Tifa's CP Library

:heavy_check_mark: src/test_cpverifier/library-checker/stirling_number_of_the_second_kind_fixed_k.pcntt-s30.test.cpp

Depends on

Code

#define AUTO_GENERATED
#define PROBLEM "https://judge.yosupo.jp/problem/stirling_number_of_the_second_kind_fixed_k"

#include "../../code/comb/gen_stirling2_col.hpp"
#include "../../code/io/fastio.hpp"

constexpr u32 MOD = 998244353;

#include "../../code/math/mint_s30.hpp"
#include "../../code/poly/polycntt.hpp"

using mint = tifa_libs::math::mint_s30<MOD>;
using poly = tifa_libs::math::polycntt<mint>;

int main() {
  u32 n, k;
  tifa_libs::fin >> n >> k;
  auto ans = tifa_libs::math::gen_stirling2_col<poly>(n, k);
  for (u32 i = k; i <= n; ++i) tifa_libs::fout << ans[i] << " \n"[i == n];
  return 0;
}
#line 1 "src/test_cpverifier/library-checker/stirling_number_of_the_second_kind_fixed_k.pcntt-s30.test.cpp"
#define AUTO_GENERATED
#define PROBLEM "https://judge.yosupo.jp/problem/stirling_number_of_the_second_kind_fixed_k"

#line 1 "src/code/comb/gen_stirling2_col.hpp"



#line 1 "src/code/poly/inv_fps.hpp"



#line 1 "src/code/poly/poly.hpp"



#line 1 "src/code/util/util.hpp"



#include <bits/stdc++.h>

template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }

using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using i128 = __int128_t;
using isz = ptrdiff_t;

using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
using usz = size_t;

using f32 = float;
using f64 = double;
using f128 = long double;

template <class T>
using ptt = std::pair<T, T>;
template <class T>
using pt3 = std::tuple<T, T, T>;
template <class T>
using pt4 = std::tuple<T, T, T, T>;

template <class T, usz N>
using arr = std::array<T, N>;
template <class T>
using vec = std::vector<T>;
template <class T>
using vvec = vec<vec<T>>;
template <class T>
using v3ec = vec<vvec<T>>;
template <class U, class T>
using vecp = vec<std::pair<U, T>>;
template <class U, class T>
using vvecp = vvec<std::pair<U, T>>;
template <class T>
using vecpt = vec<ptt<T>>;
template <class T>
using vvecpt = vvec<ptt<T>>;

template <class T, class C = std::less<T>>
using pq = std::priority_queue<T, vec<T>, C>;
template <class T>
using pqg = std::priority_queue<T, vec<T>, std::greater<T>>;

using strn = std::string;
using strnv = std::string_view;

using vecu = vec<u32>;
using vvecu = vvec<u32>;
using v3ecu = v3ec<u32>;
using vecu64 = vec<u64>;
using vecb = vec<bool>;
using vvecb = vvec<bool>;

#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif

using namespace std::literals;

constexpr i8 operator""_i8(unsigned long long x) { return (i8)x; }
constexpr i16 operator""_i16(unsigned long long x) { return (i16)x; }
constexpr i32 operator""_i32(unsigned long long x) { return (i32)x; }
constexpr i64 operator""_i64(unsigned long long x) { return (i64)x; }
constexpr isz operator""_iz(unsigned long long x) { return (isz)x; }

constexpr u8 operator""_u8(unsigned long long x) { return (u8)x; }
constexpr u16 operator""_u16(unsigned long long x) { return (u16)x; }
constexpr u32 operator""_u32(unsigned long long x) { return (u32)x; }
constexpr u64 operator""_u64(unsigned long long x) { return (u64)x; }
constexpr usz operator""_uz(unsigned long long x) { return (usz)x; }

inline const auto fn_0 = [](auto&&...) {};


#line 5 "src/code/poly/poly.hpp"

namespace tifa_libs::math {

// clang-format off
enum ccore_t { ct_FFT, ct_3NTT, ct_NTT, ct_CNTT };
// clang-format on

template <class mint, class ccore>
requires requires(ccore cc, vec<mint> l, vec<mint> const &r, u32 sz) {
  { ccore::ct_cat } -> std::same_as<ccore_t const &>;
  cc.conv(l, r);
  cc.conv(l, r, sz);
}
class poly {
  vec<mint> d;

 public:
  using value_type = mint;
  using data_type = vec<value_type>;
  using ccore_type = ccore;
  static inline ccore_type conv_core;

  explicit constexpr poly(u32 sz = 1, value_type const &val = value_type{}) : d(sz, val) {}
  constexpr poly(typename data_type::const_iterator begin, typename data_type::const_iterator end) : d(begin, end) {}
  constexpr poly(std::initializer_list<value_type> v) : d(v) {}
  template <class T>
  explicit constexpr poly(vec<T> const &v) : d(v) {}

  friend constexpr std::istream &operator>>(std::istream &is, poly &poly) {
    for (auto &val : poly.d) is >> val;
    return is;
  }
  friend constexpr std::ostream &operator<<(std::ostream &os, poly const &poly) {
    if (!poly.size()) return os;
    for (u32 i = 1; i < poly.size(); ++i) os << poly[i - 1] << ' ';
    return os << poly.d.back();
  }

  constexpr u32 size() const { return (u32)d.size(); }
  constexpr bool empty() const {
    for (auto &&i : d)
      if (i != 0) return 0;
    return 1;
  }
  constexpr data_type &data() { return d; }
  constexpr data_type const &data() const { return d; }

  constexpr value_type &operator[](u32 x) { return d[x]; }
  constexpr value_type const &operator[](u32 x) const { return d[x]; }
  constexpr value_type operator()(value_type x) const {
    value_type ans = 0;
    for (u32 i = size() - 1; ~i; --i) ans = ans * x + d[i];
    return ans;
  }

  template <class F>
  requires requires(F f, u32 idx, mint &val) {
    f(idx, val);
  }
  constexpr void apply_range(u32 l, u32 r, F &&f) {
    assert(l < r && r <= size());
    for (u32 i = l; i < r; ++i) f(i, d[i]);
  }
  template <class F>
  constexpr void apply(F &&f) { apply_range(0, size(), std::forward<F>(f)); }
  constexpr void resize(u32 size) { d.resize(size); }
  constexpr poly pre(u32 size) const {
    poly _ = *this;
    _.resize(size);
    return _;
  }
  constexpr void strip() {
    auto it = std::find_if(d.rbegin(), d.rend(), [](auto const &x) { return x != 0; });
    d.resize(usz(d.rend() - it));
    if (d.empty()) d.push_back(value_type(0));
  }
  friend poly stripped(poly p) {
    p.strip();
    return p;
  }
  constexpr void reverse(u32 n = 0) { std::reverse(d.begin(), d.begin() + (n ? n : size())); }
  constexpr void conv(poly const &r, u32 ans_size = 0) { conv_core.conv(d, r.d, ans_size); }

  constexpr poly operator-() const {
    poly ret = *this;
    ret.apply([](u32, auto &v) { v = -v; });
    return ret;
  }

