#line 1 "No_213_\u7d20\u6570\u30b5\u30a4\u30b3\u30ed\u3068\u5408\u6210\u6570\u30b5\u30a4\u30b3\u30ed_3_Easy.cpp"
#define YRSD
#line 2 "YRS/all.hpp"

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

#include <iostream>
#include <algorithm>
#include <array>
#include <bitset>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <string>
#include <tuple>
#include <bit>
#include <chrono>
#include <functional>
#include <iomanip>
#include <utility>
#include <type_traits>
#include <cassert>
#include <cctype>
#include <cmath>
#include <cstring>
#include <ctime>
#include <limits>
#include <ranges>
#include <concepts>

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

#define ov(a, b, c, d, e, ...) e
#define FO1(a) for (int _ = 0; _ < (a); ++_)
#define FO2(i, a) for (int i = 0; i < (a); ++i)
#define FO3(i, a, b) for (int i = (a); i < (b); ++i)
#define FO4(i, a, b, c) for (int i = (a); i < (b); i += (c))
#define FOR(...) ov(__VA_ARGS__, FO4, FO3, FO2, FO1)(__VA_ARGS__)
#define FF1(a) for (int _ = (a) - 1; _ >= 0; --_)
#define FF2(i, a) for (int i = (a) - 1; i >= 0; --i)
#define FF3(i, a, b) for (int i = (b) - 1; i >= (a); --i)
#define FF4(i, a, b, c) for (int i = (b) - 1; i >= (a); i -= (c))
#define FOR_R(...) ov(__VA_ARGS__, FF4, FF3, FF2, FF1)(__VA_ARGS__)
#define FOR_subset(t, s) for (int t = (s); t > -1; t = (t == 0 ? -1 : (t - 1) & s))

#define sort ranges::sort

using namespace std;

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

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

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

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

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

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

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

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

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

Z QMAX(const Z &a) { return *max_element(all(a)); }
Z QMIN(const Z &a) { return *min_element(all(a)); }
TE Z QMAX(T l, T r) { return *max_element(l, r); }
TE Z QMIN(T l, T r) { return *min_element(l, r); }
constexpr bool chmax(Z &a, const Z &b) { return (a < b ? a = b, 1 : 0); }
constexpr bool chmin(Z &a, const Z &b) { return (a > b ? a = b, 1 : 0); }

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

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

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

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

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

TE inline void sh(vc<T> &a, int N, T b = {}) {
  a.resize(N, b);
}
#line 1 "YRS/debug.hpp"
#ifdef YRSD
void DBG() { cerr << "]" << endl; }
TES void DBG(T &&x, S &&...y) {
  cerr << x;
  if constexpr (sizeof...(S)) cerr << ", ";
  DBG(forward<S>(y)...);
}
#define debug(...) cerr << "[" << __LINE__ << "]: [" #__VA_ARGS__ "] = [", DBG(__VA_ARGS__)
void ERR() { cerr << endl; }
TES void ERR(T &&x, S &&...y) {
  cerr << x;
  if constexpr (sizeof...(S)) cerr << ", ";
  ERR(forward<S>(y)...);
}
#define err(...) cerr << "[" << __LINE__ << "]: ", ERR(__VA_ARGS__)
#define asser assert
#else
#define debug(...) void(0721)
#define err(...)   void(0721)
#endif
#line 2 "YRS/poly/fps_pow.hpp"

#line 2 "YRS/poly/fps_log.hpp"

#line 2 "YRS/poly/c/bs.hpp"

#line 2 "YRS/poly/c/fps_t.hpp"

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

#define c constexpr
template <int mod>
struct mint_t {
  using T = mint_t;
  static c uint m = mod;
  uint x;

  c inline uint val() const { return x; }

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

  c T &operator+=(T p) {
    if ((x += p.x) >= m) x -= m;
    return *this;
  }
  c T &operator-=(T p) {
    if ((x += m - p.x) >= m) x -= m;
    return *this;
  }
  c T operator+(T p) const { return T(*this) += p; }
  c T operator-(T p) const { return T(*this) -= p; }

  c T &operator*=(T p) {
    x = ull(x) * p.x % m;
    return *this;
  }
  c T operator*(T p) const { return T(*this) *= p; }

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

  c T operator-() const { return T::gen(x ? mod - x : 0); }

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

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

  c bool operator<(T p) const { return x < p.x; }
  c bool operator==(T p) const { return x == p.x; }
  c bool operator!=(T p) const { return x != p.x; }

  static c T gen(uint x) {
    T s;
    s.x = x;
    return s;
  }

  friend istream &operator>>(istream &cin, T &p) {
    ll t;
    cin >> t;
    p = t;
    return cin;
  }
  
  friend ostream &operator<<(ostream &cout, T p) { return cout << p.x; }

  static c int get_mod() { return mod; }

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

using M99 = mint_t<998244353>;
using M17 = mint_t<1000000007>;
using M11 = M17;

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

// 动态模数需要在 设置模数后 进行构造
TE struct fps_t {
  using fps = vc<T>;
  using cf = const fps &;
  static inline const uint p = T::get_mod(), t = T::ntt_info().fi,
                           r = T::ntt_info().se;
  static inline const ull M = ull(p) * p;
  // 需要动态模数反复set mod的啥比题到底是谁在出
  // static inline uint p = T::get_mod(), t = T::ntt_info().fi,
  //                    r = T::ntt_info().se;
  // static inline ull M = ull(p) * p;
  // static void reset() {
  //   p = T::get_mod();
  //   tie(t, r) = T::ntt_info();
  //   M = ull(p) * p;
  // }

  fps fa{1, 1}, ifa{1, 1}, in{0, 1};
  T inv(int);
  T fac(int);
  T ifac(int);
  T C(int, int);
  
  static constexpr int p0 = 167'772'161, p1 = 469'762'049, p2 = 754'974'721;
  using f0 = fps_t<mint_t<p0>>;
  using f1 = fps_t<mint_t<p1>>;
  using f2 = fps_t<mint_t<p2>>;

  static void sh(fps &, int);
  static int count_terms(cf);

  static T eval(cf, T);

