T>;
TE using vvc = vc<vc<T>>;
TE using T1 = tuple<T>;
TE using T2 = tuple<T, T>;
TE using T3 = tuple<T, T, T>;
TE using T4 = tuple<T, T, T, T>;
TE using max_heap = priority_queue<T>;
TE using min_heap = priority_queue<T, vc<T>, greater<T>>;
using u8 = unsigned char; using uint = unsigned int; using ll = long long;      using ull = unsigned long long;
using ld = long double;   using i128 = __int128;     using u128 = __uint128_t;  using f128 = __float128;
using u16 = uint16_t;
using PII = pair<int, int>;   using PLL = pair<ll, ll>;

#ifdef YRSD
constexpr bool dbg = 1;
#else
constexpr bool dbg = 0;
#endif
#line 2 "YRS/IO/IO.hpp"

istream &operator>>(istream &I, i128 &x) {
  static string s;
  I >> s;
  int f = s[0] == '-';
  x = 0;
  const int N = (int)s.size();
  FOR(i, f, N) x = x * 10 + s[i] - '0';
  if (f) x = -x;
  return I;
}
ostream &operator<<(ostream &O, i128 x) {
  static string s;
  s.clear();
  bool f = x < 0;
  if (f) x = -x;
  while (x) s += '0' + x % 10, x /= 10;
  if (s.empty()) s += '0';
  if (f) s += '-';
  reverse(all(s));
  return O << s;
}
istream &operator>>(istream &I, f128 &x) {
  static string s;
  I >> s, x = stold(s);
  return I;
}
ostream &operator<<(ostream &O, const f128 x) { return O << ld(x); }
template <typename ...S> istream &operator>>(istream &I, tuple<S...> &t) {
  return apply([&I](Z &...args) { ((I >> args), ...); }, t), I;
}
template <typename T, typename U>
istream &operator>>(istream &I, pair<T, U> &x) {
  return I >> x.fi >> x.se;
}
template <typename T, typename U>
ostream &operator<<(ostream &O, const pair<T, U> &x) {
  return O << x.fi << ' ' << x.se;
}
template <typename T>
requires requires(T &c) { begin(c); end(c); } and 
                          (not is_same_v<decay_t<T>, string>)
istream &operator>>(istream &I, T &c) {
  for (Z &e : c) I >> e;
  return I;
}
template <typename T>requires requires(const T &c) { begin(c); end(c); } and 
  (not is_same_v<decay_t<T>, const char*>) and 
  (not is_same_v<decay_t<T>, string>) and 
  (not is_array_v<remove_reference_t<T>> or 
   not is_same_v<remove_extent_t<remove_reference_t<T>>, char>)
ostream &operator<<(ostream &O, const T &a) {
  if (a.empty()) return O;
  Z i = a.begin();
  O << *i++;
  for (; i != a.end(); ++i) O << ' ' << *i;
  return O;
}
void IN() {}
TE void IN(T &x, Z &...s) { cin >> x, IN(s...); }
void print() { cout << '\n'; }
TES void print(T &&x, S &&...y) {
  cout << x;
  if constexpr (sizeof...(S)) cout << ' ';
  print(forward<S>(y)...);
}
void put() { cout << ' '; }
TES void put(T &&x, S &&...y) {
  cout << x;
  if constexpr (sizeof...(S)) cout << ' ';
  put(forward<S>(y)...);
}

#define INT(...)  int    __VA_ARGS__; IN(__VA_ARGS__)
#define LL(...)   ll     __VA_ARGS__; IN(__VA_ARGS__)
#define ULL(...)  ull    __VA_ARGS__; IN(__VA_ARGS__)
#define I128(...) i128   __VA_ARGS__; IN(__VA_ARGS__)
#define STR(...)  string __VA_ARGS__; IN(__VA_ARGS__)
#define CH(...)   char   __VA_ARGS__; IN(__VA_ARGS__)
#define REAL(...) re     __VA_ARGS__; IN(__VA_ARGS__)
#define VEC(T, a, n) vc<T> a(n); IN(a)
#define VVEC(T, a, n, m) vvc<T> a(n, vc<T>(m)); IN(a)

void YES(bool o = 1) { print(o ? "YES" : "NO"); }
void Yes(bool o = 1) { print(o ? "Yes" : "No"); }
void yes(bool o = 1) { print(o ? "yes" : "no"); }
void NO(bool o = 1) { YES(not o); }
void No(bool o = 1) { Yes(not o); }
void no(bool o = 1) { yes(not o); }
void ALICE(bool o = 1) { print(o ? "ALICE" : "BOB"); }
void Alice(bool o = 1) { print(o ? "Alice" : "Bob"); }
void alice(bool o = 1) { print(o ? "alice" : "bob"); }
void BOB(bool o = 1) { ALICE(not o); }
void Bob(bool o = 1) { Alice(not o); }
void bob(bool o = 1) { alice(not o); }
void POSSIBLE(bool o = 1) { print(o ? "POSSIBLE" : "IMPOSSIBLE"); }
void Possible(bool o = 1) { print(o ? "Possible" : "Impossible"); }
void possible(bool o = 1) { print(o ? "possible" : "impossible"); }
void IMPOSSIBLE(bool o = 1) { POSSIBLE(not o); }
void Impossible(bool o = 1) { Possible(not o); }
void impossible(bool o = 1) { possible(not o); }
void TAK(bool o = 1) { print(o ? "TAK" : "NIE"); }
void NIE(bool o = 1) { TAK(not o); }
#line 5 "YRS/all.hpp"

#if (__cplusplus >= 202002L)
#include <numbers>
constexpr ld pi = numbers::pi;
#endif
TE constexpr T inf = numeric_limits<T>::max();
template <> constexpr i128 inf<i128> = i128(numeric_limits<ll>::max()) * 2'000'000'000'000'000'000;
template <typename T, typename U>
constexpr pair<T, U> inf<pair<T, U>> = {inf<T>, inf<U>};

TE constexpr static inline int pc(T x) { return popcount(make_unsigned_t<T>(x)); }
constexpr static inline ll len(const Z &a) { return a.size(); }

void reverse(Z &a) { reverse(all(a)); }

void unique(Z &a) {
  sort(a);
  a.erase(unique(all(a)), a.end());
}
TE vc<int> inverse(const vc<T> &a) {
  int N = len(a);
  vc<int> b(N, -1);
  FOR(i, N) if (a[i] != -1) b[a[i]] = i;
  return b;
}

