#line 1 "main.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/2747"

#line 1 "/home/maspy/compro/library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else

// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #pragma GCC target("avx2,popcnt")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
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> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

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 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 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 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 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

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(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 floor(T a, T b) {
  return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
  return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
  return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sm = 0;
  for (auto &&a: A) sm += a;
  return sm;
}

#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()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    (check(x) ? ok : ng) = x;
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    (check(x) ? ok : ng) = 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);
}

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

template <typename T, typename U>
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;
}

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

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

template <typename T, typename... Vectors>
vc<T> concat(vc<T> &first, const Vectors &... others) {
  vc<T> res = first;
  (res.insert(res.end(), others.begin(), others.end()), ...);
  return res;
}
#endif
#line 1 "/home/maspy/compro/library/other/io.hpp"
#define FASTIO
#include <unistd.h>

// https://judge.yosupo.jp/submission/21623
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;

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() {
  memcpy(ibuf, ibuf + pil, pir - pil);
  pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
  pil = 0;
  if (pir < SZ) ibuf[pir++] = '\n';
}

inline void flush() {
  fwrite(obuf, 1, por, stdout);
  por = 0;
}

void rd(char &c) {
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
}

void rd(string &x) {
  x.clear();
  char c;
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
  do {
    x += c;
    if (pil == pir) load();
    c = ibuf[pil++];
  } while (!isspace(c));
}

template <typename T>
void rd_real(T &x) {
  string s;
  rd(s);
  x = stod(s);
}

template <typename T>
void rd_integer(T &x) {
  if (pil + 100 > pir) load();
  char c;
  do
    c = ibuf[pil++];
  while (c < '-');
  bool minus = 0;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (c == '-') { minus = 1, c = ibuf[pil++]; }
  }
  x = 0;
  while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (minus) x = -x;
  }
}

void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }

template <class T, class U>
void rd(pair<T, U> &p) {
  return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
  if constexpr (N < std::tuple_size<T>::value) {
    auto &x = std::get<N>(t);
    rd(x);
    rd_tuple<N + 1>(t);
  }
}
template <class... T>
void rd(tuple<T...> &tpl) {
  rd_tuple(tpl);
}

template <size_t N = 0, typename T>
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);
}

void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
  rd(h), read(t...);
}

void wt(const char c) {
  if (por == SZ) flush();
  obuf[por++] = c;
}
void wt(const string s) {
  for (char c: s) wt(c);
}
void wt(const char *s) {
  size_t len = strlen(s);
  for (size_t i = 0; i < len; i++) wt(s[i]);
}

template <typename T>
void wt_integer(T x) {
  if (por > SZ - 100) flush();
  if (x < 0) { obuf[por++] = '-', x = -x; }
  int outi;
  for (outi = 96; x >= 10000; outi -= 4) {
    memcpy(out + outi, pre.num[x % 10000], 4);
    x /= 10000;
  }
  if (x >= 1000) {
    memcpy(obuf + por, pre.num[x], 4);
    por += 4;
  } else if (x >= 100) {
    memcpy(obuf + por, pre.num[x] + 1, 3);
    por += 3;
  } else if (x >= 10) {
    int q = (x * 103) >> 10;
    obuf[por] = q | '0';
    obuf[por + 1] = (x - q * 10) | '0';
    por += 2;
  } else
    obuf[por++] = x | '0';
  memcpy(obuf + por, out + outi + 4, 96 - outi);
  por += 96 - outi;
}

template <typename T>
void wt_real(T x) {
  ostringstream oss;
  oss << fixed << setprecision(15) << double(x);
  string s = oss.str();
  wt(s);
}

void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }

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 < std::tuple_size<T>::value) {
    if constexpr (N > 0) { wt(' '); }
    const auto x = std::get<N>(t);
    wt(x);
    wt_tuple<N + 1>(t);
  }
}
template <class... T>
void wt(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(head);
  if (sizeof...(Tail)) wt(' ');
  print(forward<Tail>(tail)...);
}

// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::read;
using fastio::print;
using fastio::flush;

