#if defined(__GNUC__)
#include <bits/allocator.h>
#pragma GCC optimize("Ofast,unroll-loops")
#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__))))
#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
template <typename T>
T ceil(T x, T y) {
  return (x / y) + (x % y > 0);
}
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;
}();
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end())
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;
}
#define FASTIO
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
uint32_t pil = 0, pir = 0, por = 0;
bool input_eof = false;
template <class T>
constexpr bool is_signed_integer_v = is_signed_v<T> || is_same_v<T, i128>;
template <class T>
struct unsigned_integer {
  using type = make_unsigned_t<T>;
};
template <>
struct unsigned_integer<i128> {
  using type = u128;
};
template <>
struct unsigned_integer<u128> {
  using type = u128;
};
template <class T>
using unsigned_integer_t = typename unsigned_integer<T>::type;
[[noreturn]] inline void input_error(const char *message) {
  fputs(message, stderr);
  fputc('\n', stderr);
  exit(EXIT_FAILURE);
}
struct Pre {
  char num[10000][4];
  constexpr Pre() : num() {
    for (int i = 0; i < 10000; i++) {
      int n = i;
      for (int j = 3; j >= 0; j--) {
        num[i][j] = n % 10 | '0';
        n /= 10;
      }
    }
  }
} constexpr pre;
inline void load() {
  uint32_t n = pir - pil;
  memmove(ibuf, ibuf + pil, n);
  pil = 0;
  pir = n;
  if (input_eof) return;
  pir += fread(ibuf + pir, 1, SZ - pir, stdin);
  if (ferror(stdin)) input_error("fastio: input error");
  if (feof(stdin)) {
    input_eof = true;
    if (pir < SZ) ibuf[pir++] = '\n';
  }
}
inline char get_char() {
  if (pil == pir) {
    load();
    if (pil == pir) input_error("fastio: unexpected EOF");
  }
  return ibuf[pil++];
}
inline void flush() {
  fwrite(obuf, 1, por, stdout);
  por = 0;
}
void rd(char &c) {
  do c = get_char();
  while (isspace(static_cast<unsigned char>(c)));
}
void rd(string &x) {
  x.clear();
  char c;
  do c = get_char();
  while (isspace(static_cast<unsigned char>(c)));
  do {
    x += c;
    c = get_char();
  } while (!isspace(static_cast<unsigned char>(c)));
}
template <typename T>
void rd_real(T &x) {
  string s;
  rd(s);
  x = stod(s);
}
template <typename T>
void rd_integer_slow(T &x) {
  char c;
  do c = get_char();
  while (c < '-');
  bool minus = 0;
  if constexpr (is_signed_integer_v<T>) {
    if (c == '-') {
      minus = 1, c = get_char();
    }
  }
  x = 0;
  assert('0' <= c && c <= '9');
  while ('0' <= c && c <= '9') {
    x = x * 10 + (c & 15), c = get_char();
  }
  assert(isspace(static_cast<unsigned char>(c)));
  if constexpr (is_signed_integer_v<T>) {
    if (minus) x = -x;
  }
}
template <typename T>
void rd_integer(T &x) {
  if (pil + 100 > pir) {
    load();
    if (pil + 100 > pir) {
      rd_integer_slow(x);
      return;
    }
  }
  char c;
  do c = ibuf[pil++];
  while (c < '-');
  bool minus = 0;
  if constexpr (is_signed_integer_v<T>) {
    if (c == '-') {
      minus = 1, c = ibuf[pil++];
    }
  }
  x = 0;
  assert('0' <= c && c <= '9');
  while ('0' <= c && c <= '9') {
    x = x * 10 + (c & 15), c = ibuf[pil++];
  }
  assert(isspace(static_cast<unsigned char>(c)));
  if constexpr (is_signed_integer_v<T>) {
    if (minus) x = -x;
  }
}
template <class T>
enable_if_t<is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>> rd(
    T &x) {
  rd_integer(x);
}
template <class T>
enable_if_t<is_floating_point_v<T> || is_same_v<T, f128>> rd(T &x) {
  rd_real(x);
}
template <class T, class U>
void rd(pair<T, U> &p) {
  rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
  if constexpr (N < tuple_size<T>::value) {
    auto &x = get<N>(t);
    rd(x);
    rd_tuple<N + 1>(t);
  }
}
template <class... T>
void rd(tuple<T...> &tpl) {
  rd_tuple(tpl);
}
template <class T, size_t N>
void rd(array<T, N> &x) {
  for (auto &d : x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
  for (auto &d : x) rd(d);
}
template <class... T>
void read(T &...x) {
  (rd(x), ...);
}
inline void wt_range(const char *s, size_t n) {
  size_t i = 0;
  while (i < n) {
    if (por == SZ) flush();
    size_t chunk = min(n - i, (size_t)(SZ - por));
    memcpy(obuf + por, s + i, chunk);
    por += chunk;
    i += chunk;
  }
}
void wt(const char c) {
  if (por == SZ) flush();
  obuf[por++] = c;
}
void wt(const char *s) { wt_range(s, strlen(s)); }
void wt(const string &s) { wt_range(s.data(), s.size()); }
template <typename T>
void wt_integer(T x) {
  if (por > SZ - 100) flush();
