#line 1 "library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using pi = pair<ll, ll>;
using vi = vector<ll>;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;

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 vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vec(type, name, ...) vector<type> name(__VA_ARGS__)
#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define FOR4_R(i, a, b, c) for (ll i = (b)-1; i >= ll(a); i -= (c))
#define overload4(a, b, c, d, e, ...) e
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) \
  overload4(__VA_ARGS__, FOR4_R, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FOR_subset(t, s) for (ll t = s; t >= 0; t = (t == 0 ? -1 : (t - 1) & s))
#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, typename U>
T SUM(const vector<U> &A) {
  T sum = 0;
  for (auto &&a: A) sum += a;
  return sum;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
  sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

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

template <typename T>
T pick(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}

template <typename T>
T pick(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}

template <typename T>
T pick(pqg<T> &que) {
  assert(que.size());
  T a = que.top();
  que.pop();
  return a;
}

template <typename T>
T pick(vc<T> &que) {
  assert(que.size());
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename T, typename U>
T ceil(T x, U y) {
  return (x > 0 ? (x + y - 1) / y : x / y);
}

template <typename T, typename U>
T floor(T x, U y) {
  return (x > 0 ? x / y : (x - y + 1) / y);
}

template <typename T, typename U>
pair<T, T> divmod(T x, U y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename F>
ll binary_search(F check, ll ok, ll ng) {
  assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));
  }
  return ok;
}

template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x));
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = S[i] - first_char; }
  return A;
}

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

template <typename CNT, typename T>
vc<CNT> bincount(const vc<T> &A, int size) {
  vc<CNT> C(size);
  for (auto &&x: A) { ++C[x]; }
  return C;
}

// stable
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(A.size());
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return A[i] < A[j] || (A[i] == A[j] && i < j); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
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;
}
#endif
#line 1 "library/other/io.hpp"
// based on yosupo's fastio
#include <unistd.h>

namespace fastio {
// クラスが read(), print() を持っているかを判定するメタ関数
struct has_write_impl {
  template <class T>
  static auto check(T &&x) -> decltype(x.write(), std::true_type{});

  template <class T>
  static auto check(...) -> std::false_type;
};

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

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

  template <class T>
  static auto check(...) -> std::false_type;
};

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

struct Scanner {
  FILE *fp;
  char line[(1 << 15) + 1];
  size_t st = 0, ed = 0;
  void reread() {
    memmove(line, line + st, ed - st);
    ed -= st;
    st = 0;
    ed += fread(line + ed, 1, (1 << 15) - ed, fp);
    line[ed] = '\0';
  }
  bool succ() {
    while (true) {
      if (st == ed) {
        reread();
        if (st == ed) return false;
      }
      while (st != ed && isspace(line[st])) st++;
      if (st != ed) break;
    }
    if (ed - st <= 50) {
      bool sep = false;
      for (size_t i = st; i < ed; i++) {
        if (isspace(line[i])) {
          sep = true;
          break;
        }
      }
      if (!sep) reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    while (true) {
      size_t sz = 0;
      while (st + sz < ed && !isspace(line[st + sz])) sz++;
      ref.append(line + st, sz);
      st += sz;
      if (!sz || st != ed) break;
      reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    bool neg = false;
    if (line[st] == '-') {
      neg = true;
      st++;
    }
    ref = T(0);
    while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }
    if (neg) ref = -ref;
    return true;
  }
  template <typename T,
            typename enable_if<has_read<T>::value>::type * = nullptr>
  inline bool read_single(T &x) {
    x.read();
    return true;
  }
  bool read_single(double &ref) {
    string s;
    if (!read_single(s)) return false;
    ref = std::stod(s);
    return true;
  }
  bool read_single(char &ref) {
    string s;
    if (!read_single(s) || s.size() != 1) return false;
    ref = s[0];
    return true;
  }
  template <class T>
  bool read_single(vector<T> &ref) {
    for (auto &d: ref) {
      if (!read_single(d)) return false;
    }
    return true;
  }
  template <class T, class U>
  bool read_single(pair<T, U> &p) {
    return (read_single(p.first) && read_single(p.second));
  }
  template <size_t N = 0, typename T>
  void read_single_tuple(T &t) {
    if constexpr (N < std::tuple_size<T>::value) {
      auto &x = std::get<N>(t);
      read_single(x);
      read_single_tuple<N + 1>(t);
    }
  }
  template <class... T>
  bool read_single(tuple<T...> &tpl) {
    read_single_tuple(tpl);
    return true;
  }
  void read() {}
  template <class H, class... T>
  void read(H &h, T &... t) {
    bool f = read_single(h);
    assert(f);
    read(t...);
  }
  Scanner(FILE *fp) : fp(fp) {}
};

struct Printer {
  Printer(FILE *_fp) : fp(_fp) {}
  ~Printer() { flush(); }

  static constexpr size_t SIZE = 1 << 15;
  FILE *fp;
  char line[SIZE], small[50];
  size_t pos = 0;
  void flush() {
    fwrite(line, 1, pos, fp);
    pos = 0;
  }
  void write(const char val) {
    if (pos == SIZE) flush();
    line[pos++] = val;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  void write(T val) {
    if (pos > (1 << 15) - 50) flush();
    if (val == 0) {
      write('0');
      return;
    }
    if (val < 0) {
      write('-');
      val = -val; // todo min
    }
    size_t len = 0;
    while (val) {
      small[len++] = char(0x30 | (val % 10));
      val /= 10;
    }
    for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }
    pos += len;
  }
  void write(const string s) {
    for (char c: s) write(c);
  }
  void write(const char *s) {
    size_t len = strlen(s);
    for (size_t i = 0; i < len; i++) write(s[i]);
  }
  void write(const double x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  void write(const long double x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  template <typename T,
            typename enable_if<has_write<T>::value>::type * = nullptr>
  inline void write(T x) {
    x.write();
  }
  template <class T>
  void write(const vector<T> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  template <class T, class U>
  void write(const pair<T, U> val) {
    write(val.first);
    write(' ');
    write(val.second);
  }
  template <size_t N = 0, typename T>
  void write_tuple(const T t) {
    if constexpr (N < std::tuple_size<T>::value) {
      if constexpr (N > 0) { write(' '); }
      const auto x = std::get<N>(t);
      write(x);
      write_tuple<N + 1>(t);
    }
  }
  template <class... T>
  bool write(tuple<T...> tpl) {
    write_tuple(tpl);
    return true;
  }
  template <class T, size_t S>
  void write(const array<T, S> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  void write(i128 val) {
    string s;
    bool negative = 0;
    if (val < 0) {
      negative = 1;
      val = -val;
    }
    while (val) {
      s += '0' + int(val % 10);
      val /= 10;
    }
    if (negative) s += "-";
    reverse(all(s));
    if (len(s) == 0) s = "0";
    write(s);
  }
};
Scanner scanner = Scanner(stdin);
Printer printer = Printer(stdout);
void flush() { printer.flush(); }
void print() { printer.write('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  printer.write(head);
  if (sizeof...(Tail)) printer.write(' ');
  print(forward<Tail>(tail)...);
}

