結果

問題 No.2459 Stampaholic (Hard)
ユーザー risujiroh
提出日時 2023-09-01 23:31:14
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 567 ms / 4,000 ms
コード長 9,022 bytes
コンパイル時間 6,119 ms
コンパイル使用メモリ 329,112 KB
実行使用メモリ 29,588 KB
最終ジャッジ日時 2025-01-03 12:38:14
合計ジャッジ時間 13,386 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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 * 3
other AC * 19
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 #
プレゼンテーションモードにする

#if __INCLUDE_LEVEL__ == 0
#include <bits/stdc++.h>
using namespace std;
#include __BASE_FILE__
namespace {
Comb<Fp> comb(1e6);
void solve() {
  int h, w, n, k;
  cin >> tie(h, w, n, k);
  vector<Fp> pw(n + 1, 1);
  for (int i : rep(n)) {
    pw[i + 1] = pw[i] * (h - k + 1) * (w - k + 1);
  }
  int mh = min(k, h - k + 1);
  int mw = min(k, w - k + 1);
  int lh = abs(h - k * 2 + 1) + 1;
  int lw = abs(w - k * 2 + 1) + 1;
  vector<Fp> denom(n + 1);
  for (int i : rep1(0, n)) {
    denom[i] = comb.recip_fact(i + 1);
  }
  denom = inv(denom);
  vector<Fp> sh(n + 1);
  for (int i : rep1(0, n)) {
    sh[i] = (Fp(mh).pow(i + 1) - 1) * comb.recip_fact(i + 1);
  }
  sh *= denom;
  for (int i : rep1(0, n)) {
    sh[i] *= comb.fact(i);
  }
  vector<Fp> sw(n + 1);
  for (int i : rep1(0, n)) {
    sw[i] = (Fp(mw).pow(i + 1) - 1) * comb.recip_fact(i + 1);
  }
  sw *= denom;
  for (int i : rep1(0, n)) {
    sw[i] *= comb.fact(i);
  }
  Fp ans = 0;
  for (int i : rep1(0, n)) {
    ans += comb.binom(n, i) * pw[i] * Fp(-1).pow(n - i) * sh[n - i] * sw[n - i];
  }
  ans *= 4;
  for (int i : rep1(0, n)) {
    ans += comb.binom(n, i) * pw[i] * Fp(-mw).pow(n - i) * sh[n - i] * lw * 2;
  }
  for (int i : rep1(0, n)) {
    ans += comb.binom(n, i) * pw[i] * Fp(-mh).pow(n - i) * sw[n - i] * lh * 2;
  }
  ans += (pw[1] - Fp(mh) * mw).pow(n) * lh * lw;
  ans /= pw[n];
  ans = Fp(h) * w - ans;
  print(ans);
}
}  // namespace
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  solve();
}
#else  // __INCLUDE_LEVEL__
#undef assert
#define assert(expr) (expr) || (__builtin_unreachable(), 0)
#include <atcoder/convolution>
template <class T>
vector<T> make_vector_for_overwrite(int n) {
  static_assert(is_trivially_destructible_v<T>);
  vector<T> v;
  v.reserve(n);
  auto p = (T**)&v;
  p[1] = p[2];
  return v;
}
template <class T>
class Comb {
 public:
  Comb() = default;
  explicit Comb(int max_n)
      : fact_(make_vector_for_overwrite<T>(max_n + 1)),
        recip_fact_(make_vector_for_overwrite<T>(max_n + 1)) {
    fact_[0] = 1;
    for (int n = 1; n <= max_n; ++n) {
      fact_[n] = fact_[n - 1] * n;
    }
    recip_fact_[max_n] = 1 / fact_[max_n];
    for (int n = max_n; 1 <= n; --n) {
      recip_fact_[n - 1] = n * recip_fact_[n];
    }
  }
  T recip(int n) const {
    assert(n);
    return n < 0 ? -recip(-n) : recip_fact_[n] * fact_[n - 1];
  }
  T fact(int n) const {
    assert(0 <= n);
    return fact_[n];
  }
  T recip_fact(int n) const { return n < 0 ? 0 : recip_fact_[n]; }
  T falling_fact(int n, int k) const {
    assert(0 <= n || n < k);
    if (n < 0) {
      T t = falling_fact(k - n - 1, k);
      return k & 1 ? -t : t;
    }
    return n < k ? 0 : recip_fact(n - k) * fact(n);