Z QMAX(const Z &a) { return *max_element(all(a)); }
Z QMIN(const Z &a) { return *min_element(all(a)); }
constexpr bool chmax(Z &a, const Z &b) { return (a < b ? a = b, true : false); }
constexpr bool chmin(Z &a, const Z &b) { return (a > b ? a = b, true : false); }

template <typename T, typename U>
constexpr static pair<T, U> operator-(const pair<T, U> &p) {
  return pair<T, U>(-p.fi, -p.se);
}

vc<int> argsort(const Z &a) {
  vc<int> I(len(a));
  iota(all(I), 0);
  sort(I, [&](int i, int k) { return a[i] < a[k] or (a[i] == a[k] and i < k); });
  return I;
}
TE vc<T> rearrange(const vc<T> &a, const vc<int> &I) {
  int N = len(I);
  vc<T> b(N);
  FOR(i, N) b[i] = a[I[i]];
  return b;
}
template <int off = 1, typename T> 
vc<T> pre_sum(const vc<T> &a) {
  int N = len(a);
  vc<T> c(N + 1);
  FOR(i, N) c[i + 1] = c[i] + a[i];
  if constexpr (off == 0) c.erase(c.begin());
  return c;
}

TE constexpr static int topbit(T x) {
  if (x == 0) return - 1;
  if constexpr (sizeof(T) <= 4) return 31 - __builtin_clz(x);
  else return 63 - __builtin_clzll(x);
}
TE constexpr static int lowbit(T x) {
  if (x == 0) return -1;
  if constexpr (sizeof(T) <= 4) return __builtin_ctz(x);
  else return __builtin_ctzll(x);
}

TE constexpr T floor(T x, T y) { return x / y - (x % y and (x ^ y) < 0); }
TE constexpr T ceil(T x, T y) { return floor(x + y - 1, y); }
TE constexpr T bmod(T x, T y) { return x - floor(x, y) * x; }
TE constexpr pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return pair{q, x - q * y};
}
template <typename T = ll>
T SUM(const Z &v) {
  return accumulate(all(v), T(0));
}
int lb(const Z &a, Z x) { return lower_bound(all(a), x) - a.begin(); }
int ub(const Z &a, Z x) { return upper_bound(all(a), x) - a.begin(); }

template <bool ck = true>
ll bina(Z F, ll l, ll r) {
  if constexpr (ck) assert(F(l));
  while (abs(l - r) > 1) {
    ll x = (r + l) >> 1;
    (F(x) ? l : r) = x;
  }
  return l;
}
TE T bina_real(const Z &F, T l, T r, int c = 100) {
  while (c--) {
    T m = (l + r) / 2;
    (F(m) ? l : r) = m;
  }
  return (l + r) / 2;
}

Z pop(Z &s) {
  if constexpr (requires { s.pop_back(); }) {
    Z x = s.back();
    return s.pop_back(), x;
  } else if constexpr (requires { s.top(); }) {
    Z x = s.top();
    return s.pop(), x;
  } else {
    Z x = s.front();
    return s.pop(), x;
  }
}
void setp(int x) { cout << fixed << setprecision(x); }

TE inline void sh(vc<T> &a, int N) {
  a.resize(N, T(0));
}
#line 1 "YRS/debug.hpp"
#ifdef YRSD
void DBG() { cerr << "]" << endl; }
TES void DBG(T &&x, S &&...y) {
  cerr << x;
  if constexpr (sizeof...(S)) cerr << ", ";
  DBG(forward<S>(y)...);
}
#define debug(...) cerr << "[" << __LINE__ << "]: [" #__VA_ARGS__ "] = [", DBG(__VA_ARGS__)
void ERR() { cerr << endl; }
TES void ERR(T &&x, S &&...y) {
  cerr << x;
  if constexpr (sizeof...(S)) cerr << ", ";
  ERR(forward<S>(y)...);
}
#define err(...) cerr << "[" << __LINE__ << "]: ", ERR(__VA_ARGS__)
#define asser assert
#else
#define debug(...) void(0721)
#define err(...)   void(0721)
#define asser(...) void(0721)
#endif
#line 4 "No_40_\u591a\u9805\u5f0f\u306e\u5272\u308a\u7b97.cpp"
// #include "YRS/IO/fast_io.hpp"
// #include "YRS/random/rng.hpp"
#line 2 "YRS/po/all.hpp"

#line 2 "YRS/po/bs.hpp"

#line 2 "YRS/po/c/inte.hpp"

#line 2 "YRS/mod/modint.hpp"

#line 2 "YRS/mod/modint_common.hpp"

template <class T>
concept is_mint = requires(T x) {
  { T::get_mod() };
  { T::gen(0ull) } -> same_as<T>;
  x.val;
};
template <class mint>
concept has_const_mod =
    requires { integral_constant<int, (int)mint::get_mod()> {}; };

template <typename mint>
static vc<mint> &invs() {
  static vc<mint> a{0, 1};
  return a;
}
template <typename mint>
static vc<mint> &fac() {
  static vc<mint> a{1, 1};
  return a;
}
template <typename mint>
static vc<mint> &ifac() {
  static vc<mint> a{1, 1};
  return a;
}

template <typename mint>
static int Set_inv(int N) {
  static vc<mint> &inv = invs<mint>();
  if (len(inv) >= N) return N;
  inv.resize(N + 1);
  inv[0] = 1, inv[1] = 1;
  FOR(i, 1, N) inv[i + 1] = inv[i] * i;
  mint t = pop(inv).inv();
  FOR_R(i, N) inv[i] *= t, t *= i;
  return N;
}
template <typename mint>
static int Set_comb(int N) {
  static vector<mint> &fa = fac<mint>(), &ifa = ifac<mint>();
  if (len(fa) >= N) return N;
  fa.resize(N);
  ifa.resize(N);
  FOR(i, 1, N) fa[i] = fa[i - 1] * i;
  ifa[N - 1] = fa[N - 1].inv();
  FOR_R(i, N - 1) ifa[i] = ifa[i + 1] * (i + 1);
  return N;
}

template <typename mint>
mint inv(int n) {
  static const int mod = mint::get_mod();
  static vc<mint> &a = invs<mint>();
  assert(0 <= n);
  while (len(a) <= n) {
    int k = len(a);
    int q = (mod + k - 1) / k;
    int r = k * q - mod;
    a.ep(a[r] * mint(q));
  }
  return a[n];
}
template <typename mint>
mint fact(int n) {
  static const int mod = mint::get_mod();
  static vc<mint> &a = fac<mint>();
  assert(0 <= n);
  if (n >= mod) return 0;
  while (len(a) <= n) {
    int k = len(a);
    a.ep(a[k - 1] * mint(k));
  }
  return a[n];
}

template <typename mint>
mint fact_inv(int n) {
  static vc<mint> &a = ifac<mint>();
  if (n < 0) return mint(0);
  while (len(a) <= n)
    a.ep(a[len(a) - 1] * inv<mint>(len(a)));
  return a[n];
}