  T crt(ull, ull, ull);
  u128 crt_128(ull, ull, ull);

  static void ntr(T *, T *, T *, T *, T *, T *);
  static void ntt(fps &, bool);
  static void trans_ntt(fps &, bool);
  static void ntt_db(fps &f, bool = 0);

  fps conv_naive(cf, cf);
  fps conv_kara(cf, cf);
  static fps conv_ntt(fps, fps);
  fps conv_mtt(cf, cf);
  fps conv(cf, cf);
  vc<int> conv_for_big(const vc<int> &, const vc<int> &);

  static fps sq_ntt(fps);
  fps sq_mtt(cf);
  fps sq(cf);

  fps diff(cf);
  fps inte(cf);
  T inte(cf, T, T);

  fps mid_prod(cf, cf);

  fps inv_sp(cf);
  fps inv_ntt(cf);
  fps inv_mtt(cf);
  fps inv(cf);

  fps div_sp(fps, fps);
  fps div_ntt(cf, cf);
  fps div_mtt(fps, fps);
  fps div_dense(cf, cf);
  fps div(cf, cf);

  fps log_sp(cf);
  fps log_dense(cf);
  fps log(cf);

  fps exp_sp(cf);
  fps exp_ntt(cf);
  fps exp_mtt(cf);
  fps exp_dense(cf);
  fps exp(cf);

  fps pw_sp(cf, T);
  fps pw_dense(cf, T);
  fps pw(cf, T);
  fps pow(cf, ll);

  fps sqr_sp(cf);
  fps sqr_ntt(cf);
  fps sqr_dense(cf);
  fps sqr(cf);
  fps sqrt(cf);

  fps conv_all(const vc<fps> &);
  fps conv_all(fps);

  fps eval_geo(fps, T, T, int);
  fps inte_geo(fps, T, T);
  struct subprod_t;
  subprod_t subprod(cf);
  fps eval_ntt(fps, fps);
  fps eval(fps, fps);
  fps inte(fps, fps);

  fps shift(fps, T);

  T lag(cf, T);
  fps lag(cf, T, int);
  T lag(cf, cf, T);

  fps pow_proj_ntt(fps, fps, int);
  fps pow_proj(fps, fps, int);

  fps comp_slow(cf, cf);
  fps comp_ntt(fps, fps);
  fps comp_mtt(fps, fps);
  fps comp(fps, fps);
  fps comp_inv(fps);

  pair<fps, fps> divmod(fps, cf);
  fps modpow(cf, ll, cf);

  fps prod_of_f_rk_x(fps, T, int);
  fps prod_of_one_minus_xn(const vc<int> &, int);
  fps prod_of_inv_one_minus_xn(const vc<int> &, int);
  fps prod_of_one_plus_xn(const vc<int> &a, int);
  fps prod_of_inv_one_plus_xn(const vc<int> &a, int);

  pair<fps, fps> sum_of_rationals(vc<pair<fps, fps>>);
  pair<fps, fps> sum_of_rationals_sp(cf, cf);
  fps sum_of_exp_bx(cf, cf, int);
  fps sum_of_pow(cf, int);
  fps sum_of_pow(ll, ll, int);
  fps sum_of_pow(cf, cf, int);
  fps sum_of_binomail(fps, T, T);

  fps subset_sum(const vc<int> &, int k);
  fps subset_sum_lm(const vc<int> &, int k);

  T coef_of_rationals_ntt(fps, fps, ll);
  T coef_of_rationals_mtt(fps, fps, ll);
  T coef_of_rationals(fps, fps, ll);
  fps coef_of_rationals(fps, fps, ll, ll);

  fps find_line(cf);
  T line_inte(cf a, ll N);

  template <int>
  struct fac_t;
  template <int lg = 10>
  fac_t<lg> fac_large();

  fps p_to_ffp(cf);
  fps ffp_to_p(cf);
  fps ffp_conv_ntt(fps, fps);
  fps ffp_conv_mtt(fps, fps);
  fps ffp_conv(cf, cf);

  fps sin(cf);
  fps cos(cf);
  fps asin(cf);
  fps atan(cf);

  fps comp_f_ex(cf);
  fps comp_f_1_minus_ex(cf);
  fps comp_f_ex_minus_1(cf);
  fps comp_f_a_plus_bx(cf, T, T);
  fps comp_f_aplusbx_div_cplusdx_fake(cf, T, T, T, T);
  fps comp_f_aplusbx_div_cplusdx(cf, T, T, T, T);
  fps comp_f_x_plus_1_divx(cf);

  struct conv_t;
  conv_t online_conv();
  struct exp_t;
  exp_t online_exp();
  struct log_t;
  log_t online_log();
  struct inv_t;
  inv_t online_inv();
  struct div_t;
  div_t online_div();
  struct pow_t;
  pow_t online_pow(T);

  fps presum(cf, T);

  fps sinh(int);
  fps exp_x(int);
  fps exp_invx(int);
  fps E_S(int);
  fps E(int);
  fps E_n(int, int);
  fps E_odd(int);
  fps E_noempty(int);
  fps C_R(int);

  fps bell(int);
  fps derange(int);
  fps bernoulli(int);
  fps partition(int);

  fps count_label_dag(int);
  fps count_label_dag_con(int);
  fps count_label_undir(int);
  fps count_label_undir_con(int);
  fps count_label_unicycle(int);
  fps count_label_bipartite(int, bool);
  fps count_label_bcc_v(int);
  T count_label_bcc_v_N(int);
  fps count_label_bcc_e(int);
  T count_label_bcc_e_N(int);
  T count_label_tournament(int);
  fps count_label_scc(int);
  fps count_label_euler_undir(int);
  fps count_label_tree(int);
  fps count_unlabel_tree(int);
};
#line 4 "YRS/poly/c/bs.hpp"