void read() {}
template <class Head, class... Tail>
void read(Head &head, Tail &... tail) {
  scanner.read(head);
  read(tail...);
}
} // namespace fastio
using fastio::print;
using fastio::flush;
using fastio::read;

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __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)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 2 "library/mod/modint.hpp"

template <int mod>
struct modint {
  int val;
  constexpr modint(ll x = 0) noexcept {
    if (0 <= x && x < mod)
      val = x;
    else {
      x %= mod;
      val = (x < 0 ? x + mod : x);
    }
  }
  bool operator<(const modint &other) const {
    return val < other.val;
  } // To use std::map
  modint &operator+=(const modint &p) {
    if ((val += p.val) >= mod) val -= mod;
    return *this;
  }
  modint &operator-=(const modint &p) {
    if ((val += mod - p.val) >= mod) val -= mod;
    return *this;
  }
  modint &operator*=(const modint &p) {
    val = (int)(1LL * val * p.val % mod);
    return *this;
  }
  modint &operator/=(const modint &p) {
    *this *= p.inverse();
    return *this;
  }
  modint operator-() const { return modint(-val); }
  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(int64_t n) const {
    modint ret(1), mul(val);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  void write() { fastio::printer.write(val); }
  void read() { fastio::scanner.read(val); }
  static constexpr int get_mod() { return mod; }
};

struct ArbitraryModInt {
  static constexpr bool is_modint = true;
  int val;
  ArbitraryModInt() : val(0) {}
  ArbitraryModInt(int64_t y)
      : val(y >= 0 ? y % get_mod()
                   : (get_mod() - (-y) % get_mod()) % get_mod()) {}
  bool operator<(const ArbitraryModInt &other) const {
    return val < other.val;
  } // To use std::map<ArbitraryModInt, T>
  static int &get_mod() {
    static int mod = 0;
    return mod;
  }
  static void set_mod(int md) { get_mod() = md; }
  ArbitraryModInt &operator+=(const ArbitraryModInt &p) {
    if ((val += p.val) >= get_mod()) val -= get_mod();
    return *this;
  }
  ArbitraryModInt &operator-=(const ArbitraryModInt &p) {
    if ((val += get_mod() - p.val) >= get_mod()) val -= get_mod();
    return *this;
  }
  ArbitraryModInt &operator*=(const ArbitraryModInt &p) {
    long long a = (long long)val * p.val;
    int xh = (int)(a >> 32), xl = (int)a, d, m;
    asm("divl %4; \n\t" : "=a"(d), "=d"(m) : "d"(xh), "a"(xl), "r"(get_mod()));
    val = m;
    return *this;
  }
  ArbitraryModInt &operator/=(const ArbitraryModInt &p) {
    *this *= p.inverse();
    return *this;
  }
  ArbitraryModInt operator-() const { return ArbitraryModInt(get_mod() - val); }
  ArbitraryModInt operator+(const ArbitraryModInt &p) const {
    return ArbitraryModInt(*this) += p;
  }
  ArbitraryModInt operator-(const ArbitraryModInt &p) const {
    return ArbitraryModInt(*this) -= p;
  }
  ArbitraryModInt operator*(const ArbitraryModInt &p) const {
    return ArbitraryModInt(*this) *= p;
  }
  ArbitraryModInt operator/(const ArbitraryModInt &p) const {
    return ArbitraryModInt(*this) /= p;
  }
  bool operator==(const ArbitraryModInt &p) const { return val == p.val; }
  bool operator!=(const ArbitraryModInt &p) const { return val != p.val; }
  ArbitraryModInt inverse() const {
    int a = val, b = get_mod(), u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b), swap(u -= t * v, v);
    }
    return ArbitraryModInt(u);
  }
  ArbitraryModInt pow(int64_t n) const {
    ArbitraryModInt ret(1), mul(val);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  void write() { fastio::printer.write(val); }
  void read() { fastio::scanner.read(val); }
};

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

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

template <typename mint>
mint fact_inv(int n) {
  static const int mod = mint::get_mod();
  static vector<mint> dat = {1, 1};
  assert(-1 <= n && n < mod);
  if (n == -1) return mint(0);
  while (int(dat.size()) <= n) {
    int k = dat.size();
    dat.emplace_back(dat[k - 1] * inv<mint>(k));
  }
  return dat[n];
}

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

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

template <typename mint>
mint C_dense(int n, int k) {
  static vvc<mint> C;
  static int H = 0, W = 0;

  auto calc = [&](int i, int j) -> mint {
    if (i == 0) return (j == 0 ? mint(1) : mint(0));
    return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);
  };

  if (W <= k) {
    FOR(i, H) {
      C[i].resize(k + 1);
      FOR(j, W, k + 1) { C[i][j] = calc(i, j); }
    }
    W = k + 1;
  }
  if (H <= n) {
    C.resize(n + 1);
    FOR(i, H, n + 1) {
      C[i].resize(W);
      FOR(j, W) { C[i][j] = calc(i, j); }
    }
    H = n + 1;
  }
  return C[n][k];
}

