Tifa's CP Library

:heavy_check_mark: src/test_cpverifier/yukicoder/0502.pmtt-ds.test.cpp

Depends on

Code

#define AUTO_GENERATED
#define PROBLEM "https://yukicoder.me/problems/no/502"

#include "../../code/math/fact_mint.hpp"

constexpr u64 MOD = 1000000007;

#include "../../code/math/mint_ds.hpp"
#include "../../code/poly/polymtt.hpp"

using mint = tifa_libs::math::mint_ds<-1>;
using poly = tifa_libs::math::polymtt<mint>;

int main() {
  mint::set_mod(MOD);
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  u64 n;
  std::cin >> n;
  std::cout << tifa_libs::math::fact_mint<poly>(n) << '\n';
  return 0;
}
#line 1 "src/test_cpverifier/yukicoder/0502.pmtt-ds.test.cpp"
#define AUTO_GENERATED
#define PROBLEM "https://yukicoder.me/problems/no/502"

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



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



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



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



#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 6 "src/code/poly/ctsh_fps.hpp"

namespace tifa_libs::math {

template <class mint, class ccore>
constexpr poly<mint, ccore> ctsh_fps(poly<mint, ccore> const &f, mint c, vecu64 const &ifact, u32 m = 0) {
  using poly_t = poly<mint, ccore>;
  u32 n = f.size(), k = f.size() - 1;
  if (!m) m = n;
  u64 t = c.val();
  if (t <= k) {
    poly_t ret(m);
    u32 ptr = 0;
    for (u32 i = (u32)t; i <= k && ptr < m; ++i) ret[ptr++] = f[i];
    if (k + 1 < t + m) {
      auto suf = ctsh_fps<mint, ccore>(f, k + 1, ifact, m - ptr);
      for (u32 i = k + 1; i < t + m; ++i) ret[ptr++] = suf[i - (k + 1)];
    }
    return ret;
  }
  if (t + m > mint::mod()) {
    auto pref = ctsh_fps<mint, ccore>(f, t, ifact, u32(mint::mod() - t)), suf = ctsh_fps<mint, ccore>(f, 0, ifact, m - pref.size());
    std::ranges::copy(suf.data(), std::back_inserter(pref.data()));
    return pref;
  }
  poly_t d(k + 1);
  for (u32 i = 0; i <= k; ++i) {
    d[i] = ifact[i], (d[i] *= ifact[k - i]) *= f[i];
    if ((k - i) & 1) d[i] = -d[i];
  }
  poly_t h(m + k);
  for (u32 i = 0; i < m + k; ++i) h[i] = mint(t - k + i).inv();
  auto dh = d * h;
  poly_t ret(m);
  mint cur = t;
  for (u32 i = 1; i <= k; ++i) cur *= t - i;
  for (u32 i = 0; i < m; ++i) {
    ret[i] = cur * dh[k + i];
    (cur *= t + i + 1) *= h[i];
  }
  return ret;
}
template <class mint, class ccore>
constexpr poly<mint, ccore> ctsh_fps(poly<mint, ccore> const &f, mint c, u32 m = 0) { return ctsh_fps<mint, ccore>(f, c, gen_ifact(f.size(), mint::mod()), m); }

}  // namespace tifa_libs::math


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

namespace tifa_libs::math {

template <class poly>
constexpr auto fact_mint(u64 n) {
  using mint = typename poly::value_type;
  using ccore = typename poly::ccore_type;
  if (n <= 1) return mint(1);
  if (n >= mint::mod()) return mint(0);
  u64 v = 1;
  while (v * v < n) v *= 2;
  mint iv = mint(v).inv();
  poly g{1, v + 1};
  for (u64 d = 1; d != v; d *= 2) {
    poly g1 = ctsh_fps<mint, ccore>(g, mint(d) * iv), g2 = ctsh_fps<mint, ccore>(g, mint(d * v + v) * iv), g3 = ctsh_fps<mint, ccore>(g, mint(d * v + d + v) * iv);
    for (u32 i = 0; i <= d; ++i) g[i] *= g1[i], g2[i] *= g3[i];
    std::copy(g2.data().begin(), g2.data().end() - 1, std::back_inserter(g.data()));
  }
  mint res = 1;
  u64 i = 0;
  while (i + v <= n) res *= g[u32(i / v)], i += v;
  while (i < n) res *= ++i;
  return res;
}

}  // namespace tifa_libs::math


#line 5 "src/test_cpverifier/yukicoder/0502.pmtt-ds.test.cpp"

constexpr u64 MOD = 1000000007;