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

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

template <typename mint>
mint C_dense(int n, int k) {
  assert(n >= 0);
  if (k < 0 or n < k) return 0;
  static vc<vc<mint>> C;
  static int H = 0, W = 0;
  Z 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 (int i = 0; i < H; ++i) {
      C[i].resize(k + 1);
      for (int j = W; j < k + 1; ++j) {
        C[i][j] = calc(i, j);
      }
    }
    W = k + 1;
  }
  if (H <= n) {
    C.resize(n + 1);
    for (int i = H; i < n + 1; ++i) {
      C[i].resize(W);
      for (int j = 0; j < W; ++j) {
        C[i][j] = calc(i, j);
      }
    }
    H = n + 1;
  }
  return C[n][k];
}

template <typename mint>
mint C(int N, int K) {
  assert(N >= 0);
  if (K < 0 or N < K) return 0;
  return fact<mint>(N) * fact_inv<mint>(K) * fact_inv<mint>(N - K);
}

template <typename mint>
mint lucas(ll N, ll K) {
  static constexpr int P = mint::get_mod();
  if (K > N) return 0;
  if (K == 0) return 1;
  return C<mint>(N % P, K % P) * lucas<mint>(N / P, K / P);
}

template <typename mint, bool large = false, bool dense = false>
mint binom(ll n, ll k) {
  assert(n >= 0);
  if (k < 0 or n < k) return 0;
  if constexpr (dense) return C_dense<mint>(n, k);
  if constexpr (not 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 and k <= n);
  if (not large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);
  return mint(1) / binom<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 binom<mint, large, dense>(n + d - 1, d);
}

#define CC C<mint>
#define fac fact<mint>
#define ifac fact_inv<mint>
#define set_comb Set_comb<mint>
#define set_inv Set_inv<mint>
#line 4 "YRS/mod/modint.hpp"

#define M modint
#define C constexpr
template <int mod>
struct M {
  static C uint m = mod;
  uint val;

  C M() : val(0) {}
  C M(uint x) : val(x % m) {}
  C M(ull x) : val(x % m) {}
  C M(u128 x) : val(x % m) {}
  C M(int x) : val((x %= mod) < 0 ? x + mod : x) {}
  C M(ll x) : val((x %= mod) < 0 ? x + mod : x) {}
  C M(i128 x) : val((x %= mod) < 0 ? x + mod : x) {}

  C M &operator+=(M p) {
    if ((val += p.val) >= m) val -= m;
    return *this;
  }
  C M &operator-=(M p) {
    if ((val += m - p.val) >= m) val -= m;
    return *this;
  }
  C M operator+(M p) const { return M(*this) += p; }
  C M operator-(M p) const { return M(*this) -= p; }

  C M &operator*=(M p) {
    val = ull(val) * p.val % m;
    return *this;
  }
  C M operator*(M p) const { return M(*this) *= p; }

  C M &operator/=(M p) { return *this *= p.inv(); }
  C M operator/(M p) const { return M(*this) /= p; }

  C M operator-() const { return M::gen(val ? mod - val : 0); }

  C M inv() const {
    int a = val, b = mod, x = 1, y = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(x -= t * y, y);
    }
    return M(x);
  }

  C M pow(ll k) const {
    if (k < 0) return inv().pow(-k);
    M s(1), a(val);
    for (; k; k >>= 1, a *= a)
      if (k & 1) s *= a;
    return s;
  }

  C bool operator<(M p) const { return val < p.val; }
  C bool operator==(M p) const { return val == p.val; }
  C bool operator!=(M p) const { return val != p.val; }

  static C M gen(uint x) {
    M s;
    s.val = x;
    return s;
  }

  friend istream &operator>>(istream &is, M &p) {
    ll x;
    is >> x;
    p = x;
    return is;
  }
  friend ostream &operator<<(ostream &os, M p) { return os << p.val; }

  static C int get_mod() { return mod; }

  static C PII ntt_info() {
    if (mod == 167772161) return {25, 17};
    if (mod == 469762049) return {26, 30};
    if (mod == 754974721) return {24, 362};
    if (mod == 998244353) return {23, 31};
    if (mod == 120586241) return {20, 74066978};
    if (mod == 880803841) return {23, 211};
    if (mod == 943718401) return {22, 663003469};
    if (mod == 1004535809) return {21, 582313106};
    if (mod == 1012924417) return {21, 368093570};
    return {-1, -1};
  }
  
  static C bool can_ntt() { return ntt_info().fi != -1; }
};
#undef M
#undef C

using M99 = modint<998244353>;
using M17 = modint<1000000007>;

#ifdef FIO
template <int mod>
void rd(modint<mod> &x) {
  LL(y);
  x = y;
}
template <int mod>
void wt(modint<mod> x) {
  wt(x.val);
}
#endif
#line 4 "YRS/po/c/inte.hpp"

// 不定积分
template <typename mint>
vc<mint> inte(const vc<mint> &f) {
  int N = len(f);
  vc<mint> g(N + 1);
  FOR(i, 1, N + 1) g[i] = f[i - 1] * inv<mint>(i);
  return g;
}

// 定积分
template <typename mint>
mint inte(const vc<mint> &f, mint l, mint r) {
  mint s = 0, L = 1, R = 1;
  int N = len(f);
  FOR(i, N) {
    L *= l, R *= r;
    s += inv<mint>(i + 1) * f[i] * (L - R);
  }
  return s;
}
#line 2 "YRS/po/c/diff.hpp"

#line 4 "YRS/po/c/diff.hpp"

template <typename mint>
vc<mint> diff(const vc<mint> &f) {
  int N = len(f);
  if (N <= 1) return {};
  vc<mint> g(N - 1);
  FOR(i, N - 1) g[i] = f[i + 1] * mint(i + 1);
  return g;
}
#line 2 "YRS/po/convolution.hpp"

#line 2 "YRS/po/c/ntt.hpp"