TE Z fps_t<T>::inv(int n) -> T {
  assert(0 <= n);
  while (len(in) <= n) {
    int k = len(in), q = (p + k - 1) / k, r = k * q - p;
    in.ep(in[r] * T(q));
  }
  return in[n];
}

TE Z fps_t<T>::fac(int n) -> T {
  if (n >= p) return 0;
  while (len(fa) <= n) {
    int k = len(fa);
    fa.ep(fa[k - 1] * T(k));
  }
  return fa[n];
}

TE Z fps_t<T>::ifac(int n) -> T {
  if (n < 0) return T(0);
  while (len(ifa) <= n) ifa.ep(ifa.back() * inv(len(ifa)));
  return ifa[n];
}

TE Z fps_t<T>::C(int n, int k) -> T {
  assert(n >= 0);
  if (k < 0 or n < k) return 0;
  return fac(n) * ifac(k) * ifac(n - k);
}

TE Z fps_t<T>::sh(fps &a, int N) -> void { a.resize(N); }

// 非0项数量
TE Z fps_t<T>::count_terms(cf f) -> int {
  int s = 0, N = len(f);
  FOR(i, N) s += f[i].val() != 0;
  return s;
}

TE Z fps_t<T>::eval(cf f, T x) -> T {
  T s = 0, c = 1;
  int N = len(f);
  FOR(i, N) s += f[i] * c, c *= x;
  return s;
}

TE Z fps_t<T>::crt(ull a, ull b, ull c) -> T {
  constexpr ull x = 104'391'568, xx = 190'329'765;
  ull t = (b - a + p1) * x % p1, s = a + t * p0;
  t = (c - s % p2 + p2) * xx % p2;
  return T(s) + T(t) * T(ull(p0) * p1);
}

TE Z fps_t<T>::ntr(T *w, T *iw, T *r, T *ir, T *b, T *ib) -> void {
  w[t] = fps_t<T>::r, iw[t] = w[t].inv();
  FOR_R(i, t) w[i] = w[i + 1] * w[i + 1], iw[i] = iw[i + 1] * iw[i + 1];
  T s = 1, c = 1;
#define f(a, g) FOR(i, t - g + 1) a[i] = w[i + g] * s, s *= iw[i + g], i##a[i] = iw[i + g] * c, c *= w[i + g]
  f(r, 2);
  s = c = 1;
  f(b, 3);
#undef f
}


TE Z fps_t<T>::ntt(fps &a, bool in) -> void {
  assert(T::can_ntt());
  const uint m = p;
  static T w[30], iw[30], r[30], ir[30], b[30], ib[30];
  static bool ok = 0;
  if (ok == 0) ok = 1, ntr(w, iw, r, ir, b, ib);

#define f(k) a[i + of + k * p]
#define g(k) ull(f(k).val())
#define tp topbit(~s & -~s)
  int N = len(a), n = topbit(N);
  if (not in) {
    int sz = 0;
    while (sz < n) {
      if (n - sz == 1) {
        int p = 1 << (n - sz - 1);
        T c = 1;
        FOR(s, 1 << sz) {
          int of = s << (n - sz);
          FOR(i, p) {
            T l = f(0), w = f(1) * c;
            f(0) = l + w, f(1) = l - w;
          }
          c *= r[tp];
        }
        ++sz;
      } else {
        int p = 1 << (n - sz - 2);
        T c = 1, in = w[2];
        FOR(s, 1 << sz) {
          T rr = c * c, R = rr * c;
          int of = s << (n - sz);
          FOR(i, p) {
            ull x = g(0), y = g(1) * c.val(), e = g(2) * rr.val(),
                r = g(3) * R.val(), t = (y + M - r) % m * in.val();
            f(0) = x + y + e + r;
            f(1) = x + e + M + M - y - r;
            f(2) = x + M - e + t;
            f(3) = x + M + M - e - t;
          }
          c *= b[tp];
        }
        sz += 2;
      }
    }
  } else {
    T c = T(N).inv();
    FOR(i, N) a[i] *= c;
    int sz = n;
    while (sz) {
      if (sz == 1) {
        int p = 1 << (n - sz);
        T c = 1;
        FOR(s, 1 << (sz - 1)) {
          int of = s << (n - sz + 1);
          FOR(i, p) {
            ull l = g(0), r = g(1);
            f(0) = l + r, f(1) = (m + l - r) * c.val();
          }
          c *= ir[tp];
        }
        --sz;
      } else {
        int p = 1 << (n - sz);
        T c = 1, in = iw[2];
        FOR(s, 1 << (sz - 2)) {
          T rr = c * c, R = rr * c;
          int of = s << (n - sz + 2);
          FOR(i, p) {
            ull x = g(0), y = g(1), e = g(2), r = g(3),
                t = (m + e - r) * in.val() % m;
            f(0) = x + y + e + r;
            f(1) = (x + m - y + t) * c.val();
            f(2) = (x + y + m + m - e - r) * rr.val();
            f(3) = (x + m + m - y - t) * R.val();
          }
          c *= ib[tp];
        }
        sz -= 2;
      }
    }
  }
}
#undef f
#undef g
#undef tp

