#408605 (C++17) No.963 門松列列（2）

• 問題: No.963 門松列列（2）
• ユーザー: noshi91
• 提出日時: 2019-12-14 22:53:40
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 556 ms / 3,000 ms
• コード長: 7,217 bytes
• コンパイル時間: 1,777 ms
• コンパイル使用メモリ: 121,764 KB
• 最終ジャッジ日時: 2025-01-08 11:34:29
• ジャッジサーバーID （参考情報）: judge4 / judge3

ファイルパターン	結果
other	AC * 11

ソースコード

#include <cstdint>

namespace n91 {

template <std::uint_fast64_t Modulus> class modint {
  using u64 = std::uint_fast64_t;

public:
  using value_type = u64;

  static constexpr u64 mod = Modulus;

private:
  static_assert(mod < static_cast<u64>(1) << 32,
                "Modulus must be less than 2**32");

  u64 v;

  constexpr modint &negate() noexcept {
    if (v != 0)
      v = mod - v;
    return *this;
  }

public:
  constexpr modint(const u64 x = 0) noexcept : v(x % mod) {}
  constexpr u64 &value() noexcept { return v; }
  constexpr const u64 &value() const noexcept { return v; }
  constexpr modint operator+() const noexcept { return modint(*this); }
  constexpr modint operator-() const noexcept { return modint(*this).negate(); }
  constexpr modint operator+(const modint rhs) const noexcept {
    return modint(*this) += rhs;
  }
  constexpr modint operator-(const modint rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  constexpr modint operator*(const modint rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  constexpr modint operator/(const modint rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  constexpr modint &operator+=(const modint rhs) noexcept {
    v += rhs.v;
    if (v >= mod)
      v -= mod;
    return *this;
  }
  constexpr modint &operator-=(const modint rhs) noexcept {
    if (v < rhs.v)
      v += mod;
    v -= rhs.v;
    return *this;
  }
  constexpr modint &operator*=(const modint rhs) noexcept {
    v = v * rhs.v % mod;
    return *this;
  }
  constexpr modint &operator/=(modint rhs) noexcept {
    u64 exp = mod - 2;
    while (exp) {
      if (exp % 2 != 0)
        *this *= rhs;
      rhs *= rhs;
      exp /= 2;
    }
    return *this;
  }
  constexpr bool operator==(const modint rhs) const noexcept {
    return v == rhs.v;
  }
  constexpr bool operator!=(const modint rhs) const noexcept {
    return v != rhs.v;
  }
};
template <std::uint_fast64_t Modulus>
constexpr typename modint<Modulus>::u64 modint<Modulus>::mod;

} // namespace n91
#include <cstddef>
#include <utility>
#include <vector>

#include <algorithm>
#include <cassert>
#include <cstddef>
#include <cstdint>
#include <utility>
#include <vector>

#include <functional>
#include <utility>

namespace n91 {

template <class T, class U, class Operate = std::multiplies<T>>
constexpr T power(T base, U exp, const Operate &oper = Operate(), T iden = 1) {
  while (exp != 0) {
    if (exp % 2 != 0) {
      iden = oper(iden, base);
    }
    exp /= 2;
    base = oper(base, base);
  }
  return iden;
}

} // namespace n91

namespace n91 {

template <class T, class PrimitiveRoot>
std::vector<T> number_theoretic_transform(std::vector<T> a) {
  using usize = std::size_t;

  const usize size = a.size();
  const usize m = size - 1;
  std::vector<T> b(size);
  const T root = power(PrimitiveRoot::value, (T::mod - 1) / size);
  for (usize i = size; i != 1;) {
    i /= 2;
    std::swap(a, b);
    T c = 1;
    T d = root;
    for (usize j = 1; j != i; j *= 2)
      d *= d;
    for (usize j = 0; j != size; j += i) {
      const usize l = j * 2 & m;
      const usize r = l + i;
      for (usize k = 0; k != i; k += 1)
        a[j + k] = b[l + k] + b[r + k] * c;
      c *= d;
    }
  }
  return a;
}

template <class T, class PrimitiveRoot>
std::vector<T> inverse_number_theoretic_transform(std::vector<T> a) {
  a = number_theoretic_transform<T, PrimitiveRoot>(std::move(a));
  std::reverse(a.begin() + 1, a.end());
  const T inv = T::mod - (T::mod - 1) / a.size();
  for (T &e : a)
    e *= inv;
  return a;
}