  friend constexpr poly operator+(poly p, value_type c) {
    p[0] += c;
    return p;
  }
  friend constexpr poly operator+(value_type c, poly const &p) { return p + c; }
  friend constexpr poly operator-(poly p, value_type c) {
    p[0] -= c;
    return p;
  }
  friend constexpr poly operator-(value_type c, poly const &p) { return p - c; }

  constexpr poly &operator*=(value_type c) {
    apply([&c](u32, auto &v) { v *= c; });
    return *this;
  }
  friend constexpr poly operator*(poly p, value_type c) { return p *= c; }
  friend constexpr poly operator*(value_type c, poly p) { return p *= c; }

  constexpr poly &operator+=(poly const &r) {
    if (!r.size()) return *this;
    resize(std::max(size(), r.size()));
    apply_range(0, r.size(), [&r](u32 i, auto &v) { v += r[i]; });
    return *this;
  }
  friend constexpr poly operator+(poly l, poly const &r) { return l += r; }

  constexpr poly &operator-=(poly const &r) {
    if (!r.size()) return *this;
    resize(std::max(size(), r.size()));
    apply_range(0, r.size(), [&r](u32 i, auto &v) { v -= r[i]; });
    return *this;
  }
  friend constexpr poly operator-(poly l, poly const &r) { return l -= r; }

  constexpr poly &operator*=(poly const &r) {
    if (!r.size()) {
      resize(1);
      d[0] = 0;
      return *this;
    }
    conv(r);
    return *this;
  }
  friend constexpr poly operator*(poly l, poly const &r) { return l *= r; }

  constexpr auto operator<=>(poly const &r) const { return stripped(*this).d <=> stripped(r).d; }
  constexpr bool operator==(poly const &r) const { return stripped(*this).d == stripped(r).d; }
};

}  // namespace tifa_libs::math


#line 5 "src/code/poly/inv_fps.hpp"

namespace tifa_libs::math {

template <class mint, class ccore>
constexpr poly<mint, ccore> inv_fps(poly<mint, ccore> const &p, u32 n = 0) {
  assert(p[0] != 0);
  if (!n) n = p.size();
  poly<mint, ccore> a{p[0].inv()};
  for (u32 i = 1; i < n; i *= 2) a = (a * 2 - (a * a * p).pre(i * 2)).pre(i * 2);
  return a.pre(n);
}

}  // namespace tifa_libs::math


#line 1 "src/code/poly/shl_fps.hpp"



#line 5 "src/code/poly/shl_fps.hpp"

namespace tifa_libs::math {

template <class mint, class ccore>
constexpr poly<mint, ccore> shl_fps(poly<mint, ccore> const &p, usz x) {
  if (!x) return p;
  auto _ = p;
  if (x >= _.size()) {
    std::ranges::fill(_.data(), 0);
    return _;
  }
  std::fill(_.data().begin(), std::move_backward(_.data().begin(), std::prev(_.data().end(), (isz)x), _.data().end()), 0);
  return _;
}

}  // namespace tifa_libs::math


#line 1 "src/code/poly/tsh_fps.hpp"



#line 1 "src/code/comb/gen_fact.hpp"



#line 1 "src/code/math/mul_mod_u.hpp"



#line 5 "src/code/math/mul_mod_u.hpp"

namespace tifa_libs::math {

constexpr u64 mul_mod_u(u64 a, u64 b, u64 mod) {
  if (std::bit_width(a) + std::bit_width(b) <= 64) return a * b % mod;
  else return (u64)((u128)a * b % mod);
}

}  // namespace tifa_libs::math


#line 5 "src/code/comb/gen_fact.hpp"

namespace tifa_libs::math {

// i! from i=0..n-1
constexpr vecu64 gen_fact(u32 n, u64 mod) {
  if (n == 0) return {};
  if (n == 1) return {1};
  vecu64 ans(n);
  ans[0] = ans[1] = 1;
  for (u32 i = 2; i < n; ++i) ans[i] = mul_mod_u(ans[i - 1], i, mod);
  return ans;
}
// i! from i=0..n-1
template <class mint>
constexpr vec<mint> gen_fact(u32 n) {
  vec<mint> ans(n);
  auto _ = gen_fact(n, mint::mod());
  for (u32 i = 0; i < n; ++i) ans[i] = _[i];
  return ans;
}

}  // namespace tifa_libs::math


#line 1 "src/code/comb/gen_ifact.hpp"



#line 1 "src/code/comb/gen_inv.hpp"



#line 5 "src/code/comb/gen_inv.hpp"

namespace tifa_libs::math {

// i^{-1} from i=0..n-1
constexpr vecu64 gen_inv(u32 n, u64 mod) {
  if (n == 0) return {};
  if (n == 1) return {1};
  vecu64 ans(n);
  ans[0] = ans[1] = 1;
  for (u32 i = 2; i < n; ++i) ans[i] = mul_mod_u(mod - mod / i, ans[mod % i], mod);
  return ans;
}
// i^{-1} from i=0..n-1
template <class mint>
constexpr vec<mint> gen_inv(u32 n) {
  vec<mint> ans(n);
  auto _ = gen_inv(n, mint::mod());
  for (u32 i = 0; i < n; ++i) ans[i] = _[i];
  return ans;
}

}  // namespace tifa_libs::math


#line 6 "src/code/comb/gen_ifact.hpp"

namespace tifa_libs::math {

// (i!)^{-1} from i=0..n-1
constexpr vecu64 gen_ifact(u32 n, u64 mod, vecu64 inv) {
  for (u32 i = 2; i < n; ++i) inv[i] = mul_mod_u(inv[i], inv[i - 1], mod);
  return inv;
}
// (i!)^{-1} from i=0..n-1
constexpr vecu64 gen_ifact(u32 n, u64 mod) { return gen_ifact(n, mod, gen_inv(n, mod)); }
// (i!)^{-1} from i=0..n-1
template <class mint>
constexpr vec<mint> gen_ifact(u32 n, vec<mint> inv) {
  for (u32 i = 2; i < n; ++i) inv[i] *= inv[i - 1];
  return inv;
}
// (i!)^{-1} from i=0..n-1
template <class mint>
constexpr vec<mint> gen_ifact(u32 n) { return gen_ifact(n, gen_inv<mint>(n)); }

}  // namespace tifa_libs::math


#line 7 "src/code/poly/tsh_fps.hpp"

namespace tifa_libs::math {

template <class mint, class ccore>
constexpr poly<mint, ccore> tsh_fps(poly<mint, ccore> const &f, mint c, vecu64 const &fact, vecu64 const &ifact) {
  u32 n = f.size();
  if (n == 1) return f;
  poly<mint, ccore> s = f, p(f.size());
  for (u32 i = 0; i < n; ++i) p[n - i - 1] = f[i] * fact[i];
  {
    mint _ = 1;
    for (u32 i = 0; i < n; ++i, _ *= c) s[i] = _ * ifact[i];
  }
  (p *= s).resize(n);
  for (u32 i = 0; i < n; ++i) s[n - i - 1] = p[i] * ifact[n - i - 1];
  return s;
}
template <class mint, class ccore>
constexpr poly<mint, ccore> tsh_fps(poly<mint, ccore> const &f, mint c) {
  u32 n = f.size();
  if (n == 1) return f;
  return tsh_fps<mint, ccore>(f, c, gen_fact(n, mint::mod()), gen_ifact(n, mint::mod()));
}