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

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

// [x^d] (1-x) ^ {-n} の計算
template <typename mint, bool large = false, bool dense = false>
mint C_negative(ll n, ll d) {
  assert(n >= 0);
  if (d < 0) return mint(0);
  if (n == 0) { return (d == 0 ? mint(1) : mint(0)); }
  return C<mint, large, dense>(n + d - 1, d);
}

using modint107 = modint<1000000007>;
using modint998 = modint<998244353>;
using amint = ArbitraryModInt;
#line 2 "library/poly/count_terms.hpp"
template<typename mint>
int count_terms(const vc<mint>& f){
  int t = 0;
  FOR(i, len(f)) if(f[i] != mint(0)) ++t;
  return t;
}
#line 2 "library/mod/mod_inv.hpp"
// long でも大丈夫
ll mod_inv(ll val, ll mod) {
  val %= mod;
  if (val < 0) val += mod;
  ll a = val, b = mod, u = 1, v = 0, t;
  while (b > 0) {
    t = a / b;
    swap(a -= t * b, b), swap(u -= t * v, v);
  }
  if (u < 0) u += mod;
  return u;
}
#line 1 "library/poly/convolution_naive.hpp"
template <class T>
vector<T> convolution_naive(const vector<T>& a, const vector<T>& b) {
  int n = int(a.size()), m = int(b.size());
  vector<T> ans(n + m - 1);
  if (n < m) {
    FOR(j, m) FOR(i, n) ans[i + j] += a[i] * b[j];
  } else {
    FOR(i, n) FOR(j, m) ans[i + j] += a[i] * b[j];
  }
  return ans;
}
#line 2 "library/poly/ntt.hpp"

template <class mint>
struct ntt_info {
  static constexpr int bsf_constexpr(unsigned int n) {
    int x = 0;
    while (!(n & (1 << x))) x++;
    return x;
  }

  static constexpr int rank2 = bsf_constexpr(mint::get_mod() - 1);
  array<mint, rank2 + 1> root;
  array<mint, rank2 + 1> iroot;
  array<mint, max(0, rank2 - 1)> rate2;
  array<mint, max(0, rank2 - 1)> irate2;
  array<mint, max(0, rank2 - 2)> rate3;
  array<mint, max(0, rank2 - 2)> irate3;

  ntt_info() {
    int g = primitive_root(mint::get_mod());
    root[rank2] = mint(g).pow((mint::get_mod() - 1) >> rank2);
    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];
      }
    }
    {
      mint prod = 1, iprod = 1;
      for (int i = 0; i <= rank2 - 3; i++) {
        rate3[i] = root[i + 3] * prod;
        irate3[i] = iroot[i + 3] * iprod;
        prod *= iroot[i + 3];
        iprod *= root[i + 3];
      }
    }
  }

  constexpr int primitive_root(int m) {
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 880803841) return 26;
    if (m == 998244353) return 3;
    if (m == 924844053) return 5;
    return -1;
  }
};

template <class mint>
void ntt(vector<mint>& a, bool inverse) {
  int n = int(a.size());
  int h = topbit(n);
  assert(n == 1 << h);
  static const ntt_info<mint> info;
  if (!inverse) {
    int len = 0; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
    while (len < h) {
      if (h - len == 1) {
        int p = 1 << (h - len - 1);
        mint rot = 1;
        FOR(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 *= info.rate2[topbit(~s & -~s)];
        }
        len++;
      } else {
        int p = 1 << (h - len - 2);
        mint rot = 1, imag = info.root[2];
        for (int s = 0; s < (1 << len); s++) {
          mint rot2 = rot * rot;
          mint rot3 = rot2 * rot;
          int offset = s << (h - len);
          for (int i = 0; i < p; i++) {
            auto mod2 = 1ULL * mint::get_mod() * mint::get_mod();
            auto a0 = 1ULL * a[i + offset].val;
            auto a1 = 1ULL * a[i + offset + p].val * rot.val;
            auto a2 = 1ULL * a[i + offset + 2 * p].val * rot2.val;
            auto a3 = 1ULL * a[i + offset + 3 * p].val * rot3.val;
            auto a1na3imag = 1ULL * mint(a1 + mod2 - a3).val * imag.val;
            auto na2 = mod2 - a2;
            a[i + offset] = a0 + a2 + a1 + a3;
            a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
            a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
            a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
          }
          rot *= info.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) {
            auto l = a[i + offset];
            auto r = a[i + offset + p];
            a[i + offset] = l + r;
            a[i + offset + p]
                = (unsigned long long)(mint::get_mod() + l.val - r.val)
                  * irot.val;
            ;
          }
          irot *= info.irate2[topbit(~s & -~s)];
        }
        len--;
      } else {
        int p = 1 << (h - len);
        mint irot = 1, iimag = info.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++) {
            auto a0 = 1ULL * a[i + offset + 0 * p].val;
            auto a1 = 1ULL * a[i + offset + 1 * p].val;
            auto a2 = 1ULL * a[i + offset + 2 * p].val;
            auto a3 = 1ULL * a[i + offset + 3 * p].val;

            auto a2na3iimag
                = 1ULL * mint((mint::get_mod() + a2 - a3) * iimag.val).val;

            a[i + offset] = a0 + a1 + a2 + a3;
            a[i + offset + 1 * p]
                = (a0 + (mint::get_mod() - a1) + a2na3iimag) * irot.val;
            a[i + offset + 2 * p]
                = (a0 + a1 + (mint::get_mod() - a2) + (mint::get_mod() - a3))
                  * irot2.val;
            a[i + offset + 3 * p]
                = (a0 + (mint::get_mod() - a1) + (mint::get_mod() - a2na3iimag))
                  * irot3.val;
          }
          irot *= info.irate3[topbit(~s & -~s)];
        }
        len -= 2;
      }
    }
  }
}
#line 1 "library/poly/fft.hpp"
namespace CFFT {
using real = double;

struct C {
  real x, y;