#line 4 "YRS/po/c/ntt.hpp"

template <typename mint>
void ntt(vc<mint> &a, bool in) {
  assert(mint::can_ntt());
  constexpr int p = mint::ntt_info().fi;
  constexpr uint mod = mint::get_mod();
  static array<mint, 30> r, ir, ra, ira, rat, irat;
  assert(p != -1 and len(a) <= (1 << max(0, p)));
  static bool ok = 0;
  if (not ok) {
    ok = 1;
    r[p] = mint::ntt_info().se;
    ir[p] = mint(1) / r[p];
    FOR_R(i, p) {
      r[i] = r[i + 1] * r[i + 1];
      ir[i] = ir[i + 1] * ir[i + 1];
    }
    mint s = 1, in = 1;
    FOR(i, p - 1) {
      ra[i] = r[i + 2] * s;
      ira[i] = ir[i + 2] * in;
      s *= ir[i + 2];
      in *= r[i + 2];
    }
    s = 1, in = 1;
    FOR(i, p - 2) {
      rat[i] = r[i + 3] * s;
      irat[i] = ir[i + 3] * in;
      s *= ir[i + 3];
      in *= r[i + 3];
    }
  }

  int N = len(a), n = topbit(N);
  if (not in) {
    int sz = 0;
    while (sz < n) {
      if (n - sz == 1) {
        int p = 1 << (n - sz - 1);
        mint c = 1;
        FOR(s, 1 << sz) {
          int of = s << (n - sz);
          FOR(i, p) {
            mint l = a[i + of], r = a[i + of + p] * c;
            a[i + of] = l + r, a[i + of + p] = l - r;
          }
          c *= ra[topbit(~s & -~s)];
        }
        ++sz;
      } else {
        int p = 1 << (n - sz - 2);
        mint c = 1, in = r[2];
        FOR(s, 1 << sz) {
          mint r2 = c * c, r3 = r2 * c;
          int of = s << (n - sz);
          FOR(i, p) {
            constexpr ull m2 = ull(mod) * mod;
            ull a0 = a[i + of].val, a1 = ull(a[i + of + p].val) * c.val;
            ull a2 = ull(a[i + of + 2 * p].val) * r2.val;
            ull a3 = ull(a[i + of + 3 * p].val) * r3.val;
            ull t = (a1 + m2 - a3) % mod * in.val;
            ull na = m2 - a2;
            a[i + of] = a0 + a1 + a2 + a3;
            a[i + of + p] = a0 + a2 + m2 * 2 - a1 - a3;
            a[i + of + 2 * p] = a0 + na + t;
            a[i + of + 3 * p] = a0 + na + m2 - t;
          }
          c *= rat[topbit(~s & -~s)];
        }
        sz += 2;
      }
    }
  } else {
    mint c = mint(1) / mint(N);
    FOR(i, N) a[i] *= c;
    int sz = n;
    while (sz) {
      if (sz == 1) {
        int p = 1 << (n - sz);
        mint c = 1;
        FOR(s, 1 << (sz - 1)) {
          int of = s << (n - sz + 1);
          FOR(i, p) {
            ull l = a[i + of].val, r = a[i + of + p].val;
            a[i + of] = l + r;
            a[i + of + p] = (mod + l - r) * c.val;
          }
          c *= ira[topbit(~s & -~s)];
        }
        --sz;
      } else {
        int p = 1 << (n - sz);
        mint c = 1, in = ir[2];
        FOR(s, 1 << (sz - 2)) {
          mint r2 = c * c, r3 = r2 * c;
          int of = s << (n - sz + 2);
          FOR(i, p) {
            ull a0 = a[i + of].val, a1 = a[i + of + p].val;
            ull a2 = a[i + of + 2 * p].val;
            ull a3 = a[i + of + 3 * p].val;
            ull x = (mod + a2 - a3) * in.val % mod;
            a[i + of] = a0 + a1 + a2 + a3;
            a[i + of + p] = (a0 + mod - a1 + x) * c.val;
            a[i + of + 2 * p] = (a0 + a1 + 2 * mod - a2 - a3) * r2.val;
            a[i + of + 3 * p] = (a0 + 2 * mod - a1 - x) * r3.val;
          }
          c *= irat[topbit(~s & -~s)];
        }
        sz -= 2;
      }
    }
  }
}
#line 2 "YRS/mod/crt3.hpp"

constexpr uint pow_constexpr(ull a, ull b, uint mod) {
  a %= mod;
  ull res = 1;
  FOR(32) {
    if (b & 1) res = res * a % mod;
    a = a * a % mod, b >>= 1;
  }
  return res;
}

template <typename T, uint p0, uint p1>
T CRT2(ull a0, ull a1) {
  static_assert(p0 < p1);
  static constexpr ull x0_1 = pow_constexpr(p0, p1 - 2, p1);
  ull c = (a1 - a0 + p1) * x0_1 % p1;
  return a0 + c * p0;
}

template <typename T, uint p0, uint p1, uint p2>
T CRT3(ull a0, ull a1, ull a2) {
  static_assert(p0 < p1 and p1 < p2);
  static constexpr ull x1 = pow_constexpr(p0, p1 - 2, p1);
  static constexpr ull x2 = pow_constexpr(ull(p0) * p1 % p2, p2 - 2, p2);
  static constexpr ull p01 = ull(p0) * p1;
  ull c = (a1 - a0 + p1) * x1 % p1;
  ull ans_1 = a0 + c * p0;
  c = (a2 - ans_1 % p2 + p2) * x2 % p2;
  return T(ans_1) + T(c) * T(p01);
}

template <typename T, uint p0, uint p1, uint p2, uint p3>
T CRT4(ull a0, ull a1, ull a2, ull a3) {
  static_assert(p0 < p1 and p1 < p2 and p2 < p3);
  static constexpr ull x1 = pow_constexpr(p0, p1 - 2, p1);
  static constexpr ull x2 = pow_constexpr(ull(p0) * p1 % p2, p2 - 2, p2);
  static constexpr ull x3 = pow_constexpr(ull(p0) * p1 % p3 * p2 % p3, p3 - 2, p3);
  static constexpr ull p01 = ull(p0) * p1;
  ull c = (a1 - a0 + p1) * x1 % p1;
  ull 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, uint p0, uint p1, uint p2, uint p3, uint p4>
T CRT5(ull a0, ull a1, ull a2, ull a3, ull a4) {
  static_assert(p0 < p1 and p1 < p2 and p2 < p3 and p3 < p4);
  static constexpr ull x1 = pow_constexpr(p0, p1 - 2, p1);
  static constexpr ull x2 = pow_constexpr(ull(p0) * p1 % p2, p2 - 2, p2);
  static constexpr ull x3 = pow_constexpr(ull(p0) * p1 % p3 * p2 % p3, p3 - 2, p3);
  static constexpr ull x4 = pow_constexpr(ull(p0) * p1 % p4 * p2 % p4 * p3 % p4, p4 - 2, p4);
  static constexpr ull p01 = ull(p0) * p1;
  static constexpr ull p23 = ull(p2) * p3;
  ull c = (a1 - a0 + p1) * x1 % p1;
  ull 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<ull>(a3 - ans_2 % p3 + p3) * x3 % p3;
  u128 ans_3 = ans_2 + static_cast<u128>(c * p2) * p01;
  c = static_cast<ull>(a4 - ans_3 % p4 + p4) * x4 % p4;
  return T(ans_3) + T(c) * T(p01) * T(p23);
}
#line 5 "YRS/po/convolution.hpp"

