結果

問題 No.1080 Strange Squared Score Sum
コンテスト
ユーザー risujiroh
提出日時 2020-06-12 22:46:44
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,527 ms / 5,000 ms
コード長 8,239 bytes
コンパイル時間 4,356 ms
コンパイル使用メモリ 226,184 KB
最終ジャッジ日時 2025-01-11 02:47:52
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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 * 2
other AC * 20
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 # 

#include <bits/stdc++.h>
using namespace std;

#ifdef LOCAL
#include "debug.h"
#else
#define DEBUG(...)
#endif

template <class T, class Op = multiplies<T>>
constexpr T power(T a, long long n, Op op = Op(), T e = {1}) {
  assert(n >= 0);
  while (n) {
    if (n & 1) e = op(e, a);
    if (n >>= 1) a = op(a, a);
  }
  return e;
}

template <class T> vector<T> operator-(vector<T> a) {
  for (auto&& e : a) e = -e;
  return a;
}
template <class T> vector<T>& operator+=(vector<T>& a, const vector<T>& b) {
  a.resize(max(a.size(), b.size()));
  for (int i = 0; i < (int)b.size(); ++i) a[i] += b[i];
  return a;
}
template <class T> vector<T> operator+(vector<T> a, const vector<T>& b) {
  return a += b;
}
template <class T> vector<T>& operator-=(vector<T>& a, const vector<T>& b) {
  a.resize(max(a.size(), b.size()));
  for (int i = 0; i < (int)b.size(); ++i) a[i] -= b[i];
  return a;
}
template <class T> vector<T> operator-(vector<T> a, const vector<T>& b) {
  return a -= b;
}
template <class T> vector<T>& operator<<=(vector<T>& a, size_t n) {
  return a.insert(begin(a), n, 0), a;
}
template <class T> vector<T> operator<<(vector<T> a, size_t n) {
  return a <<= n;
}
template <class T> vector<T>& operator>>=(vector<T>& a, size_t n) {
  return a.erase(begin(a), begin(a) + min(a.size(), n)), a;
}
template <class T> vector<T> operator>>(vector<T> a, size_t n) {
  return a >>= n;
}
// template <class T> vector<T> operator*(const vector<T>& a, const vector<T>& b) {
//   if (a.empty() or b.empty()) return {};
//   vector<T> res(a.size() + b.size() - 1);
//   for (int i = 0; i < (int)a.size(); ++i)
//     for (int j = 0; j < (int)b.size(); ++j) res[i + j] += a[i] * b[j];
//   return res;
// }
template <class T> vector<T>& operator*=(vector<T>& a, const vector<T>& b) {
  return a = a * b;
}
template <class T> vector<T> inverse(const vector<T>& a) {
  assert(not a.empty() and not (a[0] == 0));
  vector<T> b{1 / a[0]};
  while (b.size() < a.size()) {
    vector<T> x(begin(a), begin(a) + min(a.size(), 2 * b.size()));
    x *= b * b;
    b.resize(2 * b.size());
    for (auto i = b.size() / 2; i < min(x.size(), b.size()); ++i) b[i] = -x[i];
  }
  return {begin(b), begin(b) + a.size()};
}
template <class T> vector<T> operator/(vector<T> a, vector<T> b) {
  if (a.size() < b.size()) return {};
  reverse(begin(a), end(a)), reverse(begin(b), end(b));
  int n = a.size() - b.size() + 1;
  a.resize(n), b.resize(n);
  a *= inverse(b);
  return {rend(a) - n, rend(a)};
}
template <class T> vector<T>& operator/=(vector<T>& a, const vector<T>& b) {
  return a = a / b;
}
template <class T> vector<T> operator%(vector<T> a, const vector<T>& b) {
  if (a.size() < b.size()) return a;
  a -= a / b * b;
  return {begin(a), begin(a) + (b.size() - 1)};
}
template <class T> vector<T>& operator%=(vector<T>& a, const vector<T>& b) {
  return a = a % b;
}
template <class T> vector<T> derivative(const vector<T>& a) {
  vector<T> res(max((int)a.size() - 1, 0));
  for (int i = 0; i < (int)res.size(); ++i) res[i] = (i + 1) * a[i + 1];
  return res;
}
template <class T> vector<T> primitive(const vector<T>& a) {
  vector<T> res(a.size() + 1);
  for (int i = 1; i < (int)res.size(); ++i) res[i] = a[i - 1] / i;
  return res;
}
template <class T> vector<T> logarithm(const vector<T>& a) {
  assert(not a.empty() and a[0] == 1);
  auto res = primitive(derivative(a) * inverse(a));
  return {begin(res), begin(res) + a.size()};
}
template <class T> vector<T> exponent(const vector<T>& a) {
  assert(a.empty() or a[0] == 0);
  vector<T> b{1};
  while (b.size() < a.size()) {
    vector<T> x(begin(a), begin(a) + min(a.size(), 2 * b.size()));
    x[0] += 1;
    b.resize(2 * b.size());
    x -= logarithm(b);
    x *= {begin(b), begin(b) + b.size() / 2};
    for (auto i = b.size() / 2; i < min(x.size(), b.size()); ++i) b[i] = x[i];
  }
  return {begin(b), begin(b) + a.size()};
}

