結果

問題 No.980 Fibonacci Convolution Hard
ユーザー risujiroh
提出日時 2020-01-31 21:54:44
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,059 ms / 2,000 ms
コード長 4,250 bytes
コンパイル時間 2,645 ms
コンパイル使用メモリ 200,748 KB
実行使用メモリ 156,324 KB
最終ジャッジ日時 2024-09-17 11:27:53
合計ジャッジ時間 23,123 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
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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, 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> void ntt(vector<Modular<Mod>>& a, bool inverse) {
  static vector<Modular<Mod>> dw(30), idw(30);
  if (dw[0] == 0) {
    Modular<Mod> root = 2;
    while (power(root, (Mod - 1) / 2) == 1) root += 1;
    for (int i = 0; i < 30; ++i)
      dw[i] = -power(root, (Mod - 1) >> (i + 2)), idw[i] = 1 / dw[i];
  }
  int n = a.size();
  assert((n & (n - 1)) == 0);
  if (not inverse) {
    for (int m = n; m >>= 1; ) {
      Modular<Mod> w = 1;
      for (int s = 0, k = 0; s < n; s += 2 * m) {
        for (int i = s, j = s + m; i < s + m; ++i, ++j) {
          auto x = a[i], y = a[j] * w;
          if (x.v >= Mod) x.v -= Mod;
          a[i].v = x.v + y.v, a[j].v = x.v + (Mod - y.v);
        }
        w *= dw[__builtin_ctz(++k)];
      }
    }
  } else {
    for (int m = 1; m < n; m *= 2) {
      Modular<Mod> w = 1;
      for (int s = 0, k = 0; s < n; s += 2 * m) {
        for (int i = s, j = s + m; i < s + m; ++i, ++j) {
          auto x = a[i], y = a[j];
          a[i] = x + y, a[j].v = x.v + (Mod - y.v), a[j] *= w;
        }
        w *= idw[__builtin_ctz(++k)];
      }
    }
  }
  auto c = 1 / Modular<Mod>(inverse ? n : 1);
  for (auto&& e : a) e *= c;
}
template <unsigned Mod>
vector<Modular<Mod>> operator*(vector<Modular<Mod>> l, 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;
  l.resize(sz), ntt(l, false);
  if (eq) r = l;
  else r.resize(sz), ntt(r, false);
  for (int i = 0; i < sz; ++i) l[i] *= r[i];
  ntt(l, true), l.resize(n + m - 1);
  return l;
}

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

vector<Mint> operator*(const vector<Mint>& l, const vector<Mint>& r) {
  if (l.empty() or r.empty()) return {};
  int n = l.size(), m = r.size();
  static constexpr int mod0 = 998244353, mod1 = 1300234241, mod2 = 1484783617;
  using Mint0 = Modular<mod0>;
  using Mint1 = Modular<mod1>;
  using Mint2 = Modular<mod2>;
  vector<Mint0> l0(n), r0(m);
  vector<Mint1> l1(n), r1(m);
  vector<Mint2> l2(n), r2(m);
  for (int i = 0; i < n; ++i) l0[i] = l[i].v, l1[i] = l[i].v, l2[i] = l[i].v;
  for (int j = 0; j < m; ++j) r0[j] = r[j].v, r1[j] = r[j].v, r2[j] = r[j].v;
  l0 = l0 * r0, l1 = l1 * r1, l2 = l2 * r2;
  vector<Mint> res(n + m - 1);
  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;
  for (int i = 0; i < n + m - 1; ++i) {
    int y0 = l0[i].v;
    int y1 = (im0 * (l1[i] - y0)).v;
    int y2 = (im0m1 * (l2[i] - y0) - im1 * y1).v;
    res[i] = y0 + m0 * y1 + m0m1 * y2;
  }
  return res;
}

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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