TE Z fps_t<T>::conv_naive(cf a, cf b) -> fps {
  int N = len(a), M = len(b), sz = N + M - 1;
  if (not N or not M) return {};
  if (N > M) return conv_naive(b, a);
  fps c(sz);
  FOR(i, N) FOR(k, M) c[i + k] += a[i] * b[k];
  return c;
}  

TE Z fps_t<T>::conv_kara(cf f, cf g) -> fps {
  constexpr int lm = 30;
  if (min(len(f), len(g)) <= lm) return conv_naive(f, g);
  int N = max(len(f), len(g)), M = ceil(N, 2);
  fps 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()};
  fps a = conv_kara(f1, g1);
  fps b = conv_kara(f2, g2);
  FOR(i, len(f2)) f1[i] += f2[i];
  FOR(i, len(g2)) g1[i] += g2[i];
  fps c = conv_kara(f1, g1);
  fps F(len(f) + len(g) - 1);
  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;
}

TE Z fps_t<T>::conv_ntt(fps a, fps b) -> fps {
  assert(T::can_ntt());
  int N = len(a), M = len(b), sz = 1;
  if (min(N, M) == 0) return {};
  while (sz < N + M - 1) sz <<= 1;
  sh(a, sz), sh(b, sz);
  ntt(a, 0);
  ntt(b, 0);
  FOR(i, sz) a[i] *= b[i];
  ntt(a, 1);
  sh(a, N + M - 1);
  return a;
}

TE Z fps_t<T>::conv_mtt(cf a, cf b) -> fps {
  int N = len(a), M = len(b);
  if (not N or not M) return {};
  f0::fps a0(N), b0(M);
  f1::fps a1(N), b1(M);
  f2::fps 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();
  Z c0 = f0::conv_ntt(a0, b0);
  Z c1 = f1::conv_ntt(a1, b1);
  Z c2 = f2::conv_ntt(a2, b2);
  fps c(len(c0));
  FOR(i, N + M - 1) c[i] = crt(c0[i].val(), c1[i].val(), c2[i].val());
  return c;
}

TE Z fps_t<T>::conv(cf a, cf b) -> fps {
  int N = len(a), M = len(b);
  if (min(N, M) == 0) return {};
  if (T::can_ntt()) {
    if (min(N, M) <= 50) return conv_kara(a, b);
    return conv_ntt(a, b);
  }
  if (min(N, M) <= 200) return conv_kara(a, b);
  return conv_mtt(a, b);
}

TE Z fps_t<T>::sq_ntt(fps a) -> fps {
  assert(T::can_ntt());
  int N = len(a), sz = 1;
  if (N == 0) return {};
  while (sz < N + N - 1) sz <<= 1;
  sh(a, sz);
  ntt(a, 0);
  FOR(i, sz) a[i] *= a[i];
  ntt(a, 1);
  sh(a, N + N - 1);
  return a;
}

TE Z fps_t<T>::sq_mtt(cf a) -> fps {
  int N = len(a);
  if (N == 0) return {};
  f0::fps a0(N);
  f1::fps a1(N);
  f2::fps a2(N);
  FOR(i, N) a0[i] = a[i].val(), a1[i] = a[i].val(), a2[i] = a[i].val();
  Z c0 = f0::sq_ntt(a0);
  Z c1 = f1::sq_ntt(a1);
  Z c2 = f2::sq_ntt(a2);
  fps c(len(c0));
  FOR(i, N + N - 1) c[i] = crt(c0[i].val(), c1[i].val(), c2[i].val());
  return c;
}

TE Z fps_t<T>::sq(cf a) -> fps {
  int N = len(a);
  if (T::can_ntt()) {
    if (N <= 50) return conv_naive(a, a);
    return sq_ntt(a);
  }
  if (N <= 150) return conv_kara(a, a);
  return sq_mtt(a);
}

// 微分
TE Z fps_t<T>::diff(cf f) -> fps {
  int N = len(f);
  if (N <= 1) return {};
  fps g(N - 1);
  FOR(i, N - 1) g[i] = f[i + 1] * T(i + 1);
  return g;
}

// 积分
TE Z fps_t<T>::inte(cf f) -> fps {
  int N = len(f);
  fps g(N + 1);
  FOR(i, 1, N + 1) g[i] = f[i - 1] * inv(i);
  return g;
}

// 定积分
TE Z fps_t<T>::inte(cf f, T l, T r) -> T {
  T s = 0, L = 1, R = 1;
  int N = len(f);
  FOR(i, N) {
    L *= l, R *= r;
    s += inv(i + 1) * f[i] * (L - R);
  }
  return s;
}
#line 2 "YRS/poly/fps_div.hpp"

#line 2 "YRS/poly/fps_inv.hpp"

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

TE Z fps_t<T>::inv_sp(cf f) -> fps {
  int N = len(f);
  vc<pair<int, T>> a;
  FOR(i, 1, N) if (f[i] != T(0)) a.ep(i, f[i]);
  fps g(N);
  T t = T(1) / f[0];
  g[0] = t;
  FOR(i, 1, N) {
    T s = 0;
    for (Z &&[x, y] : a) {
      if (x > i) break;
      s -= y * g[i - x];
    }
    g[i] = s * t;
  }
  return g;
}