template <class T> void ntt(vector<T>& a, bool inverse) {
  int n = size(a);
  assert((n & (n - 1)) == 0);
  if (n < 2) return;
  assert((T::mod - 1) % n == 0);
  static vector<T> w{1}, iw{1};
  for (int m = size(w); m < n / 2; m *= 2) {
    static T root = 2;
    while (power(root, (T::mod - 1) / 2) == 1) root += 1;
    T dw = power(root, (T::mod - 1) / (4 * m)), idw = 1 / dw;
    w.resize(2 * m), iw.resize(2 * m);
    for (int i = 0; i < m; ++i) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * idw;
  }
  if (not inverse) {
    for (int m = n; m >>= 1; ) {
      for (int s = 0, k = 0; s < n; s += 2 * m, ++k) {
        for (int i = s, j = s + m; i < s + m; ++i, ++j) {
          T x = a[i], y = a[j] * w[k];
          a[i] = x + y, a[j] = x - y;
        }
      }
    }
  } else {
    for (int m = 1; m < n; m *= 2) {
      for (int s = 0, k = 0; s < n; s += 2 * m, ++k) {
        for (int i = s, j = s + m; i < s + m; ++i, ++j) {
          T x = a[i], y = a[j];
          a[i] = x + y, a[j] = (x - y) * iw[k];
        }
      }
    }
    auto inv = 1 / T(n);
    for (auto&& e : a) e *= inv;
  }
}
template <class T> vector<T> operator*(vector<T> a, vector<T> b) {
  if (empty(a) or empty(b)) return {};
  int n = size(a), m = size(b), sz = 1 << __lg(2 * (n + m - 1) - 1);
  a.resize(sz), ntt(a, false);
  b.resize(sz), ntt(b, false);
  for (int i = 0; i < sz; ++i) a[i] *= b[i];
  ntt(a, true), a.resize(n + m - 1);
  return a;
}

template <unsigned M> struct modular {
  using m = modular;
  static constexpr unsigned mod = M;
  unsigned v;
  modular(long long x = 0) : v((x %= mod) < 0 ? x + mod : x) {}
  m operator-() const { return m() -= *this; }
  m& operator+=(m b) { if ((int)(v += b.v - mod) < 0) v += mod; return *this; }
  m& operator-=(m b) { if ((int)(v -= b.v) < 0) v += mod; return *this; }
  m& operator*=(m b) { v = (uint64_t)v * b.v % mod; return *this; }
  m& operator/=(m b) { return *this *= power(b, mod - 2); }
  friend m operator+(m a, m b) { return a += b; }
  friend m operator-(m a, m b) { return a -= b; }
  friend m operator*(m a, m b) { return a *= b; }
  friend m operator/(m a, m b) { return a /= b; }
  friend bool operator==(m a, m b) { return a.v == b.v; }
};

using mint = modular<power(10, 9) + 9>;

vector<mint> operator*(const vector<mint>& a, const vector<mint>& b) {
  if (a.empty() or b.empty()) return {};
  int n = a.size(), m = b.size();
  static constexpr int mod0 = 998244353, mod1 = 1300234241, mod2 = 1484783617;
  using mint0 = modular<mod0>;
  using mint1 = modular<mod1>;
  using mint2 = modular<mod2>;
  vector<mint0> a0(n), b0(m);
  vector<mint1> a1(n), b1(m);
  vector<mint2> a2(n), b2(m);
  for (int i = 0; i < n; ++i) a0[i] = a[i].v, a1[i] = a[i].v, a2[i] = a[i].v;
  for (int j = 0; j < m; ++j) b0[j] = b[j].v, b1[j] = b[j].v, b2[j] = b[j].v;
  a0 = a0 * b0, a1 = a1 * b1, a2 = a2 * b2;
  static const mint1 im0 = 1 / mint1(mod0);
  static const mint2 im1 = 1 / mint2(mod1), im0m1 = im1 / mod0;
  static const mint m0 = mod0, m0m1 = m0 * mod1;
  vector<mint> res(n + m - 1);
  for (int i = 0; i < n + m - 1; ++i) {
    int y0 = a0[i].v;
    int y1 = (im0 * (a1[i] - y0)).v;
    int y2 = (im0m1 * (a2[i] - y0) - im1 * y1).v;
    res[i] = y0 + m0 * y1 + m0m1 * y2;
  }
  return res;
}

vector<mint> fact, inv_fact, minv;
void prepare(int n) {
  fact.resize(n + 1), inv_fact.resize(n + 1), minv.resize(n + 1);
  for (int i = 0; i <= n; ++i) fact[i] = i ? fact[i - 1] * i : 1;
  inv_fact[n] = power(fact[n], mint::mod - 2);
  for (int i = n; i--; ) inv_fact[i] = (i + 1) * inv_fact[i + 1];
  for (int i = 1; i <= n; ++i) minv[i] = inv_fact[i] * fact[i - 1];
}
mint binom(int n, int k) {
  if (k < 0 or k > n) return 0;
  return fact[n] * inv_fact[k] * inv_fact[n - k];
}
template <> mint& mint::operator/=(mint b) {
  return *this *= b.v < minv.size() ? minv[b.v] : power(b, mod - 2);
}

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  int n;
  cin >> n;
  prepare(n + 1);
  auto z = power<mint>(13, (mint::mod - 1) / 4);
  vector<mint> f(n + 1), g(n + 1);
  for (int i = 1; i <= n; ++i) {
    f[i] = z * (i + 1) * (i + 1);
    g[i] = -f[i];
  }
  f = exponent(f);
  g = exponent(g);
  f *= vector<mint>{fact[n]};
  g *= vector<mint>{fact[n]};
  f = (f + g) - (f - g) * vector<mint>{z};
  f *= vector<mint>{minv[2]};
  for (int i = 1; i <= n; ++i) {
    cout << f[i].v << '\n';
  }
}
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