}  // namespace tifa_libs::math


#line 7 "src/code/comb/gen_stirling2_col.hpp"

namespace tifa_libs::math {

// stirling2[i] = {i \\brack k}, i=0,1,...,n
template <class poly>
constexpr poly gen_stirling2_col(u32 n, u32 k, vecu64 const& fact, vecu64 const& ifact) {
  using mint = typename poly::value_type;
  if (k > n) return poly(n + 1);

  auto dfs = [&](auto&& dfs, poly& f, u32 n) -> void {
    if (n == 1) return;
    if (n & 1) {
      dfs(dfs, f, n - 1);
      f.data().push_back(0);
      for (u32 i = n; i; --i) f[i] = f[i - 1] - (n - 1) * f[i];
      f[0] = (-f[0]) * (n - 1);
      return;
    }
    dfs(dfs, f, n / 2);
    f.data().push_back(0);
    f *= tsh_fps(f, mint(mint::mod() - n / 2), fact, ifact);
    f.resize(n + 1);
  };

  poly f{0, 1};
  dfs(dfs, f, k + 1);
  f.resize(k + 2);
  for (u32 i = 0; i < k + 1; ++i) f[i] = f[i + 1];
  f.reverse(k + 1);
  f[k + 1] = 0;
  f.resize(n - k + 1);
  f = inv_fps(f).pre(n + 1);
  return shl_fps(f, k);
}
// stirling2[i] = {i \\brack k}, i=0,1,...,n
template <class poly>
constexpr poly gen_stirling2_col(u32 n, u32 k) {
  using mint = typename poly::value_type;
  return gen_stirling2_col<poly>(n, k, gen_fact(n + 1, mint::mod()), gen_ifact(n + 1, mint::mod()));
}

}  // namespace tifa_libs::math


#line 1 "src/code/io/fastio.hpp"



#line 1 "src/code/fast/u32tostr.hpp"



#line 5 "src/code/fast/u32tostr.hpp"

namespace tifa_libs {

constexpr u32 u32tostr_si16(u64 x, char *s) {
  if (x <= 9) {
    *s = (char)(x | 0x30);
    return 1;
  } else if (x <= 99) {
    u64 low = x;
    u64 ll = ((low * 103) >> 9) & 0x1E;
    low += ll * 3;
    ll = ((low & 0xF0) >> 4) | ((low & 0x0F) << 8);
    *(u16 *)s = (u16)(ll | 0x3030);
    return 2;
  }
  return 0;
}
constexpr u32 u32tostr_si32(u64 x, char *s) {
  u64 low = 0, ll = 0;
  u32 digits = 0;
  if (x <= 99) return u32tostr_si16(x, s);
  low = x;
  digits = (low > 999) ? 4 : 3;
  ll = ((low * 5243) >> 19) & 0xFF;
  low -= ll * 100;
  low = (low << 16) | ll;
  ll = ((low * 103) >> 9) & 0x1E001E;
  low += ll * 3;
  ll = ((low & 0x00F000F0) << 28) | (low & 0x000F000F) << 40;
  ll |= 0x3030303000000000;
  u8 *p = (u8 *)&ll;
  if (digits == 4) *(u32 *)s = *(u32 *)(&p[4]);
  else {
    *(u16 *)s = *(u16 *)(&p[5]);
    *(((u8 *)s) + 2) = p[7];
  }

  return digits;
}

constexpr u32 u32tostr(u64 x, char *s) {
  u64 low = 0, ll = 0;
  u32 digits = 0;
  if (x <= 9999) return u32tostr_si32(x, s);
  if (x < 100000000) {
    if ((low = x) > 999999) digits = (low > 9999999) ? 8 : 7;
    else digits = (low > 99999) ? 6 : 5;
  } else {
    u64 high = (x * 0x55E63B89) >> 57;
    low = x - (high * 100000000);
    digits = u32tostr_si16(high, s);
    digits += 8;
  }

  ll = (low * 109951163) >> 40;
  (low -= ll * 10000) |= ll << 32;
  ll = ((low * 5243) >> 19) & 0x000000FF000000FF;
  low -= ll * 100;
  low = (low << 16) | ll;
  ll = ((low * 103) >> 9) & 0x001E001E001E001E;
  low += ll * 3;
  ll = ((low & 0x00F000F000F000F0) >> 4) | (low & 0x000F000F000F000F) << 8;
  ll = (ll >> 32) | (ll << 32) | 0x3030303030303030;

  if (digits >= 8) memcpy(s + digits - 8, &ll, 8);
  else {
    u32 d = digits;
    char *s1 = s, *pll = &(((char *)&ll)[8 - digits]);
    if (d >= 4) {
      memcpy(s1, pll, 4);
      s1 += 4, pll += 4, d -= 4;
    }
    if (d >= 2) {
      memcpy(s1, pll, 2);
      s1 += 2, pll += 2, d -= 2;
    }
    if (d > 0) *(u8 *)s1 = *(u8 *)pll;
  }
  return digits;
}

}  // namespace tifa_libs


#line 1 "src/code/util/traits.hpp"



#line 5 "src/code/util/traits.hpp"

namespace tifa_libs {

template <class T>
concept iterable_c = requires(T v) {
  { v.begin() } -> std::same_as<typename T::iterator>;
  { v.end() } -> std::same_as<typename T::iterator>;
};

template <class T>
concept container_c = iterable_c<T> && !std::derived_from<T, std::basic_string<typename T::value_type>>;

template <class T>
constexpr bool is_char_v = std::is_same_v<T, char> || std::is_same_v<T, signed char> || std::is_same_v<T, unsigned char>;
template <class T>
concept char_c = is_char_v<T>;

template <class T>
constexpr bool is_s128_v = std::is_same_v<T, __int128_t> || std::is_same_v<T, __int128>;
template <class T>
concept s128_c = is_s128_v<T>;

template <class T>
constexpr bool is_u128_v = std::is_same_v<T, __uint128_t> || std::is_same_v<T, unsigned __int128>;
template <class T>
concept u128_c = is_u128_v<T>;

template <class T>
constexpr bool is_i128_v = is_s128_v<T> || is_u128_v<T>;
template <class T>
concept i128_c = is_u128_v<T>;

template <class T>
constexpr bool is_int_v = std::is_integral_v<T> || is_i128_v<T>;
template <class T>
concept int_c = is_int_v<T>;

template <class T>
constexpr bool is_sint_v = is_s128_v<T> || (is_int_v<T> && std::is_signed_v<T>);
template <class T>
concept sint_c = is_sint_v<T>;

template <class T>
constexpr bool is_uint_v = is_u128_v<T> || (is_int_v<T> && std::is_unsigned_v<T>);
template <class T>
concept uint_c = is_uint_v<T>;

template <class T>
concept mint_c = requires(T x) {
  { x.mod() } -> uint_c;
  { x.val() } -> uint_c;
};

template <class T>
constexpr bool is_arithm_v = std::is_arithmetic_v<T> || is_int_v<T>;
template <class T>
concept arithm_c = is_arithm_v<T>;

template <class T>
struct to_sint : std::make_signed<T> {};
template <>
struct to_sint<u128> {
  using type = u128;
};
template <>
struct to_sint<i128> {
  using type = u128;
};
template <class T>
using to_sint_t = typename to_sint<T>::type;

template <class T>
struct to_uint : std::make_unsigned<T> {};
template <>
struct to_uint<u128> {
  using type = u128;
};
template <>
struct to_uint<i128> {
  using type = u128;
};
template <class T>
using to_uint_t = typename to_uint<T>::type;