#line 1 "src/code/math/mint_ds.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 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 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_ds.hpp"

namespace tifa_libs::math {

template <i32 ID>
class mint_ds : public mint<mint_ds<ID>, u32> {
  using base = mint<mint_ds<ID>, u32>;
  friend base;

  struct barrett {
    u32 m_;
    u64 im;
    // @param m `1 <= m < 2^31`
    explicit constexpr barrett(u32 m = 998244353) : m_(m), im(-1_u64 / m + 1) {}
    // @return m
    constexpr u32 umod() const { return m_; }
    constexpr u32 mul(u32 a, u32 b) const {
      u64 z = (u64)a * b, x = (u64)(((u128)z * im) >> 64);
      u32 v = (u32)(z - x * m_);
      return v + (m_ <= v ? m_ : 0);
    }
  };

  static inline barrett bt_;

 public:
  static constexpr bool FIXED_MOD = false;
  static constexpr void set_mod(u32 m) {
    assert(1 <= m);
    bt_ = barrett(m);
  }

  constexpr mint_ds() {}
  template <int_c T>
  constexpr mint_ds(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) {
    i64 x = i64(v % (i64)mod_());
    return raw_t(x + (x < 0 ? mod_() : 0));
  }
  template <uint_c T>
  static constexpr raw_t mod_(T v) { return raw_t(v % mod_()); }
  static constexpr raw_t mod_() { return bt_.umod(); }
  constexpr raw_t val_() const { return this->v_; }
  constexpr raw_t &data_() { return this->v_; }

  constexpr mint_ds neg_() const { return -(sraw_t)val_(); }
  constexpr mint_ds &adde_(mint_ds const &r) {
    data_() += r.val_();
    if (val_() >= mod_()) data_() -= mod_();
    return *this;
  }
  constexpr mint_ds &sube_(mint_ds const &r) {
    data_() -= r.val_();
    if (val_() >= mod_()) data_() += mod_();
    return *this;
  }
  constexpr mint_ds &mule_(mint_ds const &r) {
    data_() = bt_.mul(val_(), r.val_());
    return *this;
  }
};

}  // namespace tifa_libs::math


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



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



#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 1 "src/code/conv/fft.hpp"



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

namespace tifa_libs::math {

template <std::floating_point FP>
struct FFT {
  using C = std::complex<FP>;
  using data_t = C;

  explicit constexpr FFT() : rev(), w() {}

  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));
    w.resize(n);
    w[0].real(1);
    for (u32 i = 1; i < n; ++i) w[i] = {std::cos(TAU * (FP)i / (FP)n), std::sin(TAU * (FP)i / (FP)n)};
  }

  constexpr void dif(vec<C> &f, u32 n = 0) const {
    if (!n) n = size();
    if (f.size() < n) f.resize(n);
    assert(n <= size());
    for (u32 i = 0; i < n; ++i)
      if (i < rev[i]) std::swap(f[rev[i]], f[i]);
#pragma GCC diagnostic ignored "-Wsign-conversion"
    for (u32 i = 2, d = n / 2; i <= n; i *= 2, d /= 2)
      for (u32 j = 0; j < n; j += i) {
        auto l = f.begin() + j, r = f.begin() + j + i / 2;
        auto p = w.begin();
        for (u32 k = 0; k < i / 2; ++k, ++l, ++r, p += d) {
          C tmp = *r * *p;
          *r = *l - tmp;
          *l = *l + tmp;
        }
      }
#pragma GCC diagnostic warning "-Wsign-conversion"
  }
  constexpr void dit(vec<C> &f, u32 n = 0) const {
    if (!n) n = size();
    dif(f, n);
    for (u32 i = 0; i < n; ++i) f[i] /= (FP)n;
  }

 private:
  const FP TAU = std::acos((FP)-1.) * 2;

  vecu rev;
  vec<C> w;
};

