結果

問題 No.980 Fibonacci Convolution Hard
ユーザー risujiroh
提出日時 2020-01-31 23:17:56
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 78 ms / 2,000 ms
コード長 5,667 bytes
コンパイル時間 1,818 ms
コンパイル使用メモリ 181,036 KB
実行使用メモリ 20,320 KB
最終ジャッジ日時 2024-09-17 11:41:25
合計ジャッジ時間 5,482 ms
ジャッジサーバーID
（参考情報） 		judge6 / judge1
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ファイルパターン 結果
other AC * 17
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;

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>& l, const vector<T>& r) {
  l.resize(max(l.size(), r.size()));
  for (int i = 0; i < (int)r.size(); ++i) l[i] += r[i];
  return l;
}
template <class T> vector<T> operator+(vector<T> l, const vector<T>& r) {
  return l += r;
}
template <class T> vector<T>& operator-=(vector<T>& l, const vector<T>& r) {
  l.resize(max(l.size(), r.size()));
  for (int i = 0; i < (int)r.size(); ++i) l[i] -= r[i];
  return l;
}
template <class T> vector<T> operator-(vector<T> l, const vector<T>& r) {
  return l -= r;
}
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>& l, const vector<T>& r) {
  if (l.empty() or r.empty()) return {};
  vector<T> res(l.size() + r.size() - 1);
  for (int i = 0; i < (int)l.size(); ++i)
    for (int j = 0; j < (int)r.size(); ++j) res[i + j] += l[i] * r[j];
  return res;
}
template <class T> vector<T>& operator*=(vector<T>& l, const vector<T>& r) {
  return l = l * r;
}
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> l, vector<T> r) {
  if (l.size() < r.size()) return {};
  reverse(begin(l), end(l)), reverse(begin(r), end(r));
  int n = l.size() - r.size() + 1;
  l.resize(n), r.resize(n);
  l *= inverse(r);
  return {rend(l) - n, rend(l)};
}
template <class T> vector<T>& operator/=(vector<T>& l, const vector<T>& r) {
  return l = l / r;
}
template <class T> vector<T> operator%(vector<T> l, const vector<T>& r) {
  if (l.size() < r.size()) return l;
  l -= l / r * r;
  return {begin(l), begin(l) + (r.size() - 1)};
}
template <class T> vector<T>& operator%=(vector<T>& l, const vector<T>& r) {
  return l = l % r;
}
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> vector<T> berlekamp_massey(const vector<T>& a) {
  T d = 1;
  vector<T> c{1}, nc{1};
  int n = a.size(), k = 0, m = 1;
  for (int i = 0; i < n; ++i) {
    T nd = inner_product(rbegin(nc), rend(nc), begin(a) + (i - k), (T)0);
    if (nd == 0) ++m;
    else if (2 * k <= i) {
      auto t = nc;
      nc -= vector<T>{nd / d} * (c << m);
      c = t, d = nd;
      k = i + 1 - k, m = 1;
    } else {
      nc -= vector<T>{nd / d} * (c << m);
      ++m;
    }
  }
  return {rbegin(nc), rend(nc)};
}

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 < r.v) v += Mod; v -= r.v; 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; }
};

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

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  int p;
  cin >> p;
  vector<Mint> a(8);
  for (int i = 0; i < 8; ++i) {
    if (i < 2) {
      a[i] = i;
    } else {
      a[i] = p * a[i - 1] + a[i - 2];
    }
  }
  a *= a;
  a.resize(8);
  auto c = berlekamp_massey(a);
  while (a.size() < 2e6) {
    int n = a.size();
    Mint an;
    for (int i = 0; i < 4; ++i) {
      an -= c[i] * a[n - 4 + i];
    }
    a.push_back(an);
  }
  int q;
  cin >> q;
  while (q--) {
    int i;
    cin >> i;
    i -= 2;
    cout << a[i].v << '\n';
  }
}
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