template <typename mint>
vc<mint> conv_naive(const vc<mint> &a, const vc<mint> &b) {
  int N = len(a), M = len(b), sz = N + M - 1;
  if (not N or not M) return {};
  if (N > M) return conv_naive(b, a);
  vc<mint> c(sz);
  FOR(i, N) FOR(k, M) c[i + k] += a[i] * b[k];
  return c;
}

template <typename mint>
vc<mint> conv_ntt(vc<mint> a, vc<mint> b) {
  static_assert(mint::can_ntt());
  if (a.empty() or b.empty()) return {};
  int N = len(a), M = len(b), sz = 1;
  while (sz < N + M - 1) sz <<= 1;
  sh(a, sz), sh(b, sz);
  bool ok = a == b;
  ntt(a, 0);
  if (ok) b = a;
  else ntt(b, 0);
  FOR(i, sz) a[i] *= b[i];
  ntt(a, 1);
  sh(a, N + M - 1);
  return a;
}

template <typename mint>
vc<mint> conv_mtt(const vc<mint> &a, const vc<mint> &b) {
  int N = len(a), M = len(b);
  if (not N or not M) return {};
  static constexpr int p0 = 167772161;
  static constexpr int p1 = 469762049;
  static constexpr int p2 = 754974721;
  using M0 = modint<p0>;
  using M1 = modint<p1>;
  using M2 = modint<p2>;
  vc<M0> a0(N), b0(M);
  vc<M1> a1(N), b1(M);
  vc<M2> 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;
  vc<M0> c0 = conv_ntt<M0>(a0, b0);
  vc<M1> c1 = conv_ntt<M1>(a1, b1);
  vc<M2> c2 = conv_ntt<M2>(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;
}

template <typename mint>
vc<mint> convolution(const vc<mint> &a, const vc<mint> &b) {
  int N = len(a), M = len(b);
  if (not N or not M) return {};
  if (min(N, M) <= 30) return conv_naive(a, b);
  if constexpr (mint::can_ntt()) return conv_ntt(a, b);
  return conv_mtt(a, b);
}
#line 6 "YRS/po/bs.hpp"

template <typename mint>
vc<mint> &operator+=(vc<mint> &a, const vc<mint> &b) {
  int N = len(b);
  if (N > len(a)) sh(a, N);
  FOR(i, N) a[i] += b[i];
  return a;
}
template <typename mint>
vc<mint> operator+(const vc<mint> &a, const vc<mint> &b) {
  vc<mint> c(a);
  return c += b;
}
template <typename mint>
vc<mint> &operator-=(vc<mint> &a, const vc<mint> &b) {
  int N = len(b);
  if (N > len(a)) sh(a, N);
  FOR(i, N) a[i] -= b[i];
  return a;
}
template <typename mint>
vc<mint> operator-(const vc<mint> &a, const vc<mint> &b) {
  vc<mint> c(a);
  return c -= b;
}
template <typename mint>
vc<mint> operator*(const vc<mint> &a, const vc<mint> &b) {
  return convolution(a, b);
}

#define D_poly() vc<mint> operator"" _p(ull x) { return vc<mint>{x}; } vc<mint> operator"" _p(const char *s, size_t le) {vc<mint> res;int sgn = 1, op = 0, coef = 0, ch = 0, sz = le;ll x = 0;Z re = [&](int i) {if (len(res) <= i) res.resize(i + 1);};Z cl = [&]() {if (op == -1) re(1), res[1] += sgn * coef;else if (op == 0) re(0), res[0] += sgn * (int)x;else if (op == 1) re(x), res[x] += sgn * coef;else assert(0);op = 0, x = 0, ch = 0;};FOR(i, sz) {if (s[i] == '+') cl(), sgn = 1;else if (s[i] == '-') cl(), sgn = -1;else if (isdigit(s[i])) {assert(op == 0 or op == 1);if (op == 0) ch = 1, x = (x * 10ll + s[i] - 48) % mint::get_mod();else x = x * 10ll + s[i] - 48, assert(x < 1e8);} else if (s[i] == 'x') {assert(s[i + 1] == '^' or s[i + 1] == '+' or s[i + 1] == '-' or s[i + 1] == 0);op = -1;coef = ch ? x : 1;x = 0;} else if (s[i] == '^') {assert(op == -1);op = 1;}}cl();return res; }
#line 2 "YRS/po/fps_inv.hpp"

#line 2 "YRS/po/c/count_terms.hpp"

// 非 0 数量
template<typename mint>
int count_terms(const vc<mint> &f){
  int t = 0, N = len(f);
  FOR(i, N) if(f[i] != mint(0)) ++t;
  return t;
}
#line 5 "YRS/po/fps_inv.hpp"

// O(NK)
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.ep(i, f[i]);
  vc<mint> g(N);
  mint t = mint(1) / f[0];
  g[0] = t;
  FOR(i, 1, N) {
    mint s = 0;
    for (Z &&[x, y] : dat) {
      if (x > i) break;
      s -= y * g[i - x];
    }
    g[i] = s * t;
  }
  return g;
}

template <typename mint>
vc<mint> fps_inv_dense_ntt(const vc<mint> &a) {
  vc<mint> s{mint(1) / a[0]};
  int N = len(a), n = 1;
  s.reserve(N);
  for (; n < N; n <<= 1) {
    vc<mint> f(n << 1), g(n << 1);
    int L = min(N, n << 1);
    FOR(i, L) f[i] = a[i];
    FOR(i, n) g[i] = s[i];
    ntt(f, 0);
    ntt(g, 0);
    FOR(i, n << 1) f[i] *= g[i];
    ntt(f, 1);
    FOR(i, n) f[i] = 0;
    ntt(f, 0);
    FOR(i, n << 1) f[i] *= g[i];
    ntt(f, 1);
    FOR(i, n, L) s.ep(-f[i]);
  }
  return s;
}

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

template <typename mint>
vc<mint> fps_inv(const vc<mint> &f) {
  assert(f[0] != mint(0));
  int sz = count_terms(f), c = mint::can_ntt() ? 160 : 820;
  return sz <= c ? fps_inv_sparse(f) : fps_inv_dense(f);
}
#line 2 "YRS/po/fps_exp.hpp"