TE Z fps_t<T>::inv_ntt(cf a) -> fps {
  fps s{T(1) / a[0]};
  int N = len(a), n = 1;
  s.reserve(N);
  for (; n < N; n <<= 1) {
    fps f(n << 1), g(n << 1);
    int sz = min(N, n << 1);
    FOR(i, sz) f[i] = a[i];
    FOR(i, n) g[i] = s[i];
    ntt(f, 0);
    ntt(g, 0);
    FOR(i, n << 1) f[i] *= g[i];
    ntt(f, 1);

    FOR(i, n) f[i] = 0;
    ntt(f, 0);
    FOR(i, n << 1) f[i] *= g[i];
    ntt(f, 1);
    FOR(i, n, sz) s.ep(-f[i]);
  }
  return s;
}

TE Z fps_t<T>::inv_mtt(cf a) -> fps {
  int N = len(a), n = 1;
  fps c{a[0].inv()}, p;
  for (; n < N; n <<= 1) {
    p = sq(c);
    sh(p, n << 1);
    fps f(begin(a), begin(a) + min(n << 1, N));
    p = conv(p, f);
    sh(c, n << 1);
    FOR(i, n << 1) c[i] = c[i] + c[i] - p[i];
  }
  sh(c, N);
  return c;
}

TE Z fps_t<T>::inv(cf f) -> fps {
  int t = count_terms(f), c = T::can_ntt() ? 160 : 820;
  if (t < c) return inv_sp(f);
  return T::can_ntt() ? inv_ntt(f) : inv_mtt(f);
}
#line 5 "YRS/poly/fps_div.hpp"

TE Z fps_t<T>::div_sp(fps f, fps g) -> fps {
  if (g[0].val() != 1) {
    T c = g[0].inv();
    for (T &x : f) x *= c;
    for (T &x : g) x *= c;
  }
  vc<pair<int, T>> a;
  int N = len(g);
  FOR(i, 1, N) if (g[i].val() != 0) a.ep(i, -g[i]);
  N = len(f);
  FOR(i, N) for (Z &&[x, y] : a) if (i >= x) f[i] += y * f[i - x];
  return f;
}

TE Z fps_t<T>::div_ntt(cf f, cf g) -> fps {
  int N = len(f), M = len(g);
  if (N == 1) return {f[0] / g[0]};
  int m = 1;
  while (m + m < N) m <<= 1;
  fps a(m << 1), b(m << 1), c(g);
  sh(c, m);
  c = inv(c);
  sh(c, m << 1);
  ntt(c, 0);

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

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

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

  FOR(i, m) a[i] = 0;
  FOR(i, m, min(m << 1, N)) a[i] -= f[i];
  ntt(a, 0);
  FOR(i, m << 1) a[i] *= c[i];
  ntt(a, 1);
  FOR(i, m, N) s[i] -= a[i];
  return s;
}

TE Z fps_t<T>::div_mtt(fps f, fps g) -> fps {
  int N = len(f);
  sh(g, N);
  g = inv(g);
  f = conv(f, g);
  sh(f, N);
  return f;
}

TE Z fps_t<T>::div_dense(cf f, cf g) -> fps {
  return T::can_ntt() ? div_ntt(f, g) : div_mtt(f, g);
}

TE Z fps_t<T>::div(cf f, cf g) -> fps {
  if (count_terms(g) < 50) return div_sp(f, g);
  return T::can_ntt() ? div_ntt(f, g) : div_mtt(f, g);
}
#line 5 "YRS/poly/fps_log.hpp"

TE Z fps_t<T>::log_sp(cf f) -> fps {
  int N = len(f);
  vc<pair<int, T>> a;
  FOR(i, 1, N) if (f[i].val() != 0) a.ep(i, f[i]);
  fps b(N), c(N - 1);
  FOR(i, N - 1) {
    T s = f[i + 1] * T(i + 1);
    for (Z &&[x, y] : a) {
      if (x > i) break;
      s -= y * c[i - x];
    }
    c[i] = s;
    b[i + 1] = s * inv(i + 1);
  }
  return b;
}

TE Z fps_t<T>::log_dense(cf f) -> fps {
  assert(f[0] == T(1));
  int N = len(f);
  fps c(f);
  FOR(i, N) c[i] *= i;
  c = div_dense(c, f);
  FOR(i, N) c[i] *= inv(i);
  return c;
}

TE Z fps_t<T>::log(cf f) -> fps {
  assert(f[0] == T(1));
  int c = count_terms(f), t = T::can_ntt() ? 200 : 1200;
  return c <= t ? log_sp(f) : log_dense(f);
}
#line 2 "YRS/poly/fps_exp.hpp"

#line 4 "YRS/poly/fps_exp.hpp"

TE Z fps_t<T>::exp_sp(cf f) -> fps {
  int N = len(f);
  if (N == 0) return {T(1)};
  assert(f[0].val() == 0);
  vc<pair<int, T>> a;
  FOR(i, 1, N) if (f[i].val() != 0) a.ep(i - 1, f[i] * T(i));
  fps c(N);
  c[0] = 1;
  FOR(i, 1, N) {
    T s = 0;
    for (Z &&[x, y] : a) {
      if (x > i - 1) break;
      s += y * c[i - 1 - x];
    }
    c[i] = s * inv(i);
  }
  return c;
}

TE Z fps_t<T>::exp_ntt(cf f) -> fps {
  int N = len(f);
  assert(N > 0 and f[0].val() == 0);
  vc<T> s{1, (N > 1 ? f[1] : 0)}, c{1}, a, b{1, 1};
  while (len(s) < N) {
    int m = len(s);
    fps y = s;
    sh(y, m << 1);
    ntt(y, 0);
    a = b;
    vc<T> z(m);
    FOR(i, m) z[i] = y[i] * a[i];
    ntt(z, 1);
    FOR(i, m >> 1) z[i] = 0;
    ntt(z, 0);
    FOR(i, m) z[i] *= -a[i];
    ntt(z, 1);
    c.insert(c.end(), z.begin() + m / 2, z.end());
    b = c;
    sh(b, m << 1);
    ntt(b, 0);