#if defined(LOCAL)
#define SHOW(...) \
  SHOW_IMPL(__VA_ARGS__, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, NAME, ...) NAME
#define SHOW1(x) print(#x, "=", (x)), flush()
#define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush()
#define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()
#define SHOW4(x, y, z, w) \
  print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()
#else
#define SHOW(...)
#endif

#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)

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 5 "main.cpp"

#line 2 "/home/maspy/compro/library/mod/modint_common.hpp"

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

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

template <typename mint>
mint 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 (len(dat) <= n) {
    int k = len(dat);
    int q = (mod + k - 1) / k;
    dat.eb(dat[k * q - mod] * mint::raw(q));
  }
  return dat[n];
}

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};
  while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * mint::raw(len(dat)));
  return dat[n];
}

template <typename mint>
mint fact_inv(int n) {
  static vector<mint> dat = {1, 1};
  if (n < 0) return mint(0);
  while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * inv<mint>(len(dat)));
  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 constexpr (dense) return C_dense<mint>(n, k);
  if constexpr (!large) return multinomial<mint>(n, k, n - k);
  k = min(k, n - k);
  mint x(1);
  FOR(i, k) x *= mint(n - i);
  return x * fact_inv<mint>(k);
}

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

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

template <int mod>
struct modint {
  static constexpr u32 umod = u32(mod);
  static_assert(umod < u32(1) << 31);
  u32 val;

  static modint raw(u32 v) {
    modint x;
    x.val = v;
    return x;
  }
  constexpr modint() : val(0) {}
  constexpr modint(u32 x) : val(x % umod) {}
  constexpr modint(u64 x) : val(x % umod) {}
  constexpr modint(u128 x) : val(x % umod) {}
  constexpr modint(int x) : val((x %= mod) < 0 ? x + mod : x){};
  constexpr modint(ll x) : val((x %= mod) < 0 ? x + mod : x){};
  constexpr modint(i128 x) : val((x %= mod) < 0 ? x + mod : x){};
  bool operator<(const modint &other) const { return val < other.val; }
  modint &operator+=(const modint &p) {
    if ((val += p.val) >= umod) val -= umod;
    return *this;
  }
  modint &operator-=(const modint &p) {
    if ((val += umod - p.val) >= umod) val -= umod;
    return *this;
  }
  modint &operator*=(const modint &p) {
    val = u64(val) * p.val % umod;
    return *this;
  }
  modint &operator/=(const modint &p) {
    *this *= p.inverse();
    return *this;
  }
  modint operator-() const { return modint::raw(val ? mod - val : u32(0)); }
  modint operator+(const modint &p) const { return modint(*this) += p; }
  modint operator-(const modint &p) const { return modint(*this) -= p; }
  modint operator*(const modint &p) const { return modint(*this) *= p; }
  modint operator/(const modint &p) const { return modint(*this) /= p; }
  bool operator==(const modint &p) const { return val == p.val; }
  bool operator!=(const modint &p) const { return val != p.val; }
  modint inverse() const {
    int a = val, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b), swap(u -= t * v, v);
    }
    return modint(u);
  }
  modint pow(ll n) const {
    assert(n >= 0);
    modint ret(1), mul(val);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  static constexpr int get_mod() { return mod; }
  // (n, r), r は 1 の 2^n 乗根
  static constexpr pair<int, int> ntt_info() {
    if (mod == 120586241) return {20, 74066978};
    if (mod == 167772161) return {25, 17};
    if (mod == 469762049) return {26, 30};
    if (mod == 754974721) return {24, 362};
    if (mod == 880803841) return {23, 211};
    if (mod == 943718401) return {22, 663003469};
    if (mod == 998244353) return {23, 31};
    if (mod == 1004535809) return {21, 836905998};
    if (mod == 1045430273) return {20, 363};
    if (mod == 1051721729) return {20, 330};
    if (mod == 1053818881) return {20, 2789};
    return {-1, -1};
  }
  static constexpr bool can_ntt() { return ntt_info().fi != -1; }
};

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

using modint107 = modint<1000000007>;
using modint998 = modint<998244353>;
#line 2 "/home/maspy/compro/library/poly/convolution_all.hpp"

#line 2 "/home/maspy/compro/library/mod/mod_inv.hpp"