  C() : x(0), y(0) {}

  C(real x, real y) : x(x), y(y) {}
  inline C operator+(const C& c) const { return C(x + c.x, y + c.y); }
  inline C operator-(const C& c) const { return C(x - c.x, y - c.y); }
  inline C operator*(const C& c) const {
    return C(x * c.x - y * c.y, x * c.y + y * c.x);
  }

  inline C conj() const { return C(x, -y); }
};

const real PI = acosl(-1);
int base = 1;
vector<C> rts = {{0, 0}, {1, 0}};
vector<int> rev = {0, 1};

void ensure_base(int nbase) {
  if (nbase <= base) return;
  rev.resize(1 << nbase);
  rts.resize(1 << nbase);
  for (int i = 0; i < (1 << nbase); i++) {
    rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
  }
  while (base < nbase) {
    real angle = PI * 2.0 / (1 << (base + 1));
    for (int i = 1 << (base - 1); i < (1 << base); i++) {
      rts[i << 1] = rts[i];
      real angle_i = angle * (2 * i + 1 - (1 << base));
      rts[(i << 1) + 1] = C(cos(angle_i), sin(angle_i));
    }
    ++base;
  }
}

void fft(vector<C>& a, int n) {
  assert((n & (n - 1)) == 0);
  int zeros = __builtin_ctz(n);
  ensure_base(zeros);
  int shift = base - zeros;
  for (int i = 0; i < n; i++) {
    if (i < (rev[i] >> shift)) { swap(a[i], a[rev[i] >> shift]); }
  }
  for (int k = 1; k < n; k <<= 1) {
    for (int i = 0; i < n; i += 2 * k) {
      for (int j = 0; j < k; j++) {
        C z = a[i + j + k] * rts[j + k];
        a[i + j + k] = a[i + j] - z;
        a[i + j] = a[i + j] + z;
      }
    }
  }
}
} // namespace CFFT
#line 7 "library/poly/convolution.hpp"

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

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

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

template <typename mint>
vector<mint> convolution_garner(const vector<mint>& a, const vector<mint>& b) {
  int n = len(a), m = len(b);
  if (!n || !m) return {};
  static const long long nttprimes[] = {754974721, 167772161, 469762049};
  using mint0 = modint<754974721>;
  using mint1 = modint<167772161>;
  using mint2 = modint<469762049>;
  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);
  static const long long m01 = 1LL * nttprimes[0] * nttprimes[1];
  static const long long m0_inv_m1 = mint1(nttprimes[0]).inverse().val;
  static const long long m01_inv_m2 = mint2(m01).inverse().val;
  static const int mod = mint::get_mod();
  auto garner = [&](mint0 x0, mint1 x1, mint2 x2) -> mint {
    int r0 = x0.val, r1 = x1.val, r2 = x2.val;
    int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1];
    auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * mint2(m01_inv_m2);
    return mint(r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val);
  };
  vc<mint> c(len(c0));
  FOR(i, len(c)) c[i] = garner(c0[i], c1[i], c2[i]);
  return c;
}

template <typename R>
vc<double> convolution_fft(const vc<R>& a, const vc<R>& b) {
  using C = CFFT::C;
  int need = (int)a.size() + (int)b.size() - 1;
  int nbase = 1;
  while ((1 << nbase) < need) nbase++;
  CFFT::ensure_base(nbase);
  int sz = 1 << nbase;
  vector<C> fa(sz);
  for (int i = 0; i < sz; i++) {
    int x = (i < (int)a.size() ? a[i] : 0);
    int y = (i < (int)b.size() ? b[i] : 0);
    fa[i] = C(x, y);
  }
  CFFT::fft(fa, sz);
  C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
  for (int i = 0; i <= (sz >> 1); i++) {
    int j = (sz - i) & (sz - 1);
    C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
    fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
    fa[i] = z;
  }
  for (int i = 0; i < (sz >> 1); i++) {
    C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
    C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * CFFT::rts[(sz >> 1) + i];
    fa[i] = A0 + A1 * s;
  }
  CFFT::fft(fa, sz >> 1);
  vector<double> ret(need);
  for (int i = 0; i < need; i++) {
    ret[i] = (i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
  }
  return ret;
}

vector<ll> convolution(const vector<ll>& a, const vector<ll>& b) {
  int n = len(a), m = len(b);
  if (!n || !m) return {};
  if (min(n, m) <= 60) return convolution_naive(a, b);
  ll abs_sum_a = 0, abs_sum_b = 0;
  ll LIM = 1e15;
  FOR(i, n) abs_sum_a = min(LIM, abs_sum_a + abs(a[i]));
  FOR(i, n) abs_sum_b = min(LIM, abs_sum_b + abs(b[i]));
  if (i128(abs_sum_a) * abs_sum_b < 1e15) {
    vc<double> c = convolution_fft<ll>(a, b);
    vc<ll> res(len(c));
    FOR(i, len(c)) res[i] = ll(floor(c[i] + .5));
    return res;
  }

  static constexpr unsigned long long MOD1 = 754974721; // 2^24
  static constexpr unsigned long long MOD2 = 167772161; // 2^25
  static constexpr unsigned long long MOD3 = 469762049; // 2^26
  static constexpr unsigned long long M2M3 = MOD2 * MOD3;
  static constexpr unsigned long long M1M3 = MOD1 * MOD3;
  static constexpr unsigned long long M1M2 = MOD1 * MOD2;
  static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;

  static const unsigned long long i1 = mod_inv(MOD2 * MOD3, MOD1);
  static const unsigned long long i2 = mod_inv(MOD1 * MOD3, MOD2);
  static const unsigned long long i3 = mod_inv(MOD1 * MOD2, MOD3);

  using mint1 = modint<MOD1>;
  using mint2 = modint<MOD2>;
  using mint3 = modint<MOD3>;

  vc<mint1> a1(n), b1(m);
  vc<mint2> a2(n), b2(m);
  vc<mint3> a3(n), b3(m);
  FOR(i, n) a1[i] = a[i], a2[i] = a[i], a3[i] = a[i];
  FOR(i, m) b1[i] = b[i], b2[i] = b[i], b3[i] = b[i];

  auto c1 = convolution_ntt<mint1>(a1, b1);
  auto c2 = convolution_ntt<mint2>(a2, b2);
  auto c3 = convolution_ntt<mint3>(a3, b3);

  vc<ll> c(n + m - 1);
  FOR(i, n + m - 1) {
    u64 x = 0;
    x += (c1[i].val * i1) % MOD1 * M2M3;
    x += (c2[i].val * i2) % MOD2 * M1M3;
    x += (c3[i].val * i3) % MOD3 * M1M2;
    ll diff = c1[i].val - ((long long)(x) % (long long)(MOD1));
    if (diff < 0) diff += MOD1;
    static constexpr unsigned long long offset[5]
        = {0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
    x -= offset[diff % 5];
    c[i] = x;
  }
  return c;
}