}  // namespace tifa_libs


#line 6 "src/code/io/fastio.hpp"

namespace tifa_libs {
namespace fastio_impl_ {
//! UB if EOF occured during reading
template <u32 BUF>
class fastin {
  char bf_[BUF], *now_ = bf_, *end_ = bf_;
  FILE *f_;

 public:
  explicit fastin(FILE *f = stdin) : f_(f) {}

  char get() { return now_ == end_ && (end_ = (now_ = bf_) + fread(bf_, 1, BUF, f_), now_ == end_) ? EOF : *(now_)++; }
  char peek() { return now_ == end_ && (end_ = (now_ = bf_) + fread(bf_, 1, BUF, f_), now_ == end_) ? EOF : *(now_); }
  void rebind(FILE *f) {
    f_ = f;
    now_ = end_ = bf_;
  }

  bool iseof() { return peek() == EOF; }

  template <class T>
  requires(sint_c<T> && !char_c<T>)
  fastin &read(T &n) {
    bool is_neg = false;
    char ch = get();
    while (!isdigit(ch)) {
      is_neg |= ch == '-';
      ch = get();
    }
    n = 0;
    while (isdigit(ch)) {
      (n *= 10) += ch & 15;
      ch = get();
    }
    if (is_neg) n = -n;
    return *this;
  }
  template <class T>
  requires(uint_c<T> && !char_c<T>)
  fastin &read(T &n) {
    char ch = get();
    while (!isdigit(ch)) ch = get();
    n = 0;
    while (isdigit(ch)) {
      (n *= 10) += ch & 15;
      ch = get();
    }
    return *this;
  }
  template <mint_c T>
  fastin &read(T &n) {
    decltype(std::declval<T>().sval()) x;
    read(x);
    n = T(x);
    return *this;
  }
  //! ignore cntrl and space
  template <char_c T>
  fastin &read(T &n) {
    while (!isgraph(n = get()));
    return *this;
  }
  fastin &read(char *n) {
    char *n_ = n;
    while (!isgraph(*n_ = get()));
    while (isgraph(*(++n_) = get()));
    *n_ = '\0';
    return *this;
  }
  fastin &read(strn &n) {
    n.clear();
    char n_;
    while (!isgraph(n_ = get()));
    n.push_back(n_);
    while (isgraph(n_ = get())) n.push_back(n_);
    return *this;
  }
  template <class T, class U>
  fastin &read(std::pair<T, U> &p) { return read(p.first).read(p.second); }
  template <class... Ts>
  fastin &read(std::tuple<Ts...> &p) {
    std::apply([&](Ts &...targs) { ((read(targs)), ...); }, p);
    return *this;
  }
  template <container_c T>
  fastin &read(T &p) {
    if (p.begin() == p.end()) return *this;
    for (auto &i : p) read(i);
    return *this;
  }

  fastin &getline(char *n) {
    char *n_ = n;
    while (!isprint(*n_ = get()));
    while (isprint(*(++n_) = get()));
    *n_ = '\0';
    return *this;
  }
  fastin &getline(strn &n) {
    char n_;
    while (!isprint(n_ = get()));
    n.push_back(n_);
    while (isprint(n_ = get())) n.push_back(n_);
    return *this;
  }

  //! NOT ignore cntrl and space
  template <char_c T>
  fastin &strict_read(T &n) {
    n = get();
    return *this;
  }

  template <class T>
  fastin &operator>>(T &val) { return read(val); }
};
template <u32 BUF, u32 INTBUF>
class fastout {
  char int_bf_[INTBUF], *now_ib_ = int_bf_;

  FILE *f_;
  char *now_, bf_[BUF];
  const char *const end_ = bf_ + BUF;

 public:
  explicit fastout(FILE *file = stdout) : f_(file), now_(bf_) {}

  fastout &operator=(fastout const &r) {
    f_ = r.f_;
    now_ = bf_ + (r.now_ - r.bf_);
    memcpy(bf_, r.bf_, sizeof(*bf_) * (r.now_ - r.bf_));
    return *this;
  }
  fastout(fastout const &r) { *this = r; }

  ~fastout() { flush(); }

  void flush() {
    fwrite(bf_, 1, usz(now_ - bf_), f_);
    now_ = bf_;
  }
  void rebind(FILE *file) { f_ = file; }

  template <char_c T>
  fastout &write(T const &n) {
    if (now_ == end_) flush();
    *(now_++) = n;
    return *this;
  }
  fastout &write(const char *n) {
    usz len = strlen(n), l_;
    const char *n_ = n;
    while (now_ + len >= end_) {
      memcpy(now_, n_, l_ = usz(end_ - now_));
      now_ += l_;
      n_ += l_;
      len -= l_;
      flush();
    }
    memcpy(now_, n_, len);
    now_ += len;
    return *this;
  }
  template <class T>
  requires(sint_c<T> && !char_c<T>)
  fastout &write(T n) {
    if (n < 0) {
      write('-');
      n = -n;
    }
    return write(to_uint_t<T>(n));
  }
  template <class T>
  requires(uint_c<T> && !char_c<T>)
  fastout &write(T n) {
    if constexpr (sizeof(T) <= 4) {
      memset(now_ib_ = int_bf_, 0, 11);
      u32tostr(n, now_ib_);
      return write(now_ib_);
    }
    now_ib_ = int_bf_ + INTBUF - 1;
    do {
      *(--(now_ib_)) = char(n % 10) | '0';
    } while (n /= 10);
    return write(now_ib_);
  }
  template <mint_c T>
  fastout &write(T n) { return write(n.val()); }
  fastout &write(strn const &str) { return write(str.c_str()); }
  template <class T, class U>
  fastout &write(std::pair<T, U> const &p) { return write(p.first).space().write(p.second); }
  template <class... Ts>
  fastout &write(std::tuple<Ts...> const &p) {
    std::apply(
        [&](Ts const &...targs) {
          usz n{0};
          ((write(targs).space_if(++n != sizeof...(Ts))), ...);
        },
        p);
    return *this;
  }
  template <container_c T>
  fastout &write(T const &p) {
    if (p.begin() == p.end()) return *this;
    auto it = p.begin();
    write(*it++);
    for (; it != p.end(); ++it) space().write(*it);
    return *this;
  }

  fastout &linebreak() { return write('\n'); }
  fastout &linebreak_if(bool flag) { return flag ? linebreak() : *this; }
  fastout &space() { return write(' '); }
  fastout &space_if(bool flag) { return flag ? space() : *this; }

  template <class T>
  fastout &operator<<(T const &val) { return write(val); }
};
}  // namespace fastio_impl_

inline fastio_impl_::fastin<0x200005> fin;
inline fastio_impl_::fastout<0x200005, 41> fout;