} // namespace n91

namespace n91 {

template <class T, class PrimitiveRoot>
class ntt_polynomial : public std::vector<T> {
  using Self = ntt_polynomial;
  using size_t = std::size_t;

public:
  template <class... Args>
  ntt_polynomial(Args &&... args)
      : std::vector<T>(std::forward<Args>(args)...) {}

  friend Self operator+(const Self &l, const Self &r) {
    const size_t n = std::min(l.size(), r.size());
    Self ret(n);
    for (size_t i = 0; i != n; ++i)
      ret[i] = l[i] + r[i];
    return ret;
  }
  friend Self operator-(const Self &l, const Self &r) {
    const size_t n = std::min(l.size(), r.size());
    Self ret(n);
    for (size_t i = 0; i != n; ++i)
      ret[i] = l[i] - r[i];
    return ret;
  }
  friend Self operator*(Self l, Self r) {
    if (l.size() > r.size())
      std::swap(l, r);
    const size_t n = l.size();
    size_t s = 1;
    while (s < 2 * n - 1)
      s *= 2;
    l.resize(s);
    l = number_theoretic_transform<T, PrimitiveRoot>(std::move(l));
    r.resize(n);
    r.resize(s);
    r = number_theoretic_transform<T, PrimitiveRoot>(std::move(r));
    for (size_t i = 0; i != s; ++i)
      l[i] *= r[i];
    l = inverse_number_theoretic_transform<T, PrimitiveRoot>(std::move(l));
    l.resize(n);
    l.shrink_to_fit();
    return l;
  }
  friend Self operator*(const T l, Self r) {
    for (T &e : r)
      e *= l;
    return r;
  }
  Self inverse() const {
    Self ret(1);
    ret[0] = static_cast<T>(1) / this->front();
    while (ret.size() < this->size()) {
      ret.resize(ret.size() * 2);
      ret = T(2) * ret - ret * ret * (*this);
    }
    ret.shrink_to_fit();
    return ret;
  }
};

} // namespace n91
#include <chrono>
#include <cstddef>
#include <cstdint>
#include <random>

namespace n91 {

template <class T, class U, U v> class constant_type {
public:
  using value_type = T;

  static constexpr T value = v;
};
template <class T, class U, U v> constexpr T constant_type<T, U, v>::value;

} // namespace n91

namespace n91 {

template <class T> constexpr T primitive_root() {
  using size_t = std::size_t;
  using V = typename T::value_type;

  size_t c = 0;
  V exp_list[9] = {};
  {
    V q = T::mod - 1;
    for (V i = 2; i * i <= q; i += 1) {
      if (q % i == 0) {
        exp_list[c++] = i;
        do
          q /= i;
        while (q % i == 0);
      }
    }
    if (q != 1)
      exp_list[c++] = q;
  }
  for (size_t i = 0; i != c; ++i)
    exp_list[i] = (T::mod - 1) / exp_list[i];
  T cand = 1;
  while (true) {
    bool f = true;
    for (size_t i = 0; i != c; ++i)
      if (power(cand, exp_list[i]) == 1)
        f = false;
    if (f)
      return cand;
    cand += 1;
  }
}

template <class T>
using primitive_root_constant =
    constant_type<T, typename T::value_type, primitive_root<T>().value()>;

} // namespace n91

#include <cstdio>
#include <iostream>

int main() {
  using usize = std::size_t;
  using mint = n91::modint<1012924417>;
  using pr = n91::primitive_root_constant<mint>;
  using poly = n91::ntt_polynomial<mint, pr>;

  usize n;
  std::cin >> n;
  poly sin(n + 1);

  {
    mint temp = 1;
    for (usize i = 0; i <= n; ++i) {
      if (i % 2 == 1) {
        sin[i] = static_cast<mint>(1) / temp;
        temp = -temp;
      }
      temp *= i + 1;
    }
    sin[0] += 1;
  }
  poly cos(n + 1);

  {
    mint temp = 1;
    for (usize i = 0; i <= n; ++i) {
      if (i % 2 == 0) {
        cos[i] = static_cast<mint>(1) / temp;
        temp = -temp;
      }
      temp *= i + 1;
    }
  }

  const auto ans = sin * cos.inverse();
  mint temp = 2;
  for (usize i = 1; i <= n; ++i)
    temp *= i;

  std::cout << (ans[n] * temp).value() << std::endl;
}