template <typename mint>
enable_if_t<is_same<mint, modint998>::value, vc<mint>> convolution(
    const vc<mint>& a, const vc<mint>& b) {
  int n = len(a), m = len(b);
  if (!n || !m) return {};
  if (min(n, m) <= 60) return convolution_naive(a, b);
  return convolution_ntt(a, b);
}

template <typename mint>
enable_if_t<!is_same<mint, modint998>::value, vc<mint>> convolution(
    const vc<mint>& a, const vc<mint>& b) {
  int n = len(a), m = len(b);
  if (!n || !m) return {};
  if (min(n, m) <= 60) return convolution_naive(a, b);
  return convolution_garner(a, b);
}
#line 2 "library/poly/integrate.hpp"

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;
}
#line 2 "library/poly/differentiate.hpp"

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

template <typename mint>
enable_if_t<is_same<mint, modint998>::value, vc<mint>> fps_exp(vc<mint>& f) {
  if (count_terms(f) <= 300) return fps_exp_sparse(f);
  return fps_exp_dense(f);
}

template <typename mint>
enable_if_t<!is_same<mint, modint998>::value, vc<mint>> fps_exp(vc<mint>& f) {
  if (count_terms(f) <= 1000) return fps_exp_sparse(f);
  return fps_exp_dense(f);
}

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

template <typename mint>
enable_if_t<!is_same<mint, modint998>::value, vc<mint>> fps_exp_dense(
    vc<mint> h) {
  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;
}

// ntt 素数専用実装。長さ n の FFT を利用して 2n の FFT
// を行うなどの高速化をしている。
template <typename mint>
enable_if_t<is_same<mint, modint998>::value, vc<mint>> fps_exp_dense(
    vc<mint>& f) {
  const int n = len(f);
  assert(n > 0 && f[0] == mint(0));
  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;
}
#line 2 "library/poly/fps_log.hpp"

#line 4 "library/poly/fps_inv.hpp"

template <typename mint>
vc<mint> fps_inv_sparse(const vc<mint>& f) {
  assert(f[0] != mint(0));
  int N = len(f);
  vc<pair<int, mint>> dat;
  FOR3(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;
  FOR3(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>
enable_if_t<is_same<mint, modint998>::value, vc<mint>> fps_inv_dense(
    const vc<mint>& F) {
  assert(F[0] != mint(0));
  vc<mint> G = {mint(1) / F[0]};
  G.reserve(len(F));
  ll N = len(F), n = 1;
  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);
    FOR3(i, n, 2 * n) G.eb(f[i] * mint(-1));
    n *= 2;
  }
  G.resize(N);
  return G;
}

template <typename mint>
enable_if_t<!is_same<mint, modint998>::value, vc<mint>> fps_inv_dense(
    const vc<mint>& F) {
  int N = len(F);
  assert(F[0] != mint(0));
  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>
enable_if_t<is_same<mint, modint998>::value, vc<mint>> fps_inv(
    const vc<mint>& f) {
  if (count_terms(f) <= 200) return fps_inv_sparse<mint>(f);
  return fps_inv_dense<mint>(f);
}

template <typename mint>
enable_if_t<!is_same<mint, modint998>::value, vc<mint>> fps_inv(
    const vc<mint>& f) {
  if (count_terms(f) <= 700) return fps_inv_sparse<mint>(f);
  return fps_inv_dense<mint>(f);
}
#line 5 "library/poly/fps_log.hpp"

template <typename mint>
vc<mint> fps_log_dense(const vc<mint>& f) {
  assert(f[0] == mint(1));
  ll N = len(f);
  vc<mint> df = f;
  FOR(i, N) df[i] *= mint(i);
  df.erase(df.begin());
  auto f_inv = fps_inv(f);
  auto g = convolution(df, f_inv);
  g.resize(N - 1);
  g.insert(g.begin(), 0);
  FOR(i, 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));
  if(count_terms(f) <= 200) return fps_log_sparse(f);
  return fps_log_dense(f);
}
#line 5 "library/poly/fps_pow.hpp"

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

template <typename mint>
vc<mint> fps_pow_1_sparse(const vc<mint>& f, mint K) {
  int N = len(f);
  vc<pair<int, mint>> dat;
  FOR3(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(log_f);
}

template <typename mint>
vc<mint> fps_pow_1(const vc<mint>& f, mint K) {
  if (count_terms(f) <= 100) return fps_pow_1_sparse(f, K);
  return fps_pow_1_dense(f, K);
}
#line 2 "library/poly/from_log_differentiation.hpp"

#line 2 "library/linalg/mat_mul.hpp"

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

  template <class T>
  static auto check(...) -> std::false_type;
};

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

template <class T, typename enable_if<has_mod<T>::value>::type* = nullptr>
vc<vc<T>> mat_mul(const vc<vc<T>>& A, const vc<vc<T>>& B) {
  const int mod = T::get_mod();
  auto N = len(A), M = len(B), K = len(B[0]);
  vv(int, b, K, M);
  FOR(i, M) FOR(j, K) b[j][i] = B[i][j].val;
  vv(T, C, N, K);
  FOR(i, N) {
    FOR(j, K) {
      i128 sm = 0;
      FOR(m, M) { sm += ll(A[i][m].val) * b[j][m]; }
      C[i][j] = sm % mod;
    }
  }
  return C;
}

template <class T, typename enable_if<!has_mod<T>::value>::type* = nullptr>
vc<vc<T>> mat_mul(const vc<vc<T>>& A, const vc<vc<T>>& B) {
  auto N = len(A), M = len(B), K = len(B[0]);
  vv(T, C, N, K);
  FOR(n, N) FOR(m, M) FOR(k, K) C[n][k] += A[n][m] * B[m][k];
  return C;
}
#line 2 "library/alg/monoid/mul.hpp"

template <class T>
struct Monoid_Mul {
  using value_type = T;
  using X = T;
  static constexpr X op(const X &x, const X &y) noexcept { return x * y; }
  static constexpr X inverse(const X &x) noexcept { return X(1) / x; }
  static constexpr X unit() { return X(1); }
  static constexpr bool commute = true;
};
#line 1 "library/ds/sliding_window_aggregation.hpp"
template <class Monoid>
struct Sliding_Window_Aggregation {
  using X = typename Monoid::value_type;
  using value_type = X;
  int sz = 0;
  vc<X> dat;
  vc<X> cum_l;
  X cum_r;