// long でも大丈夫
// (val * x - 1) が mod の倍数になるようにする
// 特に mod=0 なら x=0 が満たす
ll mod_inv(ll val, ll mod) {
  if (mod == 0) return 0;
  mod = abs(mod);
  val %= mod;
  if (val < 0) val += mod;
  ll a = val, b = mod, u = 1, v = 0, t;
  while (b > 0) {
    t = a / b;
    swap(a -= t * b, b), swap(u -= t * v, v);
  }
  if (u < 0) u += mod;
  return u;
}
#line 2 "/home/maspy/compro/library/mod/crt3.hpp"

constexpr u32 mod_pow_constexpr(u64 a, u64 n, u32 mod) {
  a %= mod;
  u64 res = 1;
  FOR(32) {
    if (n & 1) res = res * a % mod;
    a = a * a % mod, n /= 2;
  }
  return res;
}

template <typename T, u32 p0, u32 p1>
T CRT2(u64 a0, u64 a1) {
  static_assert(p0 < p1);
  static constexpr u64 x0_1 = mod_pow_constexpr(p0, p1 - 2, p1);
  u64 c = (a1 - a0 + p1) * x0_1 % p1;
  return a0 + c * p0;
}

template <typename T, u32 p0, u32 p1, u32 p2>
T CRT3(u64 a0, u64 a1, u64 a2) {
  static_assert(p0 < p1 && p1 < p2);
  static constexpr u64 x1 = mod_pow_constexpr(p0, p1 - 2, p1);
  static constexpr u64 x2 = mod_pow_constexpr(u64(p0) * p1 % p2, p2 - 2, p2);
  static constexpr u64 p01 = u64(p0) * p1;
  u64 c = (a1 - a0 + p1) * x1 % p1;
  u64 ans_1 = a0 + c * p0;
  c = (a2 - ans_1 % p2 + p2) * x2 % p2;
  return T(ans_1) + T(c) * T(p01);
}

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

template <class T, typename enable_if<!has_mod<T>::value>::type* = nullptr>
vc<T> convolution_naive(const vc<T>& a, const vc<T>& b) {
  int n = int(a.size()), m = int(b.size());
  if (n > m) return convolution_naive<T>(b, a);
  if (n == 0) return {};
  vector<T> ans(n + m - 1);
  FOR(i, n) FOR(j, m) ans[i + j] += a[i] * b[j];
  return ans;
}

template <class T, typename enable_if<has_mod<T>::value>::type* = nullptr>
vc<T> convolution_naive(const vc<T>& a, const vc<T>& b) {
  int n = int(a.size()), m = int(b.size());
  if (n > m) return convolution_naive<T>(b, a);
  if (n == 0) return {};
  vc<T> ans(n + m - 1);
  if (n <= 16 && (T::get_mod() < (1 << 30))) {
    for (int k = 0; k < n + m - 1; ++k) {
      int s = max(0, k - m + 1);
      int t = min(n, k + 1);
      u64 sm = 0;
      for (int i = s; i < t; ++i) { sm += u64(a[i].val) * (b[k - i].val); }
      ans[k] = sm;
    }
  } else {
    for (int k = 0; k < n + m - 1; ++k) {
      int s = max(0, k - m + 1);
      int t = min(n, k + 1);
      u128 sm = 0;
      for (int i = s; i < t; ++i) { sm += u64(a[i].val) * (b[k - i].val); }
      ans[k] = T::raw(sm % T::get_mod());
    }
  }
  return ans;
}
#line 2 "/home/maspy/compro/library/poly/convolution_karatsuba.hpp"