#line 7 "YRS/po/fps_exp.hpp"

template <typename mint>
vc<mint> fps_exp_sparse(const vc<mint> &f) {
  int N = len(f);
  if (N == 0) return {mint(1)};
  assert(f[0] == 0);
  vc<pair<int, mint>> dat;
  FOR(i, 1, N) if (f[i] != mint(0)) dat.ep(i - 1, f[i] * mint(i));
  vc<mint> F(N);
  F[0] = 1;
  FOR(i, 1, N) {
    mint s = 0;
    for (Z [x, y] : dat) {
      if (x > i - 1) break;
      s += y * F[i - 1 - x];
    }
    F[i] = s * inv<mint>(i);
  }
  return F;
}

template <typename mint>
vc<mint> fps_exp_ntt(const vc<mint> &f) {
  int N = len(f);
  assert(N > 0 and f[0] == mint(0));
  vc<mint> s{1, (1 < N ? f[1] : 0)}, c{1}, a, b{1, 1};
  while (len(s) < N) {
    int m = len(s);
    Z y = s;
    sh(y, m << 1);
    ntt(y, 0);
    a = b;
    vc<mint> z(m);
    FOR(i, m) z[i] = y[i] * a[i];
    ntt(z, 1);
    FOR(i, m >> 1) z[i] = 0;
    ntt(z, 0);
    FOR(i, m) z[i] *= -a[i];
    ntt(z, 1);
    // FOR(i, m >> 1, m) c.ep(z[i]);
    c.insert(c.end(), z.begin() + m / 2, z.end());
    b = c;
    sh(b, m << 1);
    ntt(b, 0);

    vc<mint> x(f.begin(), f.begin() + m);
    FOR(i, m - 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] -= s[i + 1] * mint(i + 1);

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

    FOR(i, m, min(N, m << 1)) x[i] += f[i];
    FOR(i, m) x[i] = 0;
    ntt(x, 0);
    FOR(i, m << 1) x[i] *= y[i];
    ntt(x, 1);
    s.insert(s.end(), x.begin() + m, x.end());
  }
  sh(s, N);
  return s;
}

template <typename mint>
vc<mint> fps_exp_dense(const vc<mint> &e) {
  if constexpr (mint::can_ntt()) return fps_exp_ntt(e);
  vc<mint> h = e;
  int N = len(h);
  assert(N > 0 and h[0] == mint(0));
  int log = 0;
  while (1 << log < N) ++log;
  h.resize(1 << log);
  Z dh = diff(h);
  vc<mint> f = {1}, g = {1};
  int m = 1;
  vc<mint> p;
  FOR(log) {
    p = f * g;
    sh(p, m);
    p = p * g;
    sh(p, m);
    sh(g, m);
    FOR(i, m) g[i] += g[i] - p[i];

    p = {dh.begin(), dh.begin() + m - 1};
    p = f * p;
    sh(p, 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 = p * g;
    sh(p, m + m - 1);
    FOR(i, m - 1) p[i] += dh[i];
    p = inte(p);
    FOR(i, m + m) p[i] = h[i] - p[i];
    p[0] += mint(1);
    f = f * p;
    sh(f, m << 1);
    m <<= 1;
  }
  sh(f, N);
  return f;
}

template <typename mint>
vc<mint> fps_exp(const vc<mint> &f) {
  int n = count_terms(f), t = mint::can_ntt() ? 320 : 3000;
  return n <= t ? fps_exp_sparse(f) : fps_exp_dense(f);
}
#line 2 "YRS/po/fps_log.hpp"

#line 2 "YRS/po/fps_div.hpp"

#line 5 "YRS/po/fps_div.hpp"

template <typename mint>
vc<mint> fps_div_sprase(vc<mint> f, vc<mint> g) {
  if (g[0] != mint(1)) {
    mint c = g[0].inv();
    for (Z &x : f) x *= c;
    for (Z &x : g) x *= c;
  }
  vc<pair<int, mint>> dat;
  int N = len(g);
  FOR(i, 1, N) if (g[i] != mint(0)) dat.ep(i, -g[i]);
  N = len(f);
  FOR(i, N) for (Z [x, y] : dat) if (i >= x) f[i] += y * f[i - x];
  return f;
}

template <typename mint>
vc<mint> fps_div_dense_ntt(const vc<mint> &f, const vc<mint> &g) {
  int N = len(f), M = len(g);
  if (N == 1) return {f[0] / g[0]};
  int m = 1;
  while (m + m < N) m <<= 1;
  vc<mint> gs(g), a(m << 1), b(m << 1);
  sh(gs, m);
  gs = fps_inv(gs);
  sh(gs, m << 1);
  ntt(gs, 0);

  FOR(i, m) a[i] = f[i];
  FOR(i, m, N) a[i] = 0;
  ntt(a, 0);
  FOR(i, m << 1) a[i] *= gs[i];
  ntt(a, 1);

  vc<mint> s(N);
  FOR(i, m) s[i] = a[i];
  FOR(i, m, m << 1) a[i] = 0;
  ntt(a, 0);

  FOR(i, min(m << 1, M)) b[i] = g[i];
  FOR(i, min(m << 1, M), m << 1) b[i] = 0;
  ntt(b, 0);
  FOR(i, m << 1) a[i] *= b[i];
  ntt(a, 1);

  FOR(i, m) a[i] = 0;
  FOR(i, m, min(m << 1, N)) a[i] -= f[i];
  ntt(a, 0);
  FOR(i, m << 1) a[i] *= gs[i];
  ntt(a, 1);
  FOR(i, m, N) s[i] -= a[i];
  return s;
}
// f/g 截断的商
template <typename mint>
vc<mint> fps_div_dense(vc<mint> f, vc<mint> g) {
  int N = len(f);
  g.resize(N);
  g = fps_inv(g);
  f = convolution(f, g);
  f.resize(N);
  return f;
}

template <typename mint>
vc<mint> fps_div(const vc<mint> &f, const vc<mint> &g) {
  if (count_terms(f) < 100) return fps_div_sprase(f, g);
  if constexpr (mint::can_ntt()) return fps_div_dense_ntt(f, g);
  return fps_div_dense(f, g);
}
#line 5 "YRS/po/fps_log.hpp"

template <typename mint>
vc<mint> fps_log_sparse(const vc<mint> &a) {
  int N = len(a);
  vc<pair<int, mint>> dat;
  FOR(i, 1, N) if (a[i] != mint(0)) dat.ep(i, a[i]);
  vc<mint> f(N), g(N - 1);
  FOR(i, N - 1) {
    mint s = a[i + 1] * mint(i + 1);
    for (Z &&[x, y] : dat) {
      if (x > i) break;
      s -= y * g[i - x];
    }
    g[i] = s;
    f[i + 1] = s * inv<mint>(i + 1);
  }
  return f;
}

template <typename mint>
vc<mint> fps_log_dense(const vc<mint> &f) {
  assert(f[0] == mint(1));
  int N = len(f);
  vc<mint> fs(f);
  FOR(i, N) fs[i] *= i;
  fs = fps_div_dense_ntt(fs, f);
  FOR(i, N) fs[i] *= inv<mint>(i);
  return fs;
}

template <typename mint>
vc<mint> fps_log(const vc<mint> &f) {
  assert(f[0] == mint(1));
  int n = count_terms(f), t = mint::can_ntt() ? 200 : 1200;
  return n <= t ? fps_log_sparse(f) : fps_log_dense(f);
}
#line 2 "YRS/po/fps_pow.hpp"