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

  int size() { return sz; }

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

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

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

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

  void debug() {
    print("swag");
    print("dat", dat);
    print("cum_l", cum_l);
    print("cum_r", cum_r);
  }
};

// 定数倍は目に見えて遅くなるので、queue でよいときは使わない
template <class Monoid>
struct SWAG_deque {
  using X = typename Monoid::value_type;
  using value_type = X;
  int sz;
  vc<X> dat_l, dat_r;
  vc<X> cum_l, cum_r;

  SWAG_deque() : sz(0), cum_l({Monoid::unit()}), cum_r({Monoid::unit()}) {}

  int size() { return sz; }

  void push_back(X x) {
    ++sz;
    dat_r.eb(x);
    cum_r.eb(Monoid::op(cum_r.back(), x));
  }

  void push_front(X x) {
    ++sz;
    dat_l.eb(x);
    cum_l.eb(Monoid::op(x, cum_l.back()));
  }

  void push(X x) { push_back(x); }

  void clear() {
    sz = 0;
    dat_l.clear(), dat_r.clear();
    cum_l = {Monoid::unit()}, cum_r = {Monoid::unit()};
  }

  void pop_front() {
    if (sz == 1) return clear();
    if (dat_l.empty()) rebuild();
    --sz;
    dat_l.pop_back();
    cum_l.pop_back();
  }

  void pop_back() {
    if (sz == 1) return clear();
    if (dat_r.empty()) rebuild();
    --sz;
    dat_r.pop_back();
    cum_r.pop_back();
  }

  void pop() { pop_front(); }

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

  void debug() {
    print("swag");
    print("dat_l", dat_l);
    print("dat_r", dat_r);
    print("cum_l", cum_l);
    print("cum_r", cum_r);
  }

private:
  void rebuild() {
    vc<X> X;
    FOR_R(i, len(dat_l)) X.eb(dat_l[i]);
    X.insert(X.end(), all(dat_r));
    clear();
    int m = len(X) / 2;
    FOR_R(i, m) push_front(X[i]);
    FOR(i, m, len(X)) push_back(X[i]);
    assert(sz == len(X));
  }
};
#line 5 "library/poly/lagrange_interpolate_iota.hpp"

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

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

// Input: f(0), ..., f(n-1) and c
// Return: f(c)
// Complexity: O(n)
template <typename mint>
mint lagrange_interpolate_iota(vc<mint> &f, mint c) {
  int n = len(f);
  if (int(c.val) < n) return f[c.val];
  auto a = f;
  FOR(i, n) {
    a[i] = a[i] * fact_inv<mint>(i) * fact_inv<mint>(n - 1 - i);
    if ((n - 1 - i) & 1) a[i] = -a[i];
  }
  vc<mint> lp(n + 1), rp(n + 1);
  lp[0] = rp[n] = 1;
  FOR(i, n) lp[i + 1] = lp[i] * (c - i);
  FOR_R(i, n) rp[i] = rp[i + 1] * (c - i);
  mint ANS = 0;
  FOR(i, n) ANS += a[i] * lp[i] * rp[i + 1];
  return ANS;
}
#line 4 "library/poly/prefix_product_of_poly.hpp"

// A[k-1]...A[0] を計算する
// アルゴリズム参考：https://github.com/noshi91/n91lib_rs/blob/master/src/algorithm/polynomial_matrix_prod.rs
// 実装参考：https://nyaannyaan.github.io/library/matrix/polynomial-matrix-prefix-prod.hpp
template <typename T>
vc<vc<T>> prefix_product_of_poly_matrix(vc<vc<vc<T>>>& A, ll k) {
  int n = len(A);

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

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

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

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

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

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

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

// f[k-1]...f[0] を計算する
template <typename T>
T prefix_product_of_poly(vc<T>& f, ll k) {
  vc<vc<vc<T>>> A(1);
  A[0].resize(1);
  A[0][0] = f;
  auto res = prefix_product_of_poly_matrix(A, k);
  return res[0][0];
}
#line 2 "library/seq/kth_term_of_p_recursive.hpp"

// a0, ..., a_{r-1} および f_0, ..., f_r を与える
// a_r f_0(0) + a_{r-1}f_1(0) + ... = 0
// a_{r+1} f_0(1) + a_{r}f_1(1) + ... = 0
template <typename T>
T kth_term_of_p_recursive(vc<T> a, vc<vc<T>>& fs, ll k) {
  int r = len(a);
  assert(len(fs) == r + 1);
  if (k < r) return a[k];

  vc<vc<vc<T>>> A;
  A.resize(r);
  FOR(i, r) A[i].resize(r);
  FOR(i, r) {
    // A[0][i] = -fs[i + 1];
    for (auto&& x: fs[i + 1]) A[0][i].eb(-x);
  }
  FOR3(i, 1, r) A[i][i - 1] = fs[0];
  vc<T> den = fs[0];
  auto res = prefix_product_of_poly_matrix(A, k - r + 1);
  reverse(all(a));
  T ANS = 0;
  FOR(j, r) ANS += res[0][j] * a[j];
  ANS /= prefix_product_of_poly(den, k - r + 1);
  return ANS;
}
#line 4 "library/poly/from_log_differentiation.hpp"

// 対数微分 F'/F = a(x)/b(x) から F を復元する。
// a, b が sparse であれば、O(N(K1+K2)) 時間でできる
template <typename mint>
vc<mint> from_log_differentiation(int N, const vc<mint>& a, const vc<mint>& b) {
  assert(b[0] == mint(1));
  using P = pair<int, mint>;

  vc<P> dat_a, dat_b;
  FOR(i, len(a)) if (a[i] != mint(0)) dat_a.eb(i, a[i]);
  FOR(i, 1, len(b)) if (b[i] != mint(0)) dat_b.eb(i, b[i]);

  vc<mint> f(N + 1);
  vc<mint> df(N);
  f[0] = mint(1);
  FOR(n, N) {
    mint v = 0;
    for (auto&& [i, bi]: dat_b) {
      if (i > n) break;
      v -= bi * df[n - i];
    }
    for (auto&& [i, ai]: dat_a) {
      if (i > n) break;
      v += ai * f[n - i];
    }
    df[n] = v;
    f[n + 1] = df[n] * inv<mint>(n + 1);
  }
  return f;
}

