結果

問題 No.980 Fibonacci Convolution Hard
ユーザー risujiroh
提出日時 2020-01-31 21:52:55
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
MLE  
実行時間 -
コード長 5,282 bytes
コンパイル時間 1,994 ms
コンパイル使用メモリ 183,808 KB
実行使用メモリ 519,312 KB
最終ジャッジ日時 2024-09-17 07:59:41
合計ジャッジ時間 21,680 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
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ファイルパターン 結果
other MLE * 17
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ソースコード

diff # 

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

namespace fft {
struct C {
  double x, y;
  C(double _x = 0, double _y = 0) : x(_x), y(_y) {}
};
C operator+(C l, C r) { return {l.x + r.x, l.y + r.y}; }
C operator-(C l, C r) { return {l.x - r.x, l.y - r.y}; }
C operator*(C l, C r) { return {l.x * r.x - l.y * r.y, l.x * r.y + l.y * r.x}; }
C operator~(C a) { return {a.x, -a.y}; }
vector<C> w{1};
void ensure(int n) {
  for (int m = w.size(); m < n; m *= 2) {
    C dw{cos(acos(0) / m), sin(acos(0) / m)};
    w.resize(2 * m);
    for (int i = 0; i < m; ++i) w[m + i] = w[i] * dw;
  }
}
void fft(vector<C>& a, int n, bool inverse) {
  assert((n & (n - 1)) == 0);
  ensure(n);
  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) {
          C 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) {
          C x = a[i], y = a[j];
          a[i] = x + y, a[j] = (x - y) * ~w[k];
        }
      }
    }
    double inv = 1.0 / n;
    for (auto&& e : a) e.x *= inv, e.y *= inv;
  }
}
void real_fft(vector<C>& a) {
  if (a.size() < 2) return;
  assert(a.size() % 2 == 0);
  int n = a.size() / 2;
  for (int i = 0; i < n; ++i) a[i] = {a[2 * i].x, a[2 * i + 1].x};
  fft(a, n, false);
  for (int s = n; s >>= 1; ) for (int i = s, j = 2 * s; j-- > s; ++i) {
    C wa((1 + w[i].y) / 2, -w[i].x / 2), wb((1 - w[i].y) / 2, w[i].x / 2);
    a[2 * i] = a[i] * wa + ~a[j] * wb, a[2 * j + 1] = ~a[2 * i];
  }
  a[1] = a[0].x - a[0].y, a[0] = a[0].x + a[0].y;
}
void real_ifft(vector<C>& a) {
  if (a.size() < 2) return;
  assert(a.size() % 2 == 0);
  int n = a.size() / 2;
  for (int i = 0; i < n; ++i) {
    C wa((1 + w[i].y) / 2, w[i].x / 2), wb((1 - w[i].y) / 2, -w[i].x / 2);
    a[i] = a[2 * i] * wa + a[2 * i + 1] * wb;
  }
  fft(a, n, true);
  for (int i = n; i--; ) a[2 * i].x = a[i].x, a[2 * i + 1].x = a[i].y;
}
} // namespace fft

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

template <unsigned Mod> struct Modular {
  using M = Modular;
  unsigned v;
  Modular(long long a = 0) : v((a %= Mod) < 0 ? a + Mod : a) {}
  M operator-() const { return M() -= *this; }
  M& operator+=(M r) { if ((v += r.v) >= Mod) v -= Mod; return *this; }
  M& operator-=(M r) { if ((v += Mod - r.v) >= Mod) v -= Mod; return *this; }
  M& operator*=(M r) { v = (uint64_t)v * r.v % Mod; return *this; }
  M& operator/=(M r) { return *this *= power(r, Mod - 2); }
  friend M operator+(M l, M r) { return l += r; }
  friend M operator-(M l, M r) { return l -= r; }
  friend M operator*(M l, M r) { return l *= r; }
  friend M operator/(M l, M r) { return l /= r; }
  friend bool operator==(M l, M r) { return l.v == r.v; }
};

template <unsigned Mod, size_t K = 2, int B = __lg(Mod) / K + 1>
array<vector<fft::C>, K> mint_fft(const vector<Modular<Mod>>& a, int sz) {
  array<vector<fft::C>, K> res;
  for (size_t p = 0; p < K; ++p) {
    res[p].resize(sz);
    for (int i = 0; i < (int)a.size(); ++i)
      res[p][i] = (a[i].v >> (p * B)) & ((1 << B) - 1);
    fft::real_fft(res[p]);
  }
  return res;
}
template <unsigned Mod, size_t N, int B = __lg(Mod) / ((N + 1) / 2) + 1>
vector<Modular<Mod>> mint_ifft(array<vector<fft::C>, N> a) {
  int n = a[0].size();
  vector<Modular<Mod>> res(n);
  for (size_t p = 0; p < N; ++p) {
    fft::real_ifft(a[p]);
    auto base = power(Modular<Mod>(2), p * B);
    for (int i = 0; i < n; ++i) res[i] += round(a[p][i].x) * base;
  }
  return res;
}
template <class T, size_t K> array<vector<T>, 2 * K - 1> operator*(
    const array<vector<T>, K>& l, const array<vector<T>, K>& r) {
  int n = l[0].size();
  array<vector<T>, 2 * K - 1> res;
  for (size_t p = 0; p < K; ++p) for (size_t q = 0; q < K; ++q) {
    res[p + q].resize(n);
    for (int i = 0; i < n; ++i)
      res[p + q][i] = res[p + q][i] + l[p][i] * r[q][i];
  }
  return res;
}
template <unsigned Mod> vector<Modular<Mod>> operator*(
    const vector<Modular<Mod>>& l, const vector<Modular<Mod>>& r) {
  if (l.empty() or r.empty()) return {};
  int n = l.size(), m = r.size(), sz = 1 << __lg(2 * (n + m - 1) - 1);
  if (min(n, m) < 30) {
    vector<long long> res(n + m - 1);
    for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j)
      res[i + j] += (l[i] * r[j]).v;
    return {begin(res), end(res)};
  }
  bool eq = l == r;
  auto a = mint_fft(l, sz), b = eq ? a : mint_fft(r, sz);
  auto res = mint_ifft<Mod>(a * b);
  return {begin(res), begin(res) + (n + m - 1)};
}

constexpr long long mod = 1e9 + 7;
using Mint = Modular<mod>;

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  int p;
  cin >> p;
  int n = 2e6;
  vector<Mint> a(n);
  for (int i = 0; i < n; ++i) {
    if (i < 2) {
      a[i] = i;
    } else {
      a[i] = p * a[i - 1] + a[i - 2];
    }
  }
  a = a * a;
  int q;
  cin >> q;
  while (q--) {
    int i;
    cin >> i;
    i -= 2;
    cout << a[i].v << '\n';
  }
}
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