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

    FOR(i, m - 1) x[i] -= s[i + 1] * T(i + 1);

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

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

TE Z fps_t<T>::exp_mtt(cf e) -> fps {
  fps h(e);
  int N = len(h), n = 0, m = 1;
  assert(N > 0 and h[0] == T(0));
  while (1 << n < N) ++n;
  sh(h, 1 << n);
  Z dh = diff(h);
  fps f{1}, g{1}, p;
  FOR(n) {
    p = conv(f, g);
    sh(p, m);
    p = conv(p, g);
    sh(p, m);
    sh(g, m);
    FOR(i, m) g[i] += g[i] - p[i];

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

TE Z fps_t<T>::exp_dense(cf f) -> fps {
  return T::can_ntt() ? exp_ntt(f) : exp_mtt(f);
}

TE Z fps_t<T>::exp(cf f) -> fps {
  int n = count_terms(f), t = T::can_ntt() ? 320 : 3000;
  return n <= t ? exp_sp(f) : exp_dense(f);
}
#line 5 "YRS/poly/fps_pow.hpp"

TE Z fps_t<T>::pw_sp(cf f, T k) -> fps {
  int N = len(f);
  assert(N == 0 or f[0] == T(1));
  vc<pair<int, T>> a;
  FOR(i, 1, N) if (f[i].val() != 0) a.ep(i, f[i]);
  vc<T> g(N);
  g[0] = 1;
  FOR(i, N - 1) {
    T &s = g[i + 1];
    for (Z &&[x, y] : a) {
      if (x > i + 1) break;
      T t = y * g[i - x + 1];
      s += t * (k * T(x) - T(i - x + 1));
    }
    s *= inv(i + 1);
  }
  return g;
}

TE Z fps_t<T>::pw_dense(cf f, T k) -> fps {
  assert(f[0] == T(1));
  fps g = log(f);
  int N = len(f);
  FOR(i, N) g[i] *= k;
  return exp(g);
}

TE Z fps_t<T>::pw(cf f, T k) -> fps {
  int n = count_terms(f), t = T::can_ntt() ? 100 : 1300;
  return n <= t ? pw_sp(f, k) : pw_dense(f, k);
}

TE Z fps_t<T>::pow(cf f, ll k) -> fps {
  assert(0 <= k);
  int N = len(f);
  if (k == 0) {
    fps g(N);
    g[0] = 1;
    return g;
  }
  if (f[0] == T(1)) return pw(f, T(k));
  int d = N;
  FOR_R(i, N) if (f[i].val() != 0) d = i;
  if (d >= ceil<ll>(N, k)) return fps(N);
  int of = d * k;
  T c = f[d], in = c.inv();
  fps g(N - of);
  FOR(i, N - of) g[i] = f[d + i] * in;
  g = pw(g, T(k));
  fps s(N);
  c = c.pow(k);
  N = len(g);
  FOR(i, N) s[of + i] = g[i] * c;
  return s;
}
#line 2 "YRS/poly/coef_of_rationals.hpp"

#line 2 "YRS/poly/poly_divmod.hpp"

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

// {q, r} of f/g
TE Z fps_t<T>::divmod(fps f, cf g) -> pair<fps, fps> {
  assert(g.back() != 0);
  int N = len(f), M = len(g);
  if (N < M) return {{}, f};
  fps a = f, b = g;
  reverse(a);
  reverse(b);
  int d = N - M + 1;
  sh(a, d);
  sh(b, d);
  a = div(a, b);
  reverse(a);
  b = conv(a, g);
  FOR(i, N) f[i] -= b[i];
  while (not f.empty() and f.back().val() == 0) pop(f);
  return {a, f};
}
#line 2 "YRS/poly/c/ntt_db.hpp"

#line 2 "YRS/poly/c/trans_ntt.hpp"

#line 4 "YRS/poly/c/trans_ntt.hpp"

TE Z fps_t<T>::trans_ntt(vc<T> &a, bool in) -> void {
  assert(T::can_ntt());
  const uint m = T::get_mod();
  static T w[30], iw[30], r[30], ir[30], b[30], ib[30];
  static bool ok = 0;
  if (ok == 0) ok = 1, ntr(w, iw, r, ir, b, ib);