}  // namespace tifa_libs


#line 6 "src/test_cpverifier/library-checker/stirling_number_of_the_second_kind_fixed_k.pcntt-s30.test.cpp"

constexpr u32 MOD = 998244353;

#line 1 "src/code/math/mint_s30.hpp"



#line 1 "src/code/math/mint.hpp"



#line 1 "src/code/nt/inverse.hpp"



#line 1 "src/code/nt/inv_gcd.hpp"



#line 1 "src/code/math/safe_mod.hpp"



#line 5 "src/code/math/safe_mod.hpp"

namespace tifa_libs::math {

template <sint_c T>
constexpr T safe_mod(T x, to_uint_t<T> mod) { return ((x %= (T)mod) < 0 ? x + (T)mod : x); }

}  // namespace tifa_libs::math


#line 1 "src/code/nt/exgcd.hpp"



#line 5 "src/code/nt/exgcd.hpp"

namespace tifa_libs::math {

// Binary exgcd
template <uint_c U, bool only_x = false>
constexpr auto exgcd_b(U a, U b) {
  using T = to_sint_t<U>;
  if constexpr (only_x) {
    if (!a) return std::make_tuple(b, (T)0);
    if (!b) return std::make_tuple(a, (T)1);
  } else {
    if (!a) return std::make_tuple(b, (T)0, (T) !!b);
    if (!b) return std::make_tuple(a, (T)1, (T)0);
  }
  auto r = std::__countr_zero(a | b);
  a >>= r, b >>= r;
  T x = (T)a, y = (T)b;
  T s = 1, t = 0, u = 0, v = 1;
  while (x) {
    while (!(x & 1)) {
      x /= 2;
      if (!((s | t) & 1)) s /= 2, t /= 2;
      else s = (s + (T)b) / 2, t = (t - (T)a) / 2;
    }
    while (!(y & 1)) {
      y /= 2;
      if (!((u | v) & 1)) u /= 2, v /= 2;
      else u = (u + (T)b) / 2, v = (v - (T)a) / 2;
    }
    if (x >= y) x -= y, s -= u, t -= v;
    else y -= x, u -= s, v -= t;
  }
  if (y > 1) a /= (U)y, b /= (U)y;
  if (a && (U)abs(v) >= a) {
    T _ = v / (T)a;
    v -= _ * (T)a, u += _ * (T)b;
  }
  if (b && (U)abs(u) >= b) {
    T _ = u / (T)b;
    u -= _ * (T)b, v += _ * (T)a;
  }
  if (T u_ = u + (T)b, v_ = v - (T)a; abs(u_) + abs(v_) <= abs(u) + abs(v)) u = u_, v = v_;
  if (T u_ = u - (T)b, v_ = v + (T)a; abs(u_) + abs(v_) <= abs(u) + abs(v)) u = u_, v = v_;
  if constexpr (only_x) return std::make_tuple(U(y << r), u);
  else return std::make_tuple(U(y << r), u, v);
}
// @return then return tuple(g, x[, y]) s.t. g = gcd(a, b), xa + yb = g, |x| + |y| is the minimal (primary) and x <= y (secondarily)
template <sint_c T, bool only_x = false>
constexpr auto exgcd(T a, T b) {
  using U = to_uint_t<T>;
  if (auto [x, y] = std::minmax(a, b); x >= 0 && y <= T(U(-1) >> sizeof(U))) return exgcd_b<U, only_x>((U)a, (U)b);
  if constexpr (only_x) {
    T s = 1, u = 0;
    while (b) {
      T c = a / b;
      std::tie(s, u, a, b) = std::make_tuple(u, s - u * c, b, a - b * c);
    }
    return std::make_tuple((U)a, s);
  } else {
    T s = 1, t = 0, u = 0, v = 1;
    while (b) {
      T c = a / b;
      std::tie(s, t, u, v, a, b) = std::make_tuple(u, v, s - u * c, t - v * c, b, a - b * c);
    }
    return std::make_tuple((U)a, s, t);
  }
}

}  // namespace tifa_libs::math


#line 6 "src/code/nt/inv_gcd.hpp"

namespace tifa_libs::math {

template <uint_c T>
constexpr ptt<T> inv_gcd(T n, T mod) {
  using U = to_sint_t<T>;
  auto [g, x] = exgcd<U, true>(U(n % mod), (U)mod);
  return {g, safe_mod(x, mod)};
}

}  // namespace tifa_libs::math


#line 5 "src/code/nt/inverse.hpp"

namespace tifa_libs::math {

template <uint_c T, uint_c U>
constexpr U inverse(T n, U mod) {
  auto [g, x] = inv_gcd(U(n % mod), mod);
  assert(g == 1);
  return x;
}

}  // namespace tifa_libs::math


#line 6 "src/code/math/mint.hpp"

namespace tifa_libs::math {

template <class D, uint_c Rt>
class mint {
  constexpr D const &d() const { return static_cast<D const &>(*this); }
  constexpr D &d() { return static_cast<D &>(*this); }

 protected:
  Rt v_{};

 public:
  constexpr mint() {}
  template <int_c T>
  constexpr mint(T v) : v_(D::mod_(v)) {}
  constexpr operator D() { return d(); }

  using raw_type = Rt;
  using sraw_type = to_sint_t<Rt>;
  static constexpr raw_type mod() { return D::mod_(); }
  static constexpr sraw_type smod() { return (sraw_type)D::mod_(); }
  constexpr raw_type val() const { return d().val_(); }
  constexpr sraw_type sval() const { return (sraw_type)d().val_(); }
  constexpr raw_type &data() { return d().data_(); }

  template <int_c T>
  explicit constexpr operator T() const { return (T)val(); }
  constexpr mint &operator+=(mint const &r) { return d().adde_(r.d()); }
  constexpr mint &operator-=(mint const &r) { return d().sube_(r.d()); }
  constexpr mint &operator*=(mint const &r) { return d().mule_(r.d()); }
  constexpr mint &operator/=(mint const &r) { return *this = *this * r.inv(); }
  constexpr mint const &operator+() const { return *this; }
  constexpr mint operator-() const { return d().neg_(); }
  constexpr mint inv() const { return inverse(val(), mod()); }
  friend constexpr mint operator+(mint l, mint const &r) { return l += r; }
  friend constexpr mint operator-(mint l, mint const &r) { return l -= r; }
  friend constexpr mint operator*(mint l, mint const &r) { return l *= r; }
  friend constexpr mint operator/(mint l, mint const &r) { return l /= r; }
  friend constexpr bool operator==(mint const &l, mint const &r) { return l.val() == r.val(); }
  friend constexpr auto operator<=>(mint const &l, mint const &r) { return l.sval() - r.sval(); }
  friend std::istream &operator>>(std::istream &is, mint &x) {
    i64 _;
    is >> _;
    x = mint(_);
    return is;
  }
  friend std::ostream &operator<<(std::ostream &os, mint const &x) { return os << x.val(); }
  friend constexpr mint abs(mint const &x) { return x.val(); }
};