  }
  T recip_falling_fact(int n, int k) const {
    assert(n < 0 || k <= n);
    return falling_fact(n - k, -k);
  }
  T rising_fact(int n, int k) const {
    assert(n <= 0 || 0 < n + k);
    return falling_fact(n + k - 1, k);
  }
  T recip_rising_fact(int n, int k) const {
    assert(0 < n || n + k <= 0);
    return falling_fact(n - 1, -k);
  }
  T binom(int n, int k) const {
    if ((n < 0) ^ (k < 0) ^ (n < k)) {
      return 0;
    }
    if (n < 0 && k < 0) {
      k = n - k;
    }
    return recip_fact(k) * falling_fact(n, k);
  }
  T recip_binom(int n, int k) const {
    assert((0 <= n) ^ (0 <= k) ^ (k <= n));
    k = max(k, n - k);
    return recip_falling_fact(n, k) * fact(k);
  }
  T multiset(int n, int k) const { return binom(n + k - 1, k); }
  T recip_multiset(int n, int k) const {
    assert((0 < n) ^ (0 <= k) ^ (0 < n + k));
    return recip_binom(n + k - 1, k);
  }
 private:
  vector<T> fact_;
  vector<T> recip_fact_;
};
template <class T, class U = T>
bool chmin(T& x, U&& y) {
  return y < x && (x = forward<U>(y), true);
}
template <class T, class U = T>
bool chmax(T& x, U&& y) {
  return x < y && (x = forward<U>(y), true);
}
namespace std {
template <class T1, class T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
  return is >> p.first >> p.second;
}
template <class... Ts>
istream& operator>>(istream& is, tuple<Ts...>& t) {
  return apply([&is](auto&... xs) -> istream& { return (is >> ... >> xs); }, t);
}
template <class... Ts>
istream& operator>>(istream& is, tuple<Ts&...>&& t) {
  return is >> t;
}
template <class R, enable_if_t<!is_convertible_v<R, string>>* = nullptr>
auto operator>>(istream& is, R&& r) -> decltype(is >> *begin(r)) {
  for (auto&& e : r) {
    is >> e;
  }
  return is;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
  return os << p.first << ' ' << p.second;
}
template <class... Ts>
ostream& operator<<(ostream& os, const tuple<Ts...>& t) {
  auto f = [&os](const auto&... xs) -> ostream& {
    [[maybe_unused]] auto sep = "";
    ((os << exchange(sep, " ") << xs), ...);
    return os;
  };
  return apply(f, t);
}
template <class R, enable_if_t<!is_convertible_v<R, string_view>>* = nullptr>
auto operator<<(ostream& os, R&& r) -> decltype(os << *begin(r)) {
  auto sep = "";
  for (auto&& e : r) {
    os << exchange(sep, " ") << e;
  }
  return os;
}
}  // namespace std
namespace atcoder {
template <class T, internal::is_modint_t<T>* = nullptr>
istream& operator>>(istream& is, T& x) {
  int v;
  is >> v;
  x = T::raw(v);
  return is;
}
template <class T, internal::is_modint_t<T>* = nullptr>
ostream& operator<<(ostream& os, const T& x) {
  return os << x.val();
}
}  // namespace atcoder
template <class... Ts>
void print(Ts&&... xs) {
  cout << tie(xs...) << '\n';
}
inline auto rep(int l, int r) { return views::iota(min(l, r), r); }
inline auto rep(int n) { return rep(0, n); }
inline auto rep1(int l, int r) { return rep(l, r + 1); }
inline auto rep1(int n) { return rep(1, n + 1); }
inline auto per(int l, int r) { return rep(l, r) | views::reverse; }
inline auto per(int n) { return per(0, n); }
inline auto per1(int l, int r) { return per(l, r + 1); }