#define f(k) a[i + of + k * p]
#define g(k) ull(f(k).val())
#define tp topbit(~s & -~s)
  int N = len(a), n = topbit(N);
  if (not in) {
    int sz = n;
    while (sz) {
      if (sz == 1) {
        int p = 1 << (n - sz);
        T c = 1;
        FOR(s, 1 << (sz - 1)) {
          int of = s << (n - sz + 1);
          FOR(i, p) {
            T l = f(0), w = f(1) * c;
            f(0) = l + w, f(1) = l - w;
          }
          c *= r[tp];
        }
        --sz;
      } else {
        int p = 1 << (n - sz);
        T c = 1, in = w[2];
        FOR(s, 1 << (sz - 2)) {
          T rr = c * c, R = rr * c;
          int of = s << (n - sz + 2);
          FOR(i, p) {
            ull x = g(0), y = g(1), e = g(2), r = g(3),
                t = (m + e - r) * in.val() % m;
            f(0) = x + y + e + r;
            f(1) = (x + m - y + t) * c.val();
            f(2) = (x + y + m + m - e - r) * rr.val();
            f(3) = (x + m + m - y - t) * R.val();
          }
          c *= b[tp];
        }
        sz -= 2;
      }
    }
  } else {
    T c = T(N).inv();
    FOR(i, N) a[i] *= c;
    int sz = 0;
    while (sz < n) {
      T c = 1;
      if (sz == n - 1) {
        int p = 1 << (n - sz - 1);
        FOR(s, 1 << sz) {
          int of = s << (n - sz);
          FOR(i, p) {
            T l = f(0), w = f(1) * c;
            f(0) = l + w, f(1) = l - w;
          }
          c *= ir[tp];
        }
        ++sz;
      } else {
        int p = 1 << (n - sz - 2);
        T in = iw[2];
        FOR(s, 1 << sz) {
          T rr = c * c, R = rr * c;
          int of = s << (n - sz);
          FOR(i, p) {
            ull x = g(0), y = g(1) * c.val(), e = g(2) * rr.val(),
                r = g(3) * R.val(), t = (y + M - r) % m * in.val();
            f(0) = x + y + e + r;
            f(1) = x + e + (2 * M - y - r);
            f(2) = x + M - e + t;
            f(3) = x + M + M - e - t;
          }
          c *= ib[tp];
        }
        sz += 2;
      }
    }
  }
}
#undef f
#undef g
#undef tp
#line 5 "YRS/poly/c/ntt_db.hpp"

TE Z fps_t<T>::ntt_db(fps &a, bool tr) -> void {
  static array<T, 30> rt;
  static bool ok = 0;
  if (not ok) {
    ok = 1;
    rt[t] = r;
    FOR_R(i, t) rt[i] = rt[i + 1] * rt[i + 1];
  }
  if (not tr) {
    int N = len(a);
    Z b = a;
    ntt(b, 1);
    T s = 1, c = rt[topbit(N << 1)];
    FOR(i, N) b[i] *= s, s *= c;
    ntt(b, 0);
    copy(all(b), back_inserter(a));
  } else {
    int N = len(a) >> 1;
    fps t{a.begin(), a.begin() + N};
    a = {a.begin() + N, a.end()};
    trans_ntt(a, 0);
    T s = 1, c = rt[topbit(N << 1)];
    FOR(i, N) a[i] *= s, s *= c;
    trans_ntt(a, 1);
    FOR(i, N) a[i] += t[i];
  }
}
#line 5 "YRS/poly/coef_of_rationals.hpp"

// https://judge.yosupo.jp/problem/kth_term_of_linearly_recurrent_sequence
// https://yukicoder.me/problems/no/213

TE Z fps_t<T>::coef_of_rationals_ntt(fps p, fps q, ll k) -> T {
  assert(len(p) + 1 == len(q) and q[0] == T(1));
  if (p.empty()) return 0;
  int N = 1;
  while (N < len(q)) N <<= 1;
  fps w(N);
  vc<int> b(N);
  int n = topbit(N);
  FOR(i, N) b[i] = (b[i >> 1] >> 1) + ((i & 1) << (n - 1));
  const int t = T::ntt_info().fi;
  const T r = T::ntt_info().se;
  T s = r.inv().pow((1 << t) / (N << 1)), c = inv(2);
  for (int i : b) w[i] = c, c *= s;
  sh(p, N << 1);
  sh(q, N << 1);
  ntt(p, 0);
  ntt(q, 0);
  while (k >= N) {
    if (not(k & 1)) {
      FOR(i, N) {
        p[i] = (p[i << 1] * q[i << 1 | 1] + p[i << 1 | 1] * q[i << 1]) * inv(2);
      }
    } else {
      FOR(i, N) {
        p[i] = (p[i << 1] * q[i << 1 | 1] - p[i << 1 | 1] * q[i << 1]) * w[i];
      }
    }
    FOR(i, N) q[i] = q[i << 1] * q[i << 1 | 1];
    sh(p, N);
    sh(q, N);
    k >>= 1;
    if (k < N) break;
    ntt_db(p), ntt_db(q);
  }
  ntt(p, 1), ntt(q, 1);
  q = inv(q);
  T res = 0;
  FOR(i, k + 1) res += p[i] * q[k - i];
  return res;
}

TE Z fps_t<T>::coef_of_rationals_mtt(fps p, fps q, ll k) -> T {
  assert(len(p) + 1 == len(q) and q[0] == T(1));
  if (p.empty()) return 0;
  while (k >= len(p)) {
    vc<T> a(q);
    int n = len(a);
    FOR(i, n) if (i & 1) a[i] = -a[i];
    p = conv(p, a);
    q = conv(q, a);
    FOR(i, n) q[i] = q[i << 1];
    FOR(i, n - 1) p[i] = p[i << 1 | (k & 1)];
    sh(p, n - 1);
    sh(q, n);
    k >>= 1;
  }
  return div(p, q)[k];
}

// [x^k]P/Q  求 ai=sum ci ai-j 则是 p / {1, -c1, -c2}
TE Z fps_t<T>::coef_of_rationals(fps p, fps q, ll k) -> T {
  if (p.empty()) return {};
  assert(len(q) > 0 and q[0] != T(0));
  while (q.back().val() == 0) pop(q);
  T c = q[0].inv(), s = 0;
  for (T &x : p) x *= c;
  for (T &x : q) x *= c;
  if (len(p) >= len(q)) {
    Z [f, g] = divmod(p, q);
    s = (k < len(f) ? f[k] : T(0));
    p = g;
  }
  sh(p, len(q) - 1);
  if (T::can_ntt()) return s + coef_of_rationals_ntt(p, q, k);
  return s + coef_of_rationals_mtt(p, q, k);
}