// F'/F = a/b の解の、[x^K]F を求める。右辺は低次の有理式。
template <typename mint>
mint from_log_differentiation_kth(int K, vc<mint>& a, vc<mint>& b) {
  assert(b[0] == mint(1));
  int r = max(len(a), len(b) - 1);
  vvc<mint> c(r + 1);
  FOR(i, r + 1) {
    mint c0 = 0, c1 = 0;
    if (i < len(b)) c0 += mint(r - i) * b[i];
    if (i < len(b)) c1 += b[i];
    if (0 <= i - 1 && i - 1 < len(b)) c0 -= a[i - 1];
    c[i] = {c0, c1};
  }
  auto f = from_log_differentiation(r - 1, a, b);
  mint ANS = kth_term_of_p_recursive(f, c, K);
  return ANS;
}
#line 1 "library/mod/factorial998.hpp"
// 1<<20
int factorial998table[1024] = {1,467742124,703158536,849331177,183632821,786787592,708945888,623860151,442444797,339076928,916211838,827641482,982515753,303461550,466748179,669060208,789885751,915736046,189957301,934038903,728735046,774755699,649374308,602288735,492352484,958678776,943233257,148504501,352124178,569334038,927469492,343841688,432351202,700916755,170721982,8283809,875807278,931632987,330722936,603566523,391470976,157944106,826756015,278928878,178606531,522053153,175494307,16217485,310769109,430912024,970167731,302127847,960178710,607169580,211863227,918097328,664502958,598427325,415194799,38321157,375608821,557298612,497769749,114695383,77784134,629192790,339438380,348348875,713806860,526342541,671850855,414726935,844082152,412454739,351143550,868784407,834684152,186057224,996072584,619190001,24770542,765280770,513490122,468949120,867194196,866447292,937135640,560788103,308335177,703539315,252044620,119916775,298069903,43651994,148641017,730387621,856452172,74265901,626807500,980602375,42825068,348086475,162321900,207340584,151258454,461547160,320321845,361026143,882876292,842563318,257705870,158156446,292795459,984763947,917068833,811332379,782439665,944504775,298167161,141501910,155584237,149720256,71954352,666430555,580966229,884747116,616367471,918981127,310328833,724405658,383796145,256700166,487819118,642491144,181867555,524937737,222137750,445244561,79921588,253457448,405659726,260707689,740044210,654653354,229885020,230551611,616689587,939003921,565960348,904184966,133298693,859220865,186139683,765071679,247651638,451157944,929341123,503724944,768266737,142218056,910573117,274579400,151387843,212671109,815271666,406331931,154251304,642676789,570372925,976277122,442985463,928799971,817581666,797627351,100113334,877639265,541537097,434482347,300960222,270085755,481153328,236088097,686884498,323505794,897572220,900787550,277507290,157634146,892066519,616420589,46056764,697140618,592483685,896871487,896388868,106444279,115102765,191484323,62322499,434613622,426026852,378184205,194359325,415197585,965735328,598860936,653751428,942602959,475099103,642401460,77868208,464952529,549976420,705774928,635299526,704085554,809044086,670938184,799176916,58985566,402328281,182103192,921913660,674272214,428301920,520916749,127424638,296779896,166780239,19634060,95873539,708947606,532272305,980167862,7015847,370183454,45567119,866949818,374428494,25583689,351370758,835388325,232690098,42002598,17055285,985022727,214528454,122907290,793349516,609331634,87133548,248246624,448572380,502875867,183097664,536117329,170926160,381772251,37038194,374439881,94285547,880631489,452052533,739811514,675382782,587926712,179133902,694266603,338843576,281485671,813341519,616512705,222785194,382494725,471654428,961907947,442140830,702296161,548575377,388901073,19119024,545916498,947169254,801677200,377657430,634980290,246239186,13175103,239754689,656729178,364003283,646568868,584909084,690387116,452007054,131381944,908149670,807287523,802277179,745423153,893994782,197548253,376096720,105840336,687751559,170787791,928507410,620382696,446955151,139665212,882526402,494793004,107171423,753993075,467588754,207595897,269813018,941027990,856873596,717085190,245280646,792026805,548741735,523767341,637697735,261200153,89666563,344573088,15832984,558492246,825051585,923222974,826620400,558080789,657328927,991078225,706029275,738905108,401212366,980043233,895405022,597894231,636951913,947342478,786075225,395095090,188433847,121279219,860403973,396099425,240442489,521535558,280382318,58023116,735594008,8696133,477645338,223630480,816606673,680021043,362424474,181667447,504295826,332167472,766361494,992840497,417671938,376941230,11880047,275790726,106186450,150546053,966438917,431896075,158021876,734833661,328332504,632143386,962477966,638741189,728804571,753715698,20536106,45105841,271673172,982138522,604809222,199722980,211807634,478008419,194715230,246865373,316443541,869035744,202922168,245262975,136244583,650969410,566222746,55188168,495968583,571946805,188658038,353720239,830419870,669127165,86710835,810103736,630008035,764354348,209246227,277861984,725469211,151404581,894191013,775554083,634671016,170299187,471849450,575347258,505276194,636730506,40086858,386228700,789875034,998219457,359035788,843760715,864829665,794240359,241486050,48334220,583177582,714653706,617669563,132782021,779225352,333301287,520569296,508276228,689073648,573645847,200419842,911561316,310562870,204959007,879280837,762843188,103128368,133300147,648946778,287218789,662474952,587555465,105622721,648151526,517033362,729251452,850555187,708613432,874408867,345608416,690718720,10813958,42384375,882264058,825490058,252850511,652942840,202604098,277615259,862885671,582470925,190843016,534488148,187675153,911660635,377262012,642854978,359397276,712333871,580131409,841639861,925383257,213683380,25291651,974815450,32032244,119030165,443676106,555727293,170519648,171131074,839941962,789829593,140975543,845347712,303299112,530420097,857005350,249174130,224087061,311280308,404814306,567648772,766512373,470895965,294358155,625218604,89534510,513216330,78173719,22818060,254922573,292417477,415060121,208989124,960117615,570018845,237661008,442774488,871349246,161574942,548661451,313471555,448096394,587422360,987939533,254478574,113844945,268886375,927289435,664834607,983476167,390569280,363763327,935767957,159015901,508613041,134148582,127417680,484767855,825835285,43847241,972918293,151969014,768480291,729490470,76727400,384998943,648970509,764966281,391326774,585299643,661473977,530021579,368308424,81083443,981417794,185781362,169555925,934957641,56005264,296483160,853982963,489694611,73207251,20297311,431253211,168162850,36271383,689526671,397669110,705876730,785504919,764896820,936514026,350141918,784778738,682324919,140913543,862125900,723248565,369074340,146936534,226913694,277886748,856792647,13654547,141461269,255233971,979535193,747662027,452683681,338311679,399620140,306913085,817524367,333578440,943193170,387930488,964713035,554372227,524201507,267870305,698863503,695139108,399857384,830659092,479624682,594238820,768224890,956955770,940576967,920740072,282055556,621677930,847367415,619094041,432519599,192780811,912052381,263304046,114280963,307107320,956809356,118706101,836710721,356893069,427113038,55360495,892694364,443807400,568616581,130165565,732273554,778059496,95936679,629634134,383940143,474733431,271200931,253893765,65679204,670721645,268831988,225698685,424701963,654858732,405695790,894299102,797306377,464723449,647679843,730366154,956550665,898568348,313188681,661403769,346715295,358990430,868898456,719464962,978551995,772931269,255694712,379904456,393101377,130818973,810783770,78951115,608848341,941552927,523163696,581658405,188869913,161971620,114600913,300038465,126906968,572973411,118017645,806069307,430432761,310699012,989119052,282768145,557792692,611036992,427168405,84497995,529589599,967936672,416953197,549641787,787274930,514952744,646568513,39329263,765390776,831388678,299074396,102522509,886062498,598990751,553048069,305737423,388746841,13007805,3445560,568306294,109543305,847740132,746222360,454654676,748993028,222910140,861308982,390243513,692742883,789475199,153430402,299806798,913070840,881332402,245792511,618823409,1817990,897836424,726794141,700802042,472214481,97004031,479899815,573979309,752576644,374801082,599964908,894966385,178103304,12240556,393873628,855241924,305678131,971858774,281586141,87362107,41844894,175133514,276243521,997376957,260427125,439339251,64661516,362212695,186181824,423316311,267640938,299252572,810040987,857956827,758991665,207700847,399398818,747579039,814755712,298373935,307448236,42074518,982127624,538863790,528558929,96501138,813255509,611769398,710541518,408153968,675346745,970094012,791931126,811516976,618049736,264048084,209805699,909045292,645349311,416989597,590393407,320547207,342653696,860169617,856611053,475149267,124801433,547187333,466598598,266454901,554467907,868909135,199244107,548833449,20952517,234169026,117025205,804238552,205574540,590283297,822322644,866010856,477388420,935768507,424373916,951967787,344871828,133969287,937034425,309380768,666909962,726492795,996576193,883938945,869749688,313581344,65216237,88860786,208895640,888760811,854567609,328142793,121852766,928690075,135269006,333105486,502240551,573712984,397698082,935117672,718828733,440474396,335628894,184935718,788258676,646732201,68099895,167036421,362572358,787671392,666366534,193503119,74429287,132805884,796935846,124574194,926012440,147265585,722608579,526866610,452261307,990444071,4595579,147427028,774597449,678783012,568563934,383628463,68242206,163493293,352851801,123192034,529859554,14733470,565063217,178575398,580871309,135817500,313966456,647215844,118781836,106243172,796669460,48496927,772979683,715961917,546863206,601711799,644312478,629259662,738295002,692301787,149995411,864799423,284186171,246177326,268779154,86400350,518698490,321709079,946212693,800553099,865864136,244789848,386206318,851633075,713794602,131117952,280474884,243820970,820033654,399700655,825581574,443639603,774376660,362476217,552383080,436759518,538430048,965968656,150434699,563163603,352073025,840124972,152029247,902082055,770264937,747653807,934664232,541451013,807031739,854866728,503502641,283479207,297947602,488469464,205196166,381583984,108455782,570592132,363674728,134077711,356931610,887112858,273780969,443297964,650953636,402662299,894089640,71844431,33030748,208583995,597099208,671156881,875032178,998244352,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};