// 任意の環でできる
template <typename T>
vc<T> convolution_karatsuba(const vc<T>& f, const vc<T>& g) {
  const int thresh = 30;
  if (min(len(f), len(g)) <= thresh) return convolution_naive(f, g);
  int n = max(len(f), len(g));
  int m = ceil(n, 2);
  vc<T> f1, f2, g1, g2;
  if (len(f) < m) f1 = f;
  if (len(f) >= m) f1 = {f.begin(), f.begin() + m};
  if (len(f) >= m) f2 = {f.begin() + m, f.end()};
  if (len(g) < m) g1 = g;
  if (len(g) >= m) g1 = {g.begin(), g.begin() + m};
  if (len(g) >= m) g2 = {g.begin() + m, g.end()};
  vc<T> a = convolution_karatsuba(f1, g1);
  vc<T> b = convolution_karatsuba(f2, g2);
  FOR(i, len(f2)) f1[i] += f2[i];
  FOR(i, len(g2)) g1[i] += g2[i];
  vc<T> c = convolution_karatsuba(f1, g1);
  vc<T> F(len(f) + len(g) - 1);
  assert(2 * m + len(b) <= len(F));
  FOR(i, len(a)) F[i] += a[i], c[i] -= a[i];
  FOR(i, len(b)) F[2 * m + i] += b[i], c[i] -= b[i];
  if (c.back() == T(0)) c.pop_back();
  FOR(i, len(c)) if (c[i] != T(0)) F[m + i] += c[i];
  return F;
}
#line 2 "/home/maspy/compro/library/poly/ntt.hpp"

template <class mint>
void ntt(vector<mint>& a, bool inverse) {
  assert(mint::can_ntt());
  const int rank2 = mint::ntt_info().fi;
  const int 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;
      }
    }
  }
}
#line 1 "/home/maspy/compro/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 9 "/home/maspy/compro/library/poly/convolution.hpp"

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

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

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

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

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++) {
    double x = (i < (int)a.size() ? a[i] : 0);
    double 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) <= 2500) 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, m) 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>
vc<mint> convolution(const vc<mint>& a, const vc<mint>& b) {
  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);
}
#line 2 "/home/maspy/compro/library/poly/ntt_doubling.hpp"

#line 4 "/home/maspy/compro/library/poly/ntt_doubling.hpp"

// 2^k 次多項式の長さ 2^k が与えられるので 2^k+1 にする
template <typename mint, bool transposed = false>
void ntt_doubling(vector<mint>& a) {
  static array<mint, 30> root;
  static bool prepared = 0;
  if (!prepared) {
    prepared = 1;
    const int rank2 = mint::ntt_info().fi;
    root[rank2] = mint::ntt_info().se;
    FOR_R(i, rank2) { root[i] = root[i + 1] * root[i + 1]; }
  }

  if constexpr (!transposed) {
    const int M = (int)a.size();
    auto b = a;
    ntt(b, 1);
    mint r = 1, zeta = root[topbit(2 * M)];
    FOR(i, M) b[i] *= r, r *= zeta;
    ntt(b, 0);
    copy(begin(b), end(b), back_inserter(a));
  } else {
    const int M = len(a) / 2;
    vc<mint> tmp = {a.begin(), a.begin() + M};
    a = {a.begin() + M, a.end()};
    transposed_ntt(a, 0);
    mint r = 1, zeta = root[topbit(2 * M)];
    FOR(i, M) a[i] *= r, r *= zeta;
    transposed_ntt(a, 1);
    FOR(i, M) a[i] += tmp[i];
  }
}
#line 5 "/home/maspy/compro/library/poly/convolution_all.hpp"

template <typename T>
vc<T> convolution_all(vc<vc<T>>& polys) {
  if (len(polys) == 0) return {T(1)};
  while (1) {
    int n = len(polys);
    if (n == 1) break;
    int m = ceil(n, 2);
    FOR(i, m) {
      if (2 * i + 1 == n) {
        polys[i] = polys[2 * i];
      } else {
        polys[i] = convolution(polys[2 * i], polys[2 * i + 1]);
      }
    }
    polys.resize(m);
  }
  return polys[0];
}