TE Z fps_t<T>::coef_of_rationals(fps p, fps q, ll l, ll r) -> fps {
  int m = r - l;
  if (m <= 0 or p.empty()) return {};
  assert(len(q) > 0 and q[0].val() != 0);
  while (q.back().val() == 0) pop(q);
  T c = q[0].inv();
  for (T &x : p) x *= c;
  for (T &x : q) x *= c;
  fps S, rem = p, res(m);
  if (len(p) >= len(q)) {
    Z [f, g] = divmod(p, q);
    S = f, p = g;
  }
  if (not S.empty()) {
    ll l0 = max<ll>(l, 0), r0 = min<ll>(r, len(S));
    for (ll i = l0; i < r0; ++i) res[i - l] += S[i];
  }
  int deg = len(q) - 1, bs = max(64, 2 * deg);
  sh(p, deg);
  

  Z f = [&](Z &&f, fps P, fps Q, ll l, ll r) -> fps {
    if (r <= l) return {};
    if (P.empty()) return fps((int)(r - l), T(0));

    while ((int)Q.size() > 1 && Q.back().val() == 0) pop(Q);

    if (r <= bs) {
      fps F((int)r);
      int up = min<int>((int)P.size(), (int)r);
      for (int i = 0; i < up; ++i) F[i] = P[i];
      fps A = div(F, Q);
      fps rs((int)(r - l));
      for (int i = 0; i < (int)(r - l); ++i) rs[i] = A[(int)l + i];
      return rs;
    }

    fps Qn = Q;
    for (int i = 1; i < (int)Qn.size(); i += 2) Qn[i] = -Qn[i];

    fps C = conv(P, Qn);
    fps D = conv(Q, Qn);

    int n = (int)Q.size();          // n = deg(Q)+1
    fps Qe(n, T(0));
    for (int i = 0; i < n; ++i) {
      int idx = i << 1;
      if (idx < (int)D.size()) Qe[i] = D[idx];
    }
    while ((int)Qe.size() > 1 && Qe.back().val() == 0) pop(Qe);

    int m = (int)Qe.size() - 1;     // = deg(Qe)
    fps Pe(m, T(0)), Po(m, T(0));
    for (int i = 0; i < m; ++i) {
      int ei = i << 1;
      int oi = ei | 1;
      if (ei < (int)C.size()) Pe[i] = C[ei];
      if (oi < (int)C.size()) Po[i] = C[oi];
    }

    ll le = (l + 1) / 2, re = (r + 1) / 2;
    ll lo = l / 2, ro = r / 2;

    fps even = f(f, Pe, Qe, le, re);
    fps odd = f(f, Po, Qe, lo, ro);

    fps rs((int)(r - l));
    for (ll k = l; k < r; ++k) {
      if ((k & 1) == 0) {
        ll n = k >> 1;
        rs[k - l] = even[n - le];
      } else {
        ll n = k >> 1;
        rs[k - l] = odd[n - lo];
      }
    }
    return rs;
  };

  ll l0 = max<ll>(0, l), r0 = max<ll>(0, r);
  if (r0 > l0) {
    fps seg = f(f, p, q, l0, r0);  // seg size = r0-l0
    for (int i = 0; i < (int)seg.size(); ++i) res[(l0 - l) + i] += seg[i];
  }

  return res;
}
#line 6 "No_213_\u7d20\u6570\u30b5\u30a4\u30b3\u30ed\u3068\u5408\u6210\u6570\u30b5\u30a4\u30b3\u30ed_3_Easy.cpp"

using mint = M11;
using fps = vc<mint>;
fps_t<mint> X;
fps gen(const vc<int> &a, int c) {
  fps go(100);
  int N = len(a);
  Z f = [&](Z &f, int n, int s, int ls) -> void {
    if (n == N) {
      go[s] += ls == 0;
      return;
    }
    FOR(i, ls + 1) f(f, n + 1, s + i * a[n], ls - i);
  };
  f(f, 0, 0, c);
  while(not go.empty() and go.back().val() == 0) pop(go);
  return go;
}
void Yorisou() {
  LL(N, P, C);
  vc<int> a{2, 3, 5, 7, 11, 13}, b{4, 6, 8, 9, 10, 12};
  fps f = X.conv(gen(a, P), gen(b, C));
  int sz = len(f);
  fps g = f, ls(sz << 1);
  for (mint &x : f) x = -x;
  f[0] += 1;
  int d = min<ll>(N, sz);
  Z coef = X.coef_of_rationals(fps{1}, f, N - d, N);
  copy(all(coef), begin(ls) + sz - d);
  // FOR(i, 1, min<ll>(N, sz) + 1) {
  //   assert(ls[sz - i] == X.coef_of_rationals(fps{1}, f, N - i));
  //   ls[sz - i] = X.coef_of_rationals(fps{1}, f, N - i);
  // }
  ls = X.conv(ls, g);
  mint s;
  FOR(i, sz, sz << 1) s += ls[i];
  print(s);
}
constexpr int tests = 0, fl = 0, DB = 10;
#line 1 "YRS/aa/main.hpp"
int main() {
  cin.tie(0)->sync_with_stdio(0);
  int T = 1;
  if (fl) cerr.tie(0);
  if (tests and not fl) IN(T);
  for (int i = 0; i < T or fl; ++i) {
    Yorisou();
    if (fl and i % DB == 0) cerr << "Case: " << i << '\n';
  }
  return 0;
}
#line 46 "No_213_\u7d20\u6570\u30b5\u30a4\u30b3\u30ed\u3068\u5408\u6210\u6570\u30b5\u30a4\u30b3\u30ed_3_Easy.cpp"