int factorial998(ll n) {
  constexpr int mod = 998244353;
  if (n >= mod) return 0;
  auto [q, r] = divmod(n, 1 << 20);
  ll x = factorial998table[q];
  int s = q << 20;
  FOR(i, r) x = x * (s + i + 1) % mod;
  return x;
}
#line 7 "main.cpp"

using mint = modint998;
using poly = vc<mint>;
const int mod = 998244353;

mint solve_1(ll N, ll K) {
  N %= mod;
  vc<mint> f(K + 1);
  f[0] = mint(1);
  f[1] = N + N;
  FOR(k, 1, K) {
    f[k + 1] = mint(N + N - k - k) * f[k]
               + mint(N + N - k + 1) * mint(k) * inv<mint>(2) * f[k - 1];
  }
  return f[K];
}

mint solve_2(ll N, ll K) {
  if (K >= mod) return 0;
  assert(K <= mod);
  poly f = {mint(2 * N), mint(N)};
  poly g = {mint(1), mint(2), inv<mint>(2)};
  mint ANS = mint(factorial998(K)) * from_log_differentiation_kth(K, f, g);
  return ANS;
}

void solve() {
  LL(N, K);
  if (K == 0) return print(1);
  bool b = K <= 100'000;
  if (b) print(solve_1(N, K));
  if (!b) print(solve_2(N, K));
}

signed main() {
  INT(T);
  FOR(T) solve();
  return 0;
}