inline auto per1(int n) { return per(1, n + 1); }
using Fp = atcoder::modint998244353;
using Fps = std::vector<Fp>;
int sz(const Fps& a) { return a.size(); }
Fps operator-(Fps a) {
  for (auto&& e : a) e = -e;
  return a;
}
Fps& operator+=(Fps& a, const Fps& b) {
  if (sz(a) < sz(b)) a.reserve(sz(b)), a.resize(sz(b));
  for (int i = 0; i < sz(b); ++i) a[i] += b[i];
  return a;
}
Fps operator+(Fps a, const Fps& b) { return std::move(a += b); }
Fps& operator-=(Fps& a, const Fps& b) {
  if (sz(a) < sz(b)) a.reserve(sz(b)), a.resize(sz(b));
  for (int i = 0; i < sz(b); ++i) a[i] -= b[i];
  return a;
}
Fps operator-(Fps a, const Fps& b) { return std::move(a -= b); }
Fps& operator*=(Fps& a, Fp b) {
  for (auto&& e : a) e *= b;
  return a;
}
Fps operator*(Fps a, Fp b) { return std::move(a *= b); }
Fps operator*(Fp a, Fps b) { return std::move(b *= a); }
Fps& operator/=(Fps& a, Fp b) {
  b = b.inv();
  for (auto&& e : a) e *= b;
  return a;
}
Fps operator/(Fps a, Fp b) { return std::move(a /= b); }
Fps fft(const Fps& a, int n) {
  Fps res(n);
  std::copy(a.begin(), a.begin() + std::min(n, sz(a)), res.begin());
  atcoder::internal::butterfly(res);
  return res;
}
Fps circ(Fps&& a, const Fps& b) {
  if (sz(a) < sz(b)) a.reserve(sz(b)), a.resize(sz(b));
  for (int i = 0; i < sz(b); ++i) a[i] *= b[i];
  return a;
}
Fps circ(Fps&& a) {
  for (auto&& e : a) e *= e;
  return a;
}
Fps ifft(Fps&& a, int size) {
  int n = sz(a);
  atcoder::internal::butterfly_inv(a);
  a.resize(size);
  a *= (1 - Fp::mod()) / n;
  return a;
}
Fps operator*(const Fps& a, const Fps& b) {
  if (a.empty() || b.empty()) return {};
  if (std::min(sz(a), sz(b)) <= 60) {
    Fps res(std::max(sz(a), sz(b)));
    for (int i = 0; i < sz(a); ++i)
      for (int j = 0; j < sz(b); ++j) {
        if (i + j == sz(res)) break;
        res[i + j] += a[i] * b[j];
      }
    return res;
  }
  int n = __bit_ceil(sz(a) + sz(b) - 1);
  auto buf = fft(a, n);
  if (&a == &b)
    buf = circ(std::move(buf));
  else
    buf = circ(std::move(buf), fft(b, n));
  return ifft(std::move(buf), std::max(sz(a), sz(b)));
}
Fps& operator*=(Fps& a, const Fps& b) { return a = a * b; }
Fps inv(const Fps& a) {
  Fps res{a[0].inv()};
  for (int n = 1; n < sz(a); n *= 2) {
    auto f_res = fft(res, 2 * n);
    Fps buf = ifft(circ(fft(a, 2 * n), f_res), 2 * n);
    std::fill(buf.begin(), buf.begin() + n, 0);
    buf = ifft(circ(fft(buf, 2 * n), f_res), std::min(2 * n, sz(a)));
    for (int i = n; i < sz(buf); ++i) res.push_back(-buf[i]);
  }
  return res;
}
Fps deriv(const Fps& a) {
  Fps res(sz(a));
  for (int i = 1; i < sz(a); ++i) res[i - 1] = a[i] * i;
  return res;
}
Fps integ(const Fps& a) {
  Fps res(sz(a));
  for (int i = 1; i < sz(res); ++i) res[i] = a[i - 1] / i;
  return res;
}
Fps log(const Fps& a) { return integ(deriv(a) * inv(a)); }
Fps exp(const Fps& a) {
  Fps res{1};
  for (res.reserve(sz(a)); sz(res) < sz(a);) {
    res.resize(std::min(2 * sz(res), sz(a)));
    res *= Fps{1} - log(res) + Fps(a.begin(), a.begin() + sz(res));
  }
  return res;
}
#endif  // __INCLUDE_LEVEL__
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