#line 5 "YRS/po/fps_pow.hpp"

template <typename mint>
vc<mint> fps_pw_sparse(const vc<mint> &f, mint k) {
  int N = len(f);
  assert(N == 0 or f[0] == mint(1));
  vc<pair<int, mint>> dat;
  FOR(i, 1, N) if (f[i] != mint(0)) dat.ep(i, f[i]);
  vc<mint> g(N);
  g[0] = 1;
  FOR(i, N - 1) {
    mint &s = g[i + 1];
    for (Z &&[x, y] : dat) {
      if (x > i + 1) break;
      mint t = y * g[i - x + 1];
      s += t * (k * mint(x) - mint(i - x + 1));
    }
    s *= inv<mint>(i + 1);
  }
  return g;
}

template <typename mint>
vc<mint> fps_pw_dense(const vc<mint> &f, mint k) {
  assert(f[0] == mint(1));
  Z g = fps_log(f);
  int N = len(f);
  FOR(i, N) g[i] *= k;
  return fps_exp_dense(g);
}

template <typename mint>
vc<mint> fps_pw(const vc<mint> &f, mint k) {
  int n = count_terms(f), t = mint::can_ntt() ? 100 : 1300;
  return n <= t ? fps_pw_sparse(f, k) : fps_pw_dense(f, k);
}

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] = 1;
    return g;
  }
  if (f[0] == mint(1)) return fps_pw(f, mint(k));
  int d = N;
  FOR_R(i, N) if (f[i] != mint(0)) d = i;
  if (d >= ceil<ll>(N, k)) return vc<mint>(N);
  int of = d * k;
  mint c = f[d], in = mint(1) / c;
  vc<mint> g(N - of);
  FOR(i, N - of) g[i] = f[d + i] * in;
  g = fps_pw(g, mint(k));
  vc<mint> r(N);
  c = c.pow(k);
  N = len(g);
  FOR(i, N) r[of + i] = g[i] * c;
  return r;
}
#line 2 "YRS/po/conv_all.hpp"

#line 2 "YRS/po/c/ntt_db.hpp"

#line 2 "YRS/po/c/transposed_ntt.hpp"

template <typename mint>
void transposed_ntt(vc<mint> &a, bool in) {
  static_assert(mint::can_ntt());
  constexpr int p = mint::ntt_info().fi;
  constexpr uint mod = mint::get_mod();
  static array<mint, 30> r, ir, rt, irt, rat, irat;

  assert(p != -1 and len(a) <= (1 << max(0, p)));

  static bool ok = 0;
  if (not ok) {
    ok = 1;
    r[p] = mint::ntt_info().se;
    ir[p] = mint(1) / r[p];
    FOR_R(i, p) {
      r[i] = r[i + 1] * r[i + 1];
      ir[i] = ir[i + 1] * ir[i + 1];
    }
    mint s = 1, in = 1;
    FOR(i, p - 1) {
      rt[i] = r[i + 2] * s;
      irt[i] = ir[i + 2] * in;
      s *= ir[i + 2];
      in *= r[i + 2];
    }
    s = 1, in = 1;
    FOR(i, p - 2) {
      rat[i] = r[i + 3] * s;
      irat[i] = ir[i + 3] * in;
      s *= ir[i + 3];
      in *= r[i + 3];
    }
  }

  int N = len(a), n = topbit(N);
  assert(N == 1 << n);
  if (not in) {
    int sz = n;
    while (sz > 0) {
      if (sz == 1) {
        int p = 1 << (n - sz);
        mint c = 1;
        FOR(s, 1 << (sz - 1)) {
          int of = s << (n - sz + 1);
          FOR(i, p) {
            ull l = a[i + of].val, r = a[i + of + p].val;
            a[i + of] = l + r, a[i + of + p] = (mod + l - r) * c.val;
          }
          c *= rt[topbit(~s & -~s)];
        }
        --sz;
      } else {
        int p = 1 << (n - sz);
        mint c = 1, in = r[2];
        FOR(s, 1 << (sz - 2)) {
          int of = s << (n - sz + 2);
          mint r2 = c * c, r3 = r2 * c;
          FOR(i, p) {
            ull a0 = a[i + of + 0 * p].val;
            ull a1 = a[i + of + 1 * p].val;
            ull a2 = a[i + of + 2 * p].val;
            ull a3 = a[i + of + 3 * p].val;
            ull x = (mod + a2 - a3) * in.val % mod;
            a[i + of] = a0 + a1 + a2 + a3;
            a[i + of + 1 * p] = (a0 + mod - a1 + x) * c.val;
            a[i + of + 2 * p] = (a0 + a1 + 2 * mod - a2 - a3) * r2.val;
            a[i + of + 3 * p] = (a0 + 2 * mod - a1 - x) * r3.val;
          }
          c *= rat[topbit(~s & -~s)];
        }
        sz -= 2;
      }
    }
  } else {
    mint c = mint(1) / mint(len(a));
    FOR(i, len(a)) a[i] *= c;
    int sz = 0;
    while (sz < n) {
      if (sz == n - 1) {
        int p = 1 << (n - sz - 1);
        mint c = 1;
        FOR(s, 1 << sz) {
          int of = s << (n - sz);
          FOR(i, p) {
            mint l = a[i + of], r = a[i + of + p] * c;
            a[i + of] = l + r, a[i + of + p] = l - r;
          }
          c *= irt[topbit(~s & -~s)];
        }
        ++sz;
      } else {
        int p = 1 << (n - sz - 2);
        mint c = 1, in = ir[2];
        FOR(s, 1 << sz) {
          mint r2 = c * c, r3 = r2 * c;
          int of = s << (n - sz);
          FOR(i, p) {
            ull m2 = ull(mod) * mod;
            ull a0 = a[i + of].val;
            ull a1 = ull(a[i + of + p].val) * c.val;
            ull a2 = ull(a[i + of + 2 * p].val) * r2.val;
            ull a3 = ull(a[i + of + 3 * p].val) * r3.val;
            ull t = (a1 + m2 - a3) % mod * in.val;
            ull na = m2 - a2;
            a[i + of] = a0 + a1 + a2 + a3;
            a[i + of + 1 * p] = a0 + a2 + (2 * m2 - a1 - a3);
            a[i + of + 2 * p] = a0 + na + t;
            a[i + of + 3 * p] = a0 + na + m2 - t;
          }
          c *= irat[topbit(~s & -~s)];
        }
        sz += 2;
      }
    }
  }
}
#line 5 "YRS/po/c/ntt_db.hpp"