// product of 1-A[i]x
template <typename mint>
vc<mint> convolution_all_1(vc<mint> A) {
  if (!mint::can_ntt()) {
    vvc<mint> polys;
    for (auto& a: A) polys.eb(vc<mint>({mint(1), -a}));
    return convolution_all(polys);
  }
  int D = 6;
  using poly = vc<mint>;
  int n = 1;
  while (n < len(A)) n *= 2;
  int k = topbit(n);
  vc<mint> F(n), nxt_F(n);
  FOR(i, len(A)) F[i] = -A[i];
  FOR(d, k) {
    int b = 1 << d;
    if (d < D) {
      fill(all(nxt_F), mint(0));
      for (int L = 0; L < n; L += 2 * b) {
        FOR(i, b) FOR(j, b) { nxt_F[L + i + j] += F[L + i] * F[L + b + j]; }
        FOR(i, b) nxt_F[L + b + i] += F[L + i] + F[L + b + i];
      }
    }
    elif (d == D) {
      for (int L = 0; L < n; L += 2 * b) {
        poly f1 = {F.begin() + L, F.begin() + L + b};
        poly f2 = {F.begin() + L + b, F.begin() + L + 2 * b};
        f1.resize(2 * b), f2.resize(2 * b), ntt(f1, 0), ntt(f2, 0);
        FOR(i, b) nxt_F[L + i] = f1[i] * f2[i] + f1[i] + f2[i];
        FOR(i, b, 2 * b) nxt_F[L + i] = f1[i] * f2[i] - f1[i] - f2[i];
      }
    }
    else {
      for (int L = 0; L < n; L += 2 * b) {
        poly f1 = {F.begin() + L, F.begin() + L + b};
        poly f2 = {F.begin() + L + b, F.begin() + L + 2 * b};
        ntt_doubling(f1), ntt_doubling(f2);
        FOR(i, b) nxt_F[L + i] = f1[i] * f2[i] + f1[i] + f2[i];
        FOR(i, b, 2 * b) nxt_F[L + i] = f1[i] * f2[i] - f1[i] - f2[i];
      }
    }
    swap(F, nxt_F);
  }
  if (k - 1 >= D) ntt(F, 1);
  F.eb(1), reverse(all(F));
  F.resize(len(A) + 1);
  return F;
}
#line 2 "/home/maspy/compro/library/poly/fps_log.hpp"

#line 2 "/home/maspy/compro/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 4 "/home/maspy/compro/library/poly/fps_inv.hpp"

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

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

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

template <typename mint>
vc<mint> fps_inv(const vc<mint>& f) {
  assert(f[0] != mint(0));
  int n = count_terms(f);
  int t = (mint::can_ntt() ? 160 : 820);
  return (n <= t ? fps_inv_sparse<mint>(f) : fps_inv_dense<mint>(f));
}
#line 5 "/home/maspy/compro/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));
  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));
}
#line 2 "/home/maspy/compro/library/poly/fps_div.hpp"

#line 5 "/home/maspy/compro/library/poly/fps_div.hpp"

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

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

  vc<pair<int, mint>> dat;
  FOR(i, 1, len(g)) if (g[i] != mint(0)) dat.eb(i, -g[i]);
  FOR(i, len(f)) {
    for (auto&& [j, x]: dat) {
      if (i >= j) f[i] += x * f[i - j];
    }
  }
  return f;
}
#line 2 "/home/maspy/compro/library/poly/sum_of_rationals.hpp"

#line 5 "/home/maspy/compro/library/poly/sum_of_rationals.hpp"

// 有理式の和を計算する。分割統治 O(Nlog^2N)。N は次数の和。
template <typename mint>
pair<vc<mint>, vc<mint>> sum_of_rationals(vc<pair<vc<mint>, vc<mint>>> dat) {
  if (len(dat) == 0) {
    vc<mint> f = {0}, g = {1};
    return {f, g};
  }
  using P = pair<vc<mint>, vc<mint>>;
  auto add = [&](P& a, P& b) -> P {
    int na = len(a.fi) - 1, da = len(a.se) - 1;
    int nb = len(b.fi) - 1, db = len(b.se) - 1;
    int n = max(na + db, da + nb);
    vc<mint> num(n + 1);
    {
      auto f = convolution(a.fi, b.se);
      FOR(i, len(f)) num[i] += f[i];
    }
    {
      auto f = convolution(a.se, b.fi);
      FOR(i, len(f)) num[i] += f[i];
    }
    auto den = convolution(a.se, b.se);
    return {num, den};
  };

  while (len(dat) > 1) {
    int n = len(dat);
    FOR(i, 1, n, 2) { dat[i - 1] = add(dat[i - 1], dat[i]); }
    FOR(i, ceil(n, 2)) dat[i] = dat[2 * i];
    dat.resize(ceil(n, 2));
  }
  return dat[0];
}

