結果

問題 No.3215 Make K types-able
ユーザー zer0-star
提出日時 2025-07-26 03:02:59
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 138 ms / 4,000 ms
コード長 11,186 bytes
コンパイル時間 6,937 ms
コンパイル使用メモリ 360,520 KB
実行使用メモリ 17,428 KB
最終ジャッジ日時 2025-09-03 09:16:44
合計ジャッジ時間 10,722 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 1
other AC * 10
権限があれば一括ダウンロードができます

ソースコード

diff # 

#define USE_ACLIBRARY 0

#if __has_include("all.hpp") && 0

#include "all.hpp"

#else

#include <bits/extc++.h>

#if __has_include(<atcoder/all>) || USE_ACLIBRARY

#include <atcoder/all>

#endif

#endif

using ll = long long int;

using pll = std::pair<ll, ll>;
using pil = std::pair<int, ll>;
using pli = std::pair<ll, int>;
using pii = std::pair<int, int>;

using namespace std::literals;

template <class T>
bool chmin(T &x, const T &val) {
  if (x > val) {
    x = val;
    return true;
  } else {
    return false;
  }
}

template <class T>
bool chmax(T &x, const T &val) {
  if (x < val) {
    x = val;
    return true;
  } else {
    return false;
  }
}

ll isqrt(ll n) {
  assert(n >= 0);
  if (n == 0) return 0;

  uint32_t c = (std::bit_width(uint64_t(n)) - 1) / 2;
  ll a = 1;
  ll d = 0;

  for (int s = std::bit_width(c) - 1; s >= 0; s--) {
    ll e = d;
    d = c >> s;
    a = (a << (d - e - 1)) + (n >> (2 * c - e - d + 1)) / a;
  }

  return a - (a * a > n);
}

#if __has_include(<atcoder/all>) || USE_ACLIBRARY

template <class mint, atcoder::internal::is_static_modint_t<mint> * = nullptr>
std::ostream &operator<<(std::ostream &os, const mint &v) {
  return os << v.val();
}

template <class mint, atcoder::internal::is_static_modint_t<mint> * = nullptr>
std::istream &operator>>(std::istream &is, mint &v) {
  int tmp;
  is >> tmp;
  v = tmp;
  return is;
}

#endif

template <class T, class U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
  return is >> p.first >> p.second;
}

template <class... T>
std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) {
  std::apply([&](auto &&...args) { (is >> ... >> args); }, tpl);
  return is;
}

template <class T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
  for (T &x : v) is >> x;
  return is;
}

template <class T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
  for (size_t i = 0; i < v.size(); i++)
    os << v[i] << (i == v.size() - 1 ? "" : " ");
  return os;
}

struct Initialization {
  Initialization() {
    std::ios_base::sync_with_stdio(false);
    std::cin.tie(nullptr);
  }
} initialization;

constexpr std::pair<int, int> dir[] = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};

template <typename T>
using infs = std::numeric_limits<T>;

template <typename T>
class factorials {
 public:
  static size_t n;
  static std::vector<T> fact, inv_fact;

  static inline void extend(size_t m) {
    if (m <= n) return;
    fact.resize(m + 1);
    inv_fact.resize(m + 1);
    for (size_t i = n + 1; i <= m; i++) fact[i] = fact[i - 1] * i;
    inv_fact[m] = fact[m].inv();
    for (size_t i = m; i > n + 1; i--) inv_fact[i - 1] = inv_fact[i] * i;
    n = m;
  }

  static T inv(int k) {
    extend(k);
    return inv_fact[k];
  }

  static T get(int k) {
    extend(k);
    return fact[k];
  }

  static T perm(int n, int k) {
    if (n < k) return 0;
    if (k < 0) return 0;
    extend(n);
    return fact[n] * inv_fact[n - k];
  }

  static T choose(int n, int k) {
    if (n < k) return 0;
    if (k < 0) return 0;
    extend(n);
    return fact[n] * inv_fact[n - k] * inv_fact[k];
  }

  static T catalan(int n) { return get(2 * n) * inv(n + 1) * inv(n); }
};

template <typename T>
size_t factorials<T>::n = 0;

template <typename T>
std::vector<T> factorials<T>::fact = {1};

template <typename T>
std::vector<T> factorials<T>::inv_fact = {1};

#if __has_include(<atcoder/all>) || USE_ACLIBRARY

using mint = atcoder::modint998244353;
// using mint = atcoder::modint1000000007;

using fs = factorials<mint>;