}  // namespace tifa_libs::math


#line 5 "src/code/math/mint_s30.hpp"

namespace tifa_libs::math {

template <u32 MOD>
class mint_s30 : public mint<mint_s30<MOD>, u32> {
  using base = mint<mint_s30<MOD>, u32>;
  friend base;

  static constexpr u32 MOD2 = MOD << 1;
  static constexpr u32 R = []() {
    u32 t = 2, iv = MOD * (t - MOD * MOD);
    iv *= t - MOD * iv, iv *= t - MOD * iv;
    return iv * (MOD * iv - t);
  }();
  static constexpr u32 R2 = -(u64)(MOD) % MOD;

  static_assert(MOD & 1);
  static_assert(-R * MOD == 1);
  static_assert((MOD >> 30) == 0);
  static_assert(MOD != 1);

  static constexpr u32 reduce(u64 x) { return u32((x + u64((u32)x * R) * MOD) >> 32); }
  static constexpr u32 norm(u32 x) { return x - (MOD & -((MOD - 1 - x) >> 31)); }

 public:
  static constexpr bool FIXED_MOD = true;
  constexpr mint_s30() {}
  template <int_c T>
  constexpr mint_s30(T v) { this->v_ = mod_(v); }

 private:
  using raw_t = typename base::raw_type;
  using sraw_t = typename base::sraw_type;
  template <sint_c T>
  static constexpr raw_t mod_(T v) { return reduce(u64(v % (i32)mod_() + (i32)mod_()) * R2); }
  template <uint_c T>
  static constexpr raw_t mod_(T v) { return reduce(u64(v % mod_()) * R2); }
  static constexpr raw_t mod_() { return MOD; }
  constexpr raw_t val_() const { return norm(reduce(this->v_)); }
  constexpr raw_t &data_() { return this->v_; }

  constexpr mint_s30 neg_() const {
    mint_s30 res;
    res.v_ = (MOD2 & -(this->v_ != 0)) - this->v_;
    return res;
  }
  constexpr mint_s30 &adde_(mint_s30 const &r) {
    this->v_ += r.v_ - MOD2, this->v_ += MOD2 & -(this->v_ >> 31);
    return *this;
  }
  constexpr mint_s30 &sube_(mint_s30 const &r) {
    this->v_ -= r.v_, this->v_ += MOD2 & -(this->v_ >> 31);
    return *this;
  }
  constexpr mint_s30 &mule_(mint_s30 const &r) {
    this->v_ = reduce(u64(this->v_) * r.v_);
    return *this;
  }
};

}  // namespace tifa_libs::math


#line 1 "src/code/poly/polycntt.hpp"



#line 1 "src/code/conv/conv_cntt.hpp"



#line 1 "src/code/conv/cntt.hpp"



#line 1 "src/code/math/qpow.hpp"



#line 5 "src/code/math/qpow.hpp"

namespace tifa_libs::math {

template <class T>
constexpr T qpow(T a, u64 b, T const& init_v = T{1}) {
  T res = init_v;
  for (; b; b >>= 1, a = a * a)
    if (b & 1) res = res * a;
  return res;
}

}  // namespace tifa_libs::math


#line 1 "src/code/nt/proot_gint.hpp"



#line 1 "src/code/math/gint.hpp"



#line 5 "src/code/math/gint.hpp"

namespace tifa_libs::math {

template <class T, i64 M>
class gint {
  T r_, i_;

 public:
  constexpr gint(T const &real = T{}, T const &imag = T{}) : r_(real), i_(imag) {}

  constexpr T const &real() const { return r_; }
  constexpr T const &imag() const { return i_; }
  constexpr T norm() const { return r_ * r_ - i_ * i_ * M; }
  constexpr T &real() { return r_; }
  constexpr T &imag() { return i_; }
  constexpr void real(T const &x) { r_ = x; }
  constexpr void imag(T const &x) { i_ = x; }
  constexpr gint &operator+=(T const &x) {
    r_ += x;
    return *this;
  }
  constexpr gint &operator-=(T const &x) {
    r_ -= x;
    return *this;
  }
  constexpr gint &operator*=(T const &x) {
    r_ *= x;
    i_ *= x;
    return *this;
  }
  constexpr gint &operator/=(T const &x) {
    r_ /= x;
    i_ /= x;
    return *this;
  }
  constexpr gint &operator+=(gint const &x) {
    r_ += x.real();
    i_ += x.imag();
    return *this;
  }
  constexpr gint &operator-=(gint const &x) {
    r_ -= x.real();
    i_ -= x.imag();
    return *this;
  }
  constexpr gint &operator*=(gint const &x) {
    T _ = r_ * x.real() + i_ * x.imag() * M;
    i_ = r_ * x.imag() + i_ * x.real();
    r_ = _;
    return *this;
  }
  constexpr gint &operator/=(gint const &x) {
    const T _ = r_ * x.real() - i_ * x.imag() * M;
    const T n_ = x.norm();
    if constexpr (std::is_integral_v<T>) {
      auto div = [](T x, T y) {
        T a = x * 2 + y, b = y * 2;
        return a / b - (a % b < 0);
      };
      i_ = div(i_ * x.real() - r_ * x.imag(), n_);
      r_ = div(_, n_);
    } else {
      i_ = (i_ * x.real() - r_ * x.imag()) / n_;
      r_ = _ / n_;
    }
    return *this;
  }
  constexpr gint &operator%=(gint const &x) { return *this -= *this / x * x; }
  friend constexpr gint operator+(gint x, T const &y) { return x += y; }
  friend constexpr gint operator-(gint x, T const &y) { return x -= y; }
  friend constexpr gint operator*(gint x, T const &y) { return x *= y; }
  friend constexpr gint operator/(gint x, T const &y) { return x /= y; }
  friend constexpr gint operator+(gint x, gint const &y) { return x += y; }
  friend constexpr gint operator-(gint x, gint const &y) { return x -= y; }
  friend constexpr gint operator*(gint x, gint const &y) { return x *= y; }
  friend constexpr gint operator/(gint x, gint const &y) { return x /= y; }
  friend constexpr gint operator%(gint x, gint const &y) { return x %= y; }
  constexpr gint operator+() const { return *this; }
  constexpr gint operator-() const { return gint(-r_, -i_); }
  friend constexpr gint conj(gint const &x) { return gint{x.r_, -x.i_}; }
  friend constexpr T norm(gint const &x) { return x.norm(); }
  friend constexpr gint gcd(gint m, gint n) {
    while (n != gint{}) std::swap(m %= n, n);
    return m;
  }
  friend constexpr bool operator==(gint const &x, gint const &y) { return x.real() == y.real() && x.imag() == y.imag(); }
  friend std::istream &operator>>(std::istream &is, gint &x) { return is >> x.r_ >> x.i_; }
  friend std::ostream &operator<<(std::ostream &os, gint const &x) { return os << x.real() << ' ' << x.imag(); }
};