// sum wt[i]/(1-A[i]x)
template <typename mint>
pair<vc<mint>, vc<mint>> sum_of_rationals_1(vc<mint> A, vc<mint> wt) {
  using poly = vc<mint>;
  if (!mint::can_ntt()) {
    vc<pair<poly, poly>> rationals;
    FOR(i, len(A)) rationals.eb(poly({wt[i]}), poly({mint(1), -A[i]}));
    return sum_of_rationals(rationals);
  }
  int n = 1;
  while (n < len(A)) n *= 2;
  int k = topbit(n);
  vc<mint> F(n), G(n);
  vc<mint> nxt_F(n), nxt_G(n);
  FOR(i, len(A)) F[i] = -A[i], G[i] = wt[i];
  int D = 6;

  FOR(d, k) {
    int b = 1 << d;
    if (d < D) {
      fill(all(nxt_F), mint(0)), fill(all(nxt_G), mint(0));
      for (int L = 0; L < n; L += 2 * b) {
        FOR(i, b) FOR(j, b) nxt_F[L + i + j] += F[L + i] * F[L + b + j];
        FOR(i, b) FOR(j, b) nxt_G[L + i + j] += F[L + i] * G[L + b + j];
        FOR(i, b) FOR(j, b) nxt_G[L + i + j] += F[L + b + i] * G[L + j];
        FOR(i, b) nxt_F[L + b + i] += F[L + i] + F[L + b + i];
        FOR(i, b) nxt_G[L + b + i] += G[L + i] + G[L + b + i];
      }
    }
    elif (d == D) {
      for (int L = 0; L < n; L += 2 * b) {
        poly f1 = {F.begin() + L, F.begin() + L + b};
        poly f2 = {F.begin() + L + b, F.begin() + L + 2 * b};
        poly g1 = {G.begin() + L, G.begin() + L + b};
        poly g2 = {G.begin() + L + b, G.begin() + L + 2 * b};
        f1.resize(2 * b), f2.resize(2 * b), g1.resize(2 * b), g2.resize(2 * b);
        ntt(f1, 0), ntt(f2, 0), ntt(g1, 0), ntt(g2, 0);
        FOR(i, b) f1[i] += 1, f2[i] += 1;
        FOR(i, b, 2 * b) f1[i] -= 1, f2[i] -= 1;
        FOR(i, 2 * b) nxt_F[L + i] = f1[i] * f2[i] - 1;
        FOR(i, 2 * b) nxt_G[L + i] = g1[i] * f2[i] + g2[i] * f1[i];
      }
    }
    else {
      for (int L = 0; L < n; L += 2 * b) {
        poly f1 = {F.begin() + L, F.begin() + L + b};
        poly f2 = {F.begin() + L + b, F.begin() + L + 2 * b};
        poly g1 = {G.begin() + L, G.begin() + L + b};
        poly g2 = {G.begin() + L + b, G.begin() + L + 2 * b};
        ntt_doubling(f1), ntt_doubling(f2), ntt_doubling(g1), ntt_doubling(g2);
        FOR(i, b) f1[i] += 1, f2[i] += 1;
        FOR(i, b, 2 * b) f1[i] -= 1, f2[i] -= 1;
        FOR(i, 2 * b) nxt_F[L + i] = f1[i] * f2[i] - 1;
        FOR(i, 2 * b) nxt_G[L + i] = g1[i] * f2[i] + g2[i] * f1[i];
      }
    }
    swap(F, nxt_F), swap(G, nxt_G);
  }
  if (k - 1 >= D) ntt(F, 1), ntt(G, 1);
  F.eb(1);
  reverse(all(F)), reverse(all(G));
  F.resize(len(A) + 1);
  G.resize(len(A));
  return {G, F};
}
#line 5 "/home/maspy/compro/library/seq/sum_of_powers.hpp"