  using U = unsigned_integer_t<T>;
  U y = static_cast<U>(x);
  if constexpr (is_signed_integer_v<T>) {
    if (x < 0) {
      obuf[por++] = '-';
      y = U(0) - y;
    }
  }
  int outi;
  for (outi = 96; y >= 10000; outi -= 4) {
    memcpy(out + outi, pre.num[y % 10000], 4);
    y /= 10000;
  }
  if (y >= 1000) {
    memcpy(obuf + por, pre.num[y], 4);
    por += 4;
  } else if (y >= 100) {
    memcpy(obuf + por, pre.num[y] + 1, 3);
    por += 3;
  } else if (y >= 10) {
    int q = (y * 103) >> 10;
    obuf[por] = q | '0';
    obuf[por + 1] = (y - q * 10) | '0';
    por += 2;
  } else
    obuf[por++] = y | '0';
  memcpy(obuf + por, out + outi + 4, 96 - outi);
  por += 96 - outi;
}
template <typename T>
inline void wt_real(T x) {
  static char buf[1000];
  int n = std::snprintf(buf, sizeof(buf), "%.15f", (double)x);
  wt_range(buf, (size_t)n);
}
template <class T>
enable_if_t<is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>> wt(
    T x) {
  wt_integer(x);
}
template <class T>
enable_if_t<is_floating_point_v<T> || is_same_v<T, f128>> wt(T x) {
  wt_real(x);
}
inline void wt(bool b) { wt(static_cast<char>('0' + (b ? 1 : 0))); }
template <class T, class U>
void wt(const pair<T, U> &val) {
  wt(val.first);
  wt(' ');
  wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T &t) {
  if constexpr (N < tuple_size<T>::value) {
    if constexpr (N > 0) wt(' ');
    wt(get<N>(t));
    wt_tuple<N + 1>(t);
  }
}
template <class... T>
void wt(const tuple<T...> &tpl) {
  wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> &val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}
template <class T>
void wt(const vector<T> &val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}
void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&...tail) {
  wt(forward<Head>(head));
  ((wt(' '), wt(forward<Tail>(tail))), ...);
  wt('\n');
}
}                     
using fastio::flush;
using fastio::print;
using fastio::read;
#define SHOW(...)
#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define U32(...)   \
  u32 __VA_ARGS__; \
  read(__VA_ARGS__)
#define U64(...)   \
  u64 __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)   \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__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)
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)); }
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 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; }
};
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 <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 <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; }
  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;
}
template <int mod>
void wt(modint<mod> x) {
  fastio::wt(x.val);
}
#endif
using modint107 = modint<1000000007>;
using modint998 = modint<998244353>;
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 <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;
}
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;
}                                      
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;
      }
    }
  }
}
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;
  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);
}                            
template <typename mint>
vc<mint> powertable_1(mint a, ll N) {
  vc<mint> f(N + 1, 1);
  FOR(i, N) f[i + 1] = a * f[i];
  return f;
}
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;
}
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;
      }
    }
  }
}
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);
  {
    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 {};
  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);
}
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;
}                              
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;
}                            
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));
}
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;
}
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;
}                        
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;
}
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;
}                          
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_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));
}
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));
}
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);
  {
    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) {
    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;