}  // namespace tifa_libs::math


#line 1 "src/code/nt/pfactors.hpp"



#line 1 "src/code/rand/gen.hpp"



#line 5 "src/code/rand/gen.hpp"

namespace tifa_libs::rand {

template <class Distri>
class Gen {
  std::conditional_t<sizeof(typename Distri::result_type) <= 4, std::mt19937, std::mt19937_64> re;
  Distri dist;

 public:
  using random_engine = decltype(re);
  using distribution = Distri;
  using result_type = typename Distri::result_type;

  constexpr Gen() : re(std::random_device{}()), dist() {}
  constexpr Gen(result_type a, result_type b) : re(std::random_device{}()), dist(a, b) {}

  constexpr void set_range(result_type a, result_type b) { dist = Distri(a, b); }
  constexpr random_engine& rand_eng() { return re; }
  constexpr Distri& distrib() { return dist; }

  void reset_seed() { re.seed((result_type)std::chrono::duration_cast<std::conditional_t<sizeof(typename Distri::result_type) <= 4, std::chrono::seconds, std::chrono::nanoseconds>>(std::chrono::high_resolution_clock::now().time_since_epoch()).count()); }
  constexpr result_type operator()() { return dist(re); }
  result_type next() { return dist(re); }
};

}  // namespace tifa_libs::rand


#line 1 "src/code/nt/gcd.hpp"



#line 5 "src/code/nt/gcd.hpp"

namespace tifa_libs::math {

namespace gcd_impl_ {
template <uint_c T, uint_c U>
constexpr std::common_type_t<T, U> gcd__(T u, U v) {
  using W = std::common_type_t<T, U>;
  if (!u || !v) return u ^ v;
  auto k = std::__countr_zero(u | v);
  u >>= k, v >>= k;
  do {
    if (W _ = v >> std::__countr_zero(v); u > _) v = u - _, u = _;
    else v = _ - u;
  } while (v);
  return u << k;
}
}  // namespace gcd_impl_

template <int_c T, int_c U>
constexpr std::common_type_t<T, U> gcd(T a, U b) { return gcd_impl_::gcd__((to_uint_t<T>)abs(a), (to_uint_t<U>)abs(b)); }

}  // namespace tifa_libs::math


#line 1 "src/code/nt/is_prime.hpp"



#line 1 "src/code/math/qpow_mod.hpp"



#line 5 "src/code/math/qpow_mod.hpp"

namespace tifa_libs::math {

constexpr u64 qpow_mod(u64 a, u64 b, u64 mod) {
  u64 res(1);
  for (a %= mod; b; b >>= 1, a = mul_mod_u(a, a, mod))
    if (b & 1) res = mul_mod_u(res, a, mod);
  return res;
}

}  // namespace tifa_libs::math


#line 6 "src/code/nt/is_prime.hpp"

namespace tifa_libs::math {

constexpr bool is_prime(u64 n) {
  if (n <= 2) return n == 2;
  if (~n & 1) return false;
  if (n < 8 || n == 61) return true;

  auto f = [n, d = (n - 1) >> std::countr_zero(n - 1)](auto const& bases) -> bool {
    for (u64 i : bases) {
      if (!(i % n)) continue;
      u64 t = d, y = qpow_mod(i, t, n);
      while (t != n - 1 && y != 1 && y != n - 1) {
        y = mul_mod_u(y, y, n);
        t *= 2;
      }
      if (y != n - 1 && (~t & 1)) return false;
    }
    return true;
  };

  if (n < (1 << 30)) {
    constexpr u64 bases[3] = {2, 7, 61};
    return f(bases);
  }
  constexpr u64 bases[7] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
  return f(bases);
}

}  // namespace tifa_libs::math


#line 8 "src/code/nt/pfactors.hpp"

namespace tifa_libs::math {
namespace pfactors_impl_ {
class PollardRho {
  rand::Gen<std::uniform_int_distribution<u64>> e;

  constexpr u64 rho(u64 n) {
    e.set_range(2, n - 1);
    auto f = [n, r = e()](u64 x) { return (mul_mod_u(x, x, n) + r) % n; };
    u64 g = 1, x = 0, y = e(), yy = 0;
    const u32 LIM = 128;
    for (u64 r = 1, q = 1; g == 1; r *= 2) {
      x = y;
      for (u64 i = 0; i < r; ++i) y = f(y);
      for (u64 k = 0; g == 1 && k < r; k += LIM) {
        yy = y;
        for (u64 i = 0; i < LIM && i < r - k; ++i) q = mul_mod_u(q, (x + (n - (y = f(y)))) % n, n);
        g = gcd(q, n);
      }
    }
    if (g == n) do {
        g = gcd((x + (n - (yy = f(yy)))) % n, n);
      } while (g == 1);
    return g == n ? rho(n) : g;
  }

 public:
  explicit constexpr PollardRho() : e() {}

  constexpr void operator()(u64 n, std::map<u64, u32> &ans) {
    if (n < 2) return;
    if (is_prime(n)) {
      ++ans[n];
      return;
    }
    auto g = rho(n);
    (*this)(n / g, ans);
    (*this)(g, ans);
  }
};
}  // namespace pfactors_impl_

inline std::map<u64, u32> pfactors(u64 n) {
  std::map<u64, u32> ans;
  if (n < 2) return ans;
  if (~n & 1) n >>= (ans[2] = (u32)std::countr_zero(n));
  pfactors_impl_::PollardRho()(n, ans);
  return ans;
}

}  // namespace tifa_libs::math


#line 7 "src/code/nt/proot_gint.hpp"

namespace tifa_libs::math {

template <class mint, i64 M = -1>
gint<mint, M> proot_gint() {
  using gint = gint<mint, M>;
  const auto m = mint::mod();
  if (m == 998244353) return {1, 1};
  if (m == 999292927) return {1, 8};
  if (m == 1000000007) return {1, 4};
  gint r = {1, 1};
  const u64 ord = (((m + 1) & 3) ? (u64)m : (u64)m * m) - 1;
  auto pf = pfactors(ord);
  while (true) {
    bool ok = 1;
    for (auto [q, k] : pf)
      if (qpow(r, ord / q) == gint{1}) {
        ok = 0;
        break;
      }
    if (ok) break;
    r.imag(r.imag() + 1);
  }
  return r;
}