// sum_{a in A} a^n を、n = 0, 1, ..., N で列挙
template <typename T>
vc<T> sum_of_powers(const vc<T>& A, ll N) {
  auto f = convolution_all_1<T>(A);
  f.resize(N + 1);
  f = fps_log(f);
  FOR(i, len(f)) f[i] = -f[i] * T(i);
  f[0] = len(A);
  return f;
}

// sum_{i in [L, R)} i^n を、n = 0, 1, ..., N で列挙
template <typename T>
vc<T> sum_of_powers_iota(ll L, ll R, ll N) {
  vc<T> F(N + 1), G(N + 1);
  T powL = 1, powR = 1;
  FOR(i, 1, N + 2) {
    powL *= T(L), powR *= T(R);
    F[i - 1] = (powR - powL) * fact_inv<T>(i);
    G[i - 1] = fact_inv<T>(i);
  }
  F = fps_div(F, G);
  FOR(i, N + 1) F[i] *= fact<T>(i);
  return F;
}

// sum ca^n を n=0,1,...,N で列挙
template <typename T>
vc<T> sum_of_powers_with_coef(const vc<T>& A, const vc<T>& C, int N) {
  auto [num, den] = sum_of_rationals_1(A, C);
  num.resize(N + 1);
  den.resize(N + 1);
  auto f = fps_inv(den);
  f = convolution(f, num);
  f.resize(N + 1);
  return f;
}
#line 2 "/home/maspy/compro/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 "/home/maspy/compro/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); }
};

// 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(); }

private:
  void rebuild() {
    vc<X> X = concat(dat_l, 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 "/home/maspy/compro/library/poly/lagrange_interpolate_iota.hpp"

// Input: f(0), ..., f(n-1) and c. Return: f(c)
template <typename T, typename enable_if<has_mod<T>::value>::type * = nullptr>
T lagrange_interpolate_iota(vc<T> &f, T 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<T>(i) * fact_inv<T>(n - 1 - i);
    if ((n - 1 - i) & 1) a[i] = -a[i];
  }
  vc<T> 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);
  T ANS = 0;
  FOR(i, n) ANS += a[i] * lp[i] * rp[i + 1];
  return ANS;
}

// mod じゃない場合。かなり低次の多項式を想定している。O(n^2)
// Input: f(0), ..., f(n-1) and c. Return: f(c)
template <typename T, typename enable_if<!has_mod<T>::value>::type * = nullptr>
T lagrange_interpolate_iota(vc<T> &f, T c) {
  const int LIM = 10;
  int n = len(f);
  assert(n < LIM);

  // (-1)^{i-j} binom(i,j)
  static vvc<int> C;
  if (C.empty()) {
    C.assign(LIM, vc<int>(LIM));
    C[0][0] = 1;
    FOR(n, 1, LIM) FOR(k, n + 1) {
      C[n][k] += C[n - 1][k];
      if (k) C[n][k] += C[n - 1][k - 1];
    }
    FOR(n, LIM) FOR(k, n + 1) if ((n + k) % 2) C[n][k] = -C[n][k];
  }
  // f(x) = sum a_i binom(x,i)
  vc<T> a(n);
  FOR(i, n) FOR(j, i + 1) { a[i] += f[j] * C[i][j]; }

  T res = 0;
  T b = 1;
  FOR(i, n) {
    res += a[i] * b;
    b = b * (c - i) / (1 + i);
  }
  return res;
}

// 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;
}
#line 1 "/home/maspy/compro/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<int>(n, 1 << 20);
  ll x = factorial998table[q];
  int s = q << 20;
  FOR(i, r) x = x * (s + i + 1) % mod;
  return x;
}
#line 10 "main.cpp"

using mint = modint998;

void solve() {
  LL(N, K);

  vc<mint> F(K + 10);
  FOR(d, 1, K + 10) {
    F[d] += mint(N * N - N) * mint(d).pow(K);
    F[d] -= mint(N - 1) * mint(d).pow(K + 1);
  }
  F = cumsum<mint>(F);

  mint ans = lagrange_interpolate_iota<mint>(F, N);
  mint ANS = mint(2) * factorial998(N - 2) * ans;
  print(ANS);
}

signed main() {
  int T = 1;
  // INT(T);
  FOR(T) solve();
  return 0;
}