#endif

template <typename T>
using pq_rev = std::priority_queue<T, std::vector<T>, std::greater<T>>;

namespace pbds = __gnu_pbds;

template <typename T>
using tree = pbds::tree<T, pbds::null_type, std::less<T>, pbds::rb_tree_tag,
                        pbds::tree_order_statistics_node_update>;

// ========= fps.hpp ========= {{{

template <typename T>
class formal_power_series {
  std::vector<T> v;

  using fps = formal_power_series;

 public:
  using value_type = T;
  using reference = T &;
  using const_reference = const T &;
  using iterator = typename std::vector<T>::iterator;
  using const_iterator = typename std::vector<T>::const_iterator;

  size_t size() const { return v.size(); }

  const std::vector<T> &data() const { return v; }

  explicit formal_power_series(int n) : v(n) {}
  formal_power_series(int n, T val) : v(n, val) {}

  formal_power_series(const std::vector<T> &v) : v(v) {}
  formal_power_series(std::vector<T> &&v) : v(v) {}

  template <class InputIterator>
  formal_power_series(InputIterator first, InputIterator last)
      : v(first, last) {}

  formal_power_series(std::initializer_list<T> init) : v(init) {}

  inline void resize(int n) { v.resize(n); }

  inline T &operator[](int i) { return v[i]; }

  inline iterator begin() { return v.begin(); }
  inline const_iterator begin() const { return v.begin(); }

  inline iterator end() { return v.end(); }
  inline const_iterator end() const { return v.end(); }

  fps take(int n) const {
    fps res(v.begin(), v.begin() + std::min(n, (int)v.size()));
    res.resize(n);
    return res;
  }

  fps diff() const {
    std::vector<T> res(v.size() - 1);
    for (int i = 0; i < res.size(); i++) res[i] = v[i + 1] * (i + 1);
    return fps(res);
  }

  fps integral() const {
    std::vector<T> res(v.size() + 1);
    for (int i = 0; i < v.size(); i++) res[i + 1] = v[i] / (i + 1);
    return fps(res);
  }

  fps inv(int deg = -1) const {
    assert(v[0] != 0);

    if (deg == -1) deg = size();
    std::vector<T> res(deg);

    res[0] = v[0].inv();

    T inv4 = T(4).inv(), invd = inv4;

    for (int d = 1; d < deg; d <<= 1) {
      std::vector<T> f(2 * d), g(2 * d);

      std::copy(v.begin(), v.begin() + std::min(2 * d, (int)v.size()),
                f.begin());
      std::copy(res.begin(), res.begin() + d, g.begin());

      atcoder::internal::butterfly(f);
      atcoder::internal::butterfly(g);

      for (int i = 0; i < 2 * d; i++) f[i] *= g[i];

      atcoder::internal::butterfly_inv(f);

      for (int i = 0; i < d; i++) f[i] = 0;

      atcoder::internal::butterfly(f);

      for (int i = 0; i < 2 * d; i++) f[i] *= g[i];

      atcoder::internal::butterfly_inv(f);

      for (int i = d; i < std::min(2 * d, deg); i++) res[i] = -f[i] * invd;

      invd *= inv4;
    }

    return res;
  }

  fps log(int deg = -1) const {
    assert(v[0] == 1);

    if (deg == -1) deg = size();

    return (this->diff() * this->inv(deg)).take(deg - 1).integral();
  }

  fps exp(int deg = -1) const {
    assert(v[0] == 0);

    if (deg == -1) deg = size();

    fps g = {1};

    for (int d = 1; d < deg; d <<= 1) {
      fps tmp = -g.log(2 * d);
      tmp += 1;
      tmp.trunc_add(*this);

      g *= tmp;

      g.resize(2 * d);
    }

    g.resize(deg);

    return g;
  }

  fps pow(ll n, int deg = -1) const {
    if (deg == -1) deg = size();

    if (n == 0) return fps({1}).take(deg);
    if (n == 1) return this->take(deg);

    for (int i = 0; i < v.size(); i++) {
      if (ll(i) * n >= deg) {
        break;
      }
      if (v[i] != 0) {
        fps res(begin() + i, end());
        res /= v[i];
        res = (res.log(deg) * n).exp(deg);
        res *= v[i].pow(n);
        res.v.insert(res.v.begin(), i * n, 0);
        res.resize(deg);
        return res;
      }
    }

    return fps(deg);
  }

  fps shift(T c) const {
    std::vector<T> res(size()), ifacts(size());

    factorials<T>::extend(size());