    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;
}
template <typename mint>
vc<mint> power_projection_0_garner(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;
  f.resize(n), wt.resize(n);
  reverse(all(wt));
  constexpr u32 p[] = {167772161, 469762049, 754974721};
  using mint0 = modint<p[0]>;
  using mint1 = modint<p[1]>;
  using mint2 = modint<p[2]>;
  vc<mint0> W0(2 * n);
  vc<mint1> W1(2 * n);
  vc<mint2> W2(2 * n);
  {
    vc<int> btr(2 * n);
    int log = topbit(2 * n);
    FOR(i, 2 * n) { btr[i] = (btr[i >> 1] >> 1) + ((i & 1) << (log - 1)); }
    {
      int t = mint0::ntt_info().fi;
      mint0 r = mint0::ntt_info().se;
      mint0 dw = r.inverse().pow((1 << t) / (4 * n));
      mint0 w = 1;
      for (auto& i: btr) { W0[i] = w, w *= dw; }
    }
    {
      int t = mint1::ntt_info().fi;
      mint1 r = mint1::ntt_info().se;
      mint1 dw = r.inverse().pow((1 << t) / (4 * n));
      mint1 w = 1;
      for (auto& i: btr) { W1[i] = w, w *= dw; }
    }
    {
      int t = mint2::ntt_info().fi;
      mint2 r = mint2::ntt_info().se;
      mint2 dw = r.inverse().pow((1 << t) / (4 * n));
      mint2 w = 1;
      for (auto& i: btr) { W2[i] = w, w *= dw; }
    }
  }
  int k = 1;
  vc<mint> P(2 * n), Q(2 * n);
  FOR(i, n) P[i] = wt[i], Q[i] = -f[i];
  while (n > 1) {
    vc<mint0> P0(4 * n * k), Q0(4 * n * k);
    vc<mint1> P1(4 * n * k), Q1(4 * n * k);
    vc<mint2> P2(4 * n * k), Q2(4 * n * k);
    FOR(i, 2 * n * k) P0[i] = P[i].val, Q0[i] = Q[i].val;
    FOR(i, 2 * n * k) P1[i] = P[i].val, Q1[i] = Q[i].val;
    FOR(i, 2 * n * k) P2[i] = P[i].val, Q2[i] = Q[i].val;
    Q0[2 * n * k] = 1, Q1[2 * n * k] = 1, Q2[2 * n * k] = 1;
    ntt(P0, 0), ntt(Q0, 0), ntt(P1, 0), ntt(Q1, 0), ntt(P2, 0), ntt(Q2, 0);
    FOR(i, 2 * n * k) {
      P0[i] = inv<mint0>(2) * W0[i]
              * (P0[2 * i] * Q0[2 * i + 1] - P0[2 * i + 1] * Q0[2 * i]);
      Q0[i] = Q0[2 * i] * Q0[2 * i + 1];
      P1[i] = inv<mint1>(2) * W1[i]
              * (P1[2 * i] * Q1[2 * i + 1] - P1[2 * i + 1] * Q1[2 * i]);
      Q1[i] = Q1[2 * i] * Q1[2 * i + 1];
      P2[i] = inv<mint2>(2) * W2[i]
              * (P2[2 * i] * Q2[2 * i + 1] - P2[2 * i + 1] * Q2[2 * i]);
      Q2[i] = Q2[2 * i] * Q2[2 * i + 1];
    }
    P0.resize(2 * n * k), Q0.resize(2 * n * k);
    P1.resize(2 * n * k), Q1.resize(2 * n * k);
    P2.resize(2 * n * k), Q2.resize(2 * n * k);
    ntt(P0, 1), ntt(Q0, 1), ntt(P1, 1), ntt(Q1, 1), ntt(P2, 1), ntt(Q2, 1);
    constexpr i128 K = u128(p[0]) * p[1] * p[2];
    auto get = [&](mint0 a, mint1 b, mint2 c) -> mint {
      i128 x = CRT3<u128, p[0], p[1], p[2]>(a.val, b.val, c.val);
      i128 y = K - x;
      return (x < y ? mint(x) : -mint(y));
    };
    fill(all(P), mint(0));
    fill(all(Q), mint(0));
    FOR(j, 2 * k) FOR(i, n / 2) {
      int k = n * j + i;
      P[k] = get(P0[k], P1[k], P2[k]);
      Q[k] = get(Q0[k], Q1[k], Q2[k]);
    }
    Q[0] = 0;
    n /= 2, k *= 2;
  }
  vc<mint> F(k);
  FOR(i, k) F[i] = P[2 * i];
  reverse(all(F));
  F.resize(m + 1);
  return F;
}
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;
  }
  if (mint::can_ntt()) { return power_projection_0_ntt(wt, f, m); }
  return power_projection_0_garner(wt, f, m);
}
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;
}
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);
    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;
}
// 0=[x^0]F, a=[x^1]F
// [2,N) で a^i != a
// このとき G, H は互いに合成逆で
// G(F(x))=aG(x), F(H(x))=H(ax)
// https://yukicoder.me/problems/no/3621
template <typename mint>
struct Schroder {
  int N;
  vc<mint> F, G, H;
  mint a;
  vc<mint> pw;
  Schroder(vc<mint> &F) : F(F) {
    N = len(F);
    a = (N <= 1 ? 1 : F[1]);
    pw.resize(N + 1, 1);
    FOR(i, N) pw[i + 1] = pw[i] * a;
    H.resize(2);
    H[1] = 1;
    while (len(H) < N) {
      int m = len(H);
      int M = min<int>(2 * m - 1, N);
      H.resize(M);
      vc<mint> f(M);
      FOR(i, M) f[i] = F[i];
      vc<mint> E = composition(f, H);
      E = {E.begin() + m, E.begin() + M};
      vc<mint> den(M - m);
      FOR(i, M - m) den[i] = H[i + 1] * pw[i] * (i + 1);
      E = fps_div<mint>(E, den);
      FOR(i, M - m) E[i] /= pw[m + i] - a;
      vc<mint> DH(M - m);
      FOR(i, M - m) { DH[i] = H[i + 1] * (i + 1); }
      E = convolution<mint>(E, DH);
      E.resize(M - m);
      FOR(i, M - m) H[m + i] = E[i];
    }
    SHOW(H);
    H.resize(N);
    G = compositional_inverse(H);
  }
};
using mint = modint998;
void solve() {
  LL(N);
  VEC(mint, F, N);
  Schroder<mint> SCH(F);
  print(SCH.G);
  print(SCH.H);
}
signed main() { solve(); }