}  // namespace tifa_libs::math


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

namespace tifa_libs::math {

template <class mint, class FP>
constexpr vec<mint> conv_mtt(FFT<FP> &fft, 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);
  using C = typename FFT<FP>::C;
  if (l.size() == 1) {
    vec<mint> ans = r;
    ans.resize(ans_size);
    for (auto &i : ans) i *= l[0];
    return ans;
  }
  if (r.size() == 1) {
    vec<mint> ans = l;
    ans.resize(ans_size);
    for (auto &i : ans) i *= r[0];
    return ans;
  }
  fft.bzr(std::max({(u32)l.size(), (u32)r.size(), std::min(u32(l.size() + r.size() - 1), ans_size)}));
  u32 n = fft.size();
  const int OFS = ((int)sizeof(decltype(mint::mod())) * 8 - std::countl_zero(mint::mod() - 1) + 1) / 2;
  const u32 MSK = ((1u << OFS) - 1);
  vec<mint> ans(ans_size);
  vec<C> a(n), b(n);
  for (u32 i = 0; i < l.size(); ++i) a[i] = {(FP)(l[i].val() & MSK), (FP)(l[i].val() >> OFS)};
  for (u32 i = 0; i < r.size(); ++i) b[i] = {(FP)(r[i].val() & MSK), (FP)(r[i].val() >> OFS)};
  fft.dif(a);
  fft.dif(b);
  {
    vec<C> p(n), q(n);
    for (u32 i = 0, j; i < n; ++i) {
      j = (n - i) & (n - 1);
      C da = (a[i] + std::conj(a[j])) * C(.5, 0), db = (a[i] - std::conj(a[j])) * C(0, -.5), dc = (b[i] + std::conj(b[j])) * C(.5, 0), dd = (b[i] - std::conj(b[j])) * C(.5, 0);
      p[j] = da * dc + da * dd;
      q[j] = db * dc + db * dd;
    }
    a = p;
    b = q;
  }
  fft.dif(a);
  fft.dif(b);
  for (u32 i = 0; i < ans_size; ++i) {
    i64 da = (i64)(a[i].real() / (FP)n + .5) % mint::smod(), db = (i64)(a[i].imag() / (FP)n + .5) % mint::smod(), dc = (i64)(b[i].real() / (FP)n + .5) % mint::smod(), dd = (i64)(b[i].imag() / (FP)n + .5) % mint::smod();
    ans[i] = da + ((db + dc) << OFS) % mint::smod() + (dd << (OFS * 2)) % mint::smod();
  }
  return ans;
}

}  // namespace tifa_libs::math


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

namespace tifa_libs::math {
namespace polymtt_impl_ {
template <class FP = f64>
struct cconv_mtt : public FFT<FP> {
  static constexpr auto ct_cat = ct_FFT;
  template <class mint>
  constexpr void conv(vec<mint>& l, vec<mint> const& r, u32 sz = 0) { l = conv_mtt(*this, l, r, sz); }
};
}  // namespace polymtt_impl_

template <class mint, class FP = f64>
using polymtt = poly<mint, polymtt_impl_::cconv_mtt<FP>>;

}  // namespace tifa_libs::math


#line 10 "src/test_cpverifier/yukicoder/0502.pmtt-ds.test.cpp"

using mint = tifa_libs::math::mint_ds<-1>;
using poly = tifa_libs::math::polymtt<mint>;

int main() {
  mint::set_mod(MOD);
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  u64 n;
  std::cin >> n;
  std::cout << tifa_libs::math::fact_mint<poly>(n) << '\n';
  return 0;
}

Test cases

Env Name Status Elapsed Memory
g++-12 00_n0.txt :heavy_check_mark: AC 8 ms 4 MB
g++-12 00_n1.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 00_n10.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 00_n100.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 00_n11.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 00_n12.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 00_n13.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 00_n14.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 00_n15.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 00_n16.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 00_n17.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 00_n18.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 00_n19.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 00_n2.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 00_n20.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 00_n3.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 00_n4.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 00_n5.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 00_n6.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 00_n7.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 00_n8.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 00_n9.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 20_small1.txt :heavy_check_mark: AC 8 ms 4 MB
g++-12 20_small10.txt :heavy_check_mark: AC 8 ms 4 MB
g++-12 20_small2.txt :heavy_check_mark: AC 8 ms 4 MB
g++-12 20_small3.txt :heavy_check_mark: AC 8 ms 4 MB
g++-12 20_small4.txt :heavy_check_mark: AC 8 ms 4 MB
g++-12 20_small5.txt :heavy_check_mark: AC 8 ms 4 MB
g++-12 20_small6.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 20_small7.txt :heavy_check_mark: AC 8 ms 4 MB
g++-12 20_small8.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 20_small9.txt :heavy_check_mark: AC 8 ms 4 MB
g++-12 30_medium1.txt :heavy_check_mark: AC 76 ms 10 MB
g++-12 30_medium10.txt :heavy_check_mark: AC 77 ms 10 MB
g++-12 30_medium2.txt :heavy_check_mark: AC 77 ms 10 MB
g++-12 30_medium3.txt :heavy_check_mark: AC 76 ms 10 MB
g++-12 30_medium4.txt :heavy_check_mark: AC 39 ms 7 MB
g++-12 30_medium5.txt :heavy_check_mark: AC 76 ms 10 MB
g++-12 30_medium6.txt :heavy_check_mark: AC 76 ms 10 MB
g++-12 30_medium7.txt :heavy_check_mark: AC 75 ms 10 MB
g++-12 30_medium8.txt :heavy_check_mark: AC 76 ms 10 MB
g++-12 30_medium9.txt :heavy_check_mark: AC 40 ms 7 MB
g++-12 40_large1.txt :heavy_check_mark: AC 8 ms 4 MB
g++-12 40_large10.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 40_large2.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 40_large3.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 40_large4.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 40_large5.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 40_large6.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 40_large7.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 40_large8.txt :heavy_check_mark: AC 7 ms 4 MB
g++-12 40_large9.txt :heavy_check_mark: AC 7 ms 4 MB
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