    T x = 1;

    for (int i = 0; i < size(); i++) {
      ifacts[i] = x * factorials<T>::inv(i);
      x *= c;
    }

    for (int i = 0; i < size(); i++) {
      res[size() - 1 - i] = v[i] * factorials<T>::get(i);
    }

    res = atcoder::convolution(res, ifacts);

    res.resize(size());

    std::ranges::reverse(res);

    for (int i = 0; i < size(); i++) {
      res[i] *= factorials<T>::inv(i);
    }

    return res;
  }

  fps &trunc_add(const fps &rhs) {
    for (int i = 0; i < v.size() && i < rhs.size(); i++) v[i] += rhs.v[i];
    return *this;
  }

  fps operator-() const {
    fps res(v.size());
    for (int i = 0; i < v.size(); i++) res[i] = -v[i];
    return res;
  }

  fps &operator+=(const fps &rhs) {
    if (v.size() < rhs.v.size()) v.resize(rhs.v.size());
    for (int i = 0; i < rhs.v.size(); i++) v[i] += rhs.v[i];
    return *this;
  }

  fps &operator-=(const fps &rhs) {
    if (v.size() < rhs.v.size()) v.resize(rhs.v.size());
    for (int i = 0; i < rhs.v.size(); i++) v[i] -= rhs.v[i];
    return *this;
  }

  fps &operator*=(const fps &rhs) {
    return *this = atcoder::convolution(v, rhs.v);
  }

  fps &operator/=(const fps &rhs) { return *this *= rhs.inv(); }

  fps &operator+=(const T &rhs) {
    if (v.size() == 0) v.resize(1);
    v[0] += rhs;
    return *this;
  }

  fps &operator-=(const T &rhs) {
    if (v.size() == 0) v.resize(1);
    v[0] -= rhs;
    return *this;
  }

  fps &operator*=(const T &rhs) {
    for (int i = 0; i < v.size(); i++) v[i] *= rhs;
    return *this;
  }

  fps &operator/=(const T &rhs) {
    T rhs_inv = rhs.inv();
    for (int i = 0; i < v.size(); i++) v[i] *= rhs_inv;
    return *this;
  }

  friend fps operator+(const fps &lhs, const fps &rhs) {
    return fps(lhs) += rhs;
  }

  friend fps operator-(const fps &lhs, const fps &rhs) {
    return fps(lhs) -= rhs;
  }

  friend fps operator*(const fps &lhs, const fps &rhs) {
    return fps(lhs) *= rhs;
  }

  friend fps operator/(const fps &lhs, const fps &rhs) {
    return fps(lhs) /= rhs;
  }

  friend fps operator+(const fps &lhs, const T &rhs) { return fps(lhs) += rhs; }

  friend fps operator-(const fps &lhs, const T &rhs) { return fps(lhs) -= rhs; }

  friend fps operator*(const fps &lhs, const T &rhs) { return fps(lhs) *= rhs; }

  friend fps operator/(const fps &lhs, const T &rhs) { return fps(lhs) /= rhs; }

  friend fps operator+(const T &lhs, const fps &rhs) { return fps(rhs) += lhs; }

  friend fps operator-(const T &lhs, const fps &rhs) {
    return -(fps(rhs) -= lhs);
  }

  friend fps operator*(const T &lhs, const fps &rhs) { return fps(rhs) *= lhs; }
};

template <typename T>
T bostan_mori(int n, formal_power_series<T> P, formal_power_series<T> Q) {
  assert(P.size() < Q.size());

  P.resize(Q.size() - 1);

  while (n) {
    formal_power_series<mint> qm = Q;
    for (int i = 1; i < Q.size(); i += 2) qm[i] = -qm[i];

    formal_power_series<mint> U = P * qm;
    formal_power_series<mint> V = Q * qm;

    for (int i = n & 1; i < U.size(); i += 2) P[i / 2] = U[i];
    for (int i = 0; i < V.size(); i += 2) Q[i / 2] = V[i];

    n /= 2;
  }

  return P[0] / Q[0];
}
// ========= fps.hpp ========= }}}

using fps = formal_power_series<mint>;

int main() {
  int N = 200000;
  int K = 10;

  std::vector<fps> fs(N, fps(K));
  fs[0][0] = 1;
  fs[0][1] = 1;

  mint m = 4;

  for (int i = 1; i < N; i++) {
    fs[i] = (fs[i - 1] * fs[i - 1]).take(K);
    fs[i][0] += m;
    m *= 2;
    m *= m;
  }

  int T;
  std::cin >> T;
  while (T--) {
    int N, K;
    std::cin >> N >> K;

    // std::cerr << fs[N - 1].data() << '\n';

    if (K == 0) {
      std::cout << 1 << '\n';
    } else {
      std::cout << fs[N - 1][K - 1] << '\n';
    }
  }
}
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