}  // namespace tifa_libs::math


#line 6 "src/code/conv/cntt.hpp"

namespace tifa_libs::math {

template <class mint, i64 M = -1>
struct CNTT {
  using Zpi = gint<mint, M>;
  using data_t = Zpi;

  explicit constexpr CNTT() : rev(), W(proot_gint<mint>()), Wn(), IWn() {}

  constexpr u32 size() const { return (u32)rev.size(); }
  constexpr void bzr(u32 len) {
    u32 n = std::max<u32>(std::bit_ceil(len), 2);
    if (n == size()) return;
    rev.resize(n, 0);
    u32 k = (u32)(std::bit_width(n) - 1);
    for (u32 i = 0; i < n; ++i) rev[i] = (rev[i / 2] / 2) | ((i & 1) << (k - 1));
    Wn.resize(k);
    IWn.resize(k);
    for (u32 i = 0, mid = 1; i < k; mid <<= 1, ++i) Wn[i] = qpow(W, ((((mint::mod() + 1) & 3) ? (u64)mint::mod() : (u64)mint::mod() * mint::mod()) - 1) / 2 / mid);
    for (u32 i = 0; i < k; ++i) IWn[i] = qpow(Wn[i], (((mint::mod() + 1) & 3) ? (u64)mint::mod() : (u64)mint::mod() * mint::mod()) - 2);
  }

  constexpr void dif(vec<Zpi> &f) const { difdit(f); }
  constexpr void dit(vec<Zpi> &f) const { difdit<true>(f); }

 private:
  vecu rev;
  const Zpi W;
  vec<Zpi> Wn, IWn;

  template <bool inv = false>
  constexpr void difdit(vec<Zpi> &f) const {
    u32 n = size();
    assert(f.size() <= n);
    f.resize(n);
    for (u32 i = 0; i < n; ++i)
      if (i < rev[i]) std::swap(f[rev[i]], f[i]);
    for (u32 mid = 1, k = 0; mid < n; mid <<= 1, ++k) {
      Zpi now;
      if constexpr (inv) now = IWn[k];
      else now = Wn[k];
      for (u32 r = mid << 1, j = 0; j < n; j += r) {
        Zpi w{1};
        for (u32 k = 0; k < mid; k++, w *= now) {
          Zpi x = f[j + k], y = w * f[j + mid + k];
          f[j + k] = x + y;
          f[j + mid + k] = x - y;
        }
      }
    }
  }
};

}  // namespace tifa_libs::math


#line 1 "src/code/conv/conv_naive.hpp"



#line 5 "src/code/conv/conv_naive.hpp"

namespace tifa_libs::math {

template <class U, class T = U>
requires(sizeof(U) <= sizeof(T))
constexpr vec<T> conv_naive(vec<U> const &l, vec<U> const &r, u32 ans_size = 0) {
  if (l.empty() || r.empty()) return {};
  if (!ans_size) ans_size = u32(l.size() + r.size() - 1);
  u32 n = (u32)l.size(), m = (u32)r.size();
  vec<T> ans(ans_size);
  if (n < m)
    for (u32 j = 0; j < m; ++j)
      for (u32 i = 0; i < n; ++i) {
        if (i + j >= ans_size) break;
        ans[i + j] += (T)l[i] * (T)r[j];
      }
  else
    for (u32 i = 0; i < n; ++i)
      for (u32 j = 0; j < m; ++j) {
        if (i + j >= ans_size) break;
        ans[i + j] += (T)l[i] * (T)r[j];
      }
  return ans;
}

}  // namespace tifa_libs::math


#line 6 "src/code/conv/conv_cntt.hpp"

namespace tifa_libs::math {

template <class mint, i64 M = -1>
constexpr vec<mint> conv_cntt(CNTT<mint, M> &cntt, vec<mint> const &l, vec<mint> const &r, u32 ans_size = 0) {
  if (!ans_size) ans_size = u32(l.size() + r.size() - 1);
  if (ans_size < 32) return conv_naive(l, r, ans_size);
  cntt.bzr(std::max({(u32)l.size(), (u32)r.size(), std::min(u32(l.size() + r.size() - 1), ans_size)}));
  vec<gint<mint, M>> v(cntt.size());
  for (u32 i = 0, ie = std::min((u32)l.size(), cntt.size()); i < ie; ++i) v[i].real(l[i]);
  for (u32 i = 0, ie = std::min((u32)r.size(), cntt.size()); i < ie; ++i) v[i].imag(r[i]);
  cntt.dif(v);
  for (u32 i = 0; i < cntt.size(); ++i) v[i] *= v[i];
  cntt.dit(v);
  vec<mint> res(ans_size);
  mint inv = mint{cntt.size() * 2}.inv();
  for (u32 i = 0; i < ans_size; ++i) res[i] = v[i].imag() * inv;
  return res;
}
template <class mint, i64 M = -1>
constexpr vec<mint> conv_cntt(CNTT<mint, M> &cntt, vecu64 const &l, vecu64 const &r, u32 ans_size = 0) {
  if (!ans_size) ans_size = u32(l.size() + r.size() - 1);
  vec<mint> l_, r_;
  l_.reserve(l.size());
  r_.reserve(r.size());
  for (auto i : l) l_.push_back(i);
  for (auto i : r) r_.push_back(i);
  return conv_cntt(cntt, l_, r_, ans_size);
}

}  // namespace tifa_libs::math


#line 6 "src/code/poly/polycntt.hpp"

namespace tifa_libs::math {
namespace polycntt_impl_ {
template <class mint, i64 M = -1>
struct cconv_cntt : public CNTT<mint, M> {
  static constexpr auto ct_cat = ct_CNTT;
  constexpr void conv(vec<mint>& l, vec<mint> const& r, u32 sz = 0) { l = conv_cntt(*this, l, r, sz); }
};
}  // namespace polycntt_impl_

template <class mint, i64 M = -1>
using polycntt = poly<mint, polycntt_impl_::cconv_cntt<mint, M>>;

}  // namespace tifa_libs::math


#line 11 "src/test_cpverifier/library-checker/stirling_number_of_the_second_kind_fixed_k.pcntt-s30.test.cpp"

using mint = tifa_libs::math::mint_s30<MOD>;
using poly = tifa_libs::math::polycntt<mint>;

int main() {
  u32 n, k;
  tifa_libs::fin >> n >> k;
  auto ans = tifa_libs::math::gen_stirling2_col<poly>(n, k);
  for (u32 i = k; i <= n; ++i) tifa_libs::fout << ans[i] << " \n"[i == n];
  return 0;
}

Test cases

Env Name Status Elapsed Memory
g++-12 0_00 :heavy_check_mark: AC 3359 ms 48 MB
g++-12 1_00 :heavy_check_mark: AC 3366 ms 48 MB
g++-12 2_00 :heavy_check_mark: AC 3379 ms 48 MB
g++-12 example_00 :heavy_check_mark: AC 8 ms 6 MB
g++-12 max_max_00 :heavy_check_mark: AC 507 ms 26 MB
g++-12 max_random_00 :heavy_check_mark: AC 1101 ms 25 MB
g++-12 max_random_01 :heavy_check_mark: AC 3061 ms 41 MB
g++-12 max_random_02 :heavy_check_mark: AC 3052 ms 41 MB
g++-12 max_random_03 :heavy_check_mark: AC 1828 ms 27 MB
g++-12 max_small_00 :heavy_check_mark: AC 3375 ms 45 MB
g++-12 max_small_01 :heavy_check_mark: AC 3360 ms 45 MB
g++-12 random_00 :heavy_check_mark: AC 789 ms 25 MB
g++-12 random_01 :heavy_check_mark: AC 346 ms 10 MB
g++-12 random_02 :heavy_check_mark: AC 1137 ms 21 MB
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