template <typename mint, bool transposed = false>
void ntt_db(vc<mint> &a) {
  static array<mint, 30> rt;
  static bool ok = 0;
  if (not ok) {
    ok = 1;
    constexpr int s = mint::ntt_info().fi;
    rt[s] = mint::ntt_info().se;
    FOR_R(i, s) rt[i] = rt[i + 1] * rt[i + 1];
  }
  if constexpr (not transposed) {
    int N = len(a);
    Z b = a;
    ntt(b, 1);
    mint r = 1, z = rt[topbit(N << 1)];
    FOR(i, N) b[i] *= r, r *= z;
    ntt(b, 0);
    copy(all(b), std::back_inserter(a));
  } else {
    int N = len(a) >> 1;
    vc<mint> t{a.begin(), a.begin() + N};
    a = {a.begin() + N, a.end()};
    transposed_ntt(a, 0);
    mint r = 1, z = rt[topbit(N << 1)];
    FOR(i, N) a[i] *= r, r *= z;
    transposed_ntt(a, 1);
    FOR(i, N) a[i] += t[i];
  }
}
#line 5 "YRS/po/conv_all.hpp"

// O(Nlog^2N) 总度数为 N ，即使fi度数很低，logfi度数也可能很大，试图用exp|log算会变成 NMlogN
template <typename mint>
vc<mint> conv_all(vc<vc<mint>> &f) {
  if (f.empty()) return {{mint(1)}};
  while (1) {
    int N = len(f);
    if (N == 1) break;
    int m = (N + 1) >> 1;
    FOR(i, m) {
      if (i + i + 1 == N) f[i] = f[i << 1];
      else f[i] = f[i << 1] * f[i << 1 | 1];
    }
    sh(f, m);
  }
  return f[0];
}

// product 1 - f[i]x
template <typename mint>
vc<mint> conv_all_1(vc<mint> f) {
  if constexpr (not mint::can_ntt()) {
    vc<vc<mint>> g;
    for (Z &x : f) g.ep(vc<mint>({mint(1), -x}));
    return conv_all(g);
  }
  int D = 6, N = 1, sz = len(f);
  while (N < sz) N <<= 1;
  int k = topbit(N);
  vc<mint> F(N), nx(N);
  FOR(i, sz) F[i] = -f[i];
  FOR(d, k) {
    int b = 1 << d;
    if (d < D) {
      fill(all(nx), mint(0));
      FOR(L, 0, N, b << 1)  {
        FOR(i, b) FOR(j, b) nx[L + i + j] += F[L + i] * F[L + b + j];
        FOR(i, b) nx[L + b + i] += F[L + i] + F[L + b + i];
      }
    } else if (d == D) {
      FOR(L, 0, N, b << 1) {
        vc<mint> f1 = {F.begin() + L, F.begin() + L + b};
        vc<mint> f2 = {F.begin() + L + b, F.begin() + L + 2 * b};
        sh(f1, b << 1), sh(f2, b << 1);
        ntt(f1, 0), ntt(f2, 0);
        FOR(i, b) nx[L + i] = f1[i] * f2[i] + f1[i] + f2[i];
        FOR(i, b, b << 1) nx[L + i] = f1[i] * f2[i] - f1[i] - f2[i];
      }
    } else {
      FOR(L, 0, N, b << 1) {
        vc<mint> f1 = {F.begin() + L, F.begin() + L + b};
        vc<mint> f2 = {F.begin() + L + b, F.begin() + L + 2 * b};
        ntt_db(f1), ntt_db(f2);
        FOR(i, b) nx[L + i] = f1[i] * f2[i] + f1[i] + f2[i];
        FOR(i, b, b << 1) nx[L + i] = f1[i] * f2[i] - f1[i] - f2[i];
      }
    }
    swap(F, nx);
  }
  if (k - 1 >= D) ntt(F, 1);
  F.ep(1), reverse(all(F));
  sh(F, sz + 1);
  return F;
}
#line 2 "YRS/po/poly_divmod.hpp"

#line 4 "YRS/po/poly_divmod.hpp"

template <typename mint>
pair<vc<mint>, vc<mint>> poly_divmod(vc<mint> f, vc<mint> g) {
  assert(g.back() != 0);
  int N = len(f), M = len(g);
  if (N < M) return {{}, f};
  vc<mint> ff = f, gg = g;
  reverse(ff);
  reverse(gg);
  int d = N - M + 1;
  sh(ff, d);
  sh(gg, d);
  gg = fps_inv(gg);
  vc<mint> q = ff * gg;
  q.resize(d);
  reverse(q);
  vc<mint> c = q * g;
  FOR(i, N) f[i] -= c[i];
  while (not f.empty() and f.back() == 0) f.pop_back();
  return {q, f};
}
#line 8 "No_40_\u591a\u9805\u5f0f\u306e\u5272\u308a\u7b97.cpp"

#define tests 0
#define fl 0
#define DB 10
using mint = M99;
using fps = vc<mint>;
D_poly()
void Yorisou() {
  INT(N);
  VEC(mint, f, N + 1);
  Z [_, g] = poly_divmod(f, "x^3-x"_p);
  if (g.empty()) g = {0};
  vc<int> res;
  for (mint &x : g) res.ep(x.val > 1000000 ? -(-x).val : x.val);
  print(len(res) - 1);
  print(res);
}
#line 1 "YRS/aa/main.hpp"
int main() {
  cin.tie(nullptr)->sync_with_stdio(false);
  int T = 1;
  if (fl) cerr.tie(0);
  if (tests and not fl) IN(T);
  for (int i = 0; i < T or fl; ++i) {
    Yorisou();
    if (fl and i % DB == 0) cerr << "Case: " << i << '\n';
  }
  return 0;
}
#line 26 "No_40_\u591a\u9805\u5f0f\u306e\u5272\u308a\u7b97.cpp"