結果

問題 No.980 Fibonacci Convolution Hard
ユーザー ei1333333
提出日時 2020-01-31 21:57:46
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,794 ms / 2,000 ms
コード長 7,784 bytes
コンパイル時間 3,098 ms
コンパイル使用メモリ 225,612 KB
最終ジャッジ日時 2025-01-08 21:05:59
ジャッジサーバーID
（参考情報） 		judge3 / judge6
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ファイルパターン 結果
other AC * 17
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ソースコード

diff # 

#include <bits/stdc++.h>

using namespace std;

using int64 = long long;
const int mod = 1e9 + 7;
//const int mod = 998244353;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;


template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 > &p) {
  os << p.first << " " << p.second;
  return os;
}

template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
  is >> p.first >> p.second;
  return is;
}

template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
  for(int i = 0; i < (int) v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
  for(T &in : v) is >> in;
  return is;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

template< typename T = int64 >
vector< T > make_v(size_t a) {
  return vector< T >(a);
}

template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
  return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}

template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
  t = v;
}

template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
  for(auto &e : t) fill_v(e, v);
}

template< typename F >
struct FixPoint : F {
  FixPoint(F &&f) : F(forward< F >(f)) {}

  template< typename... Args >
  decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, forward< Args >(args)...);
  }
};

template< typename F >
inline decltype(auto) MFP(F &&f) {
  return FixPoint< F >{forward< F >(f)};
}


static constexpr uint32_t mul_inv(uint32_t n, int e = 5, uint32_t x = 1) {
  return e == 0 ? x : mul_inv(n, e - 1, x * (2 - x * n));
}

template< uint32_t mod >
struct ModInt {
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 inv = mul_inv(mod);
  static constexpr u32 r2 = -u64(mod) % mod;

  u32 x;

  ModInt() : x(0) {}

  ModInt(const u32 &x) : x(reduce(u64(x) * r2)) {}

  u32 reduce(const u64 &w) const {
    return u32(w >> 32) + mod - u32((u64(u32(w) * inv) * mod) >> 32);
  }

  ModInt &operator+=(const ModInt &p) {
    if(int(x += p.x - 2 * mod) < 0) x += 2 * mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if(int(x -= p.x) < 0) x += 2 * mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = reduce(uint64_t(x) * p.x);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }


  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt &p) const { return get() == p.get(); }

  bool operator!=(const ModInt &p) const { return get() != p.get(); }

  int get() const { return reduce(x) % mod; }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(*this);
    while(n > 0) {
      if(n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  ModInt inverse() const {
    return pow(mod - 2);
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) {
    return os << p.get();
  }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt< mod >(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using modint = ModInt< mod >;

template< typename Mint >
struct NumberTheoreticTransformFriendlyModInt {

  vector< int > rev;
  vector< Mint > rts;
  int base, max_base;
  Mint root;

  NumberTheoreticTransformFriendlyModInt() : base(1), rev{0, 1}, rts{0, 1} {
    const auto mod = Mint::get_mod();
    assert(mod >= 3 && mod % 2 == 1);
    auto tmp = mod - 1;
    max_base = 0;
    while(tmp % 2 == 0) tmp >>= 1, max_base++;
    root = 2;
    while(root.pow((mod - 1) >> 1) == 1) root += 1;
    assert(root.pow(mod - 1) == 1);
    root = root.pow((mod - 1) >> max_base);
  }

  void ensure_base(int nbase) {
    if(nbase <= base) return;
    rev.resize(1 << nbase);
    rts.resize(1 << nbase);
    for(int i = 0; i < (1 << nbase); i++) {
      rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
    }
    assert(nbase <= max_base);
    while(base < nbase) {
      Mint z = root.pow(1 << (max_base - 1 - base));
      for(int i = 1 << (base - 1); i < (1 << base); i++) {
        rts[i << 1] = rts[i];
        rts[(i << 1) + 1] = rts[i] * z;
      }
      ++base;
    }
  }


  void ntt(vector< Mint > &a) {
    const int n = (int) a.size();
    assert((n & (n - 1)) == 0);
    int zeros = __builtin_ctz(n);
    ensure_base(zeros);
    int shift = base - zeros;
    for(int i = 0; i < n; i++) {
      if(i < (rev[i] >> shift)) {
        swap(a[i], a[rev[i] >> shift]);
      }
    }
    for(int k = 1; k < n; k <<= 1) {
      for(int i = 0; i < n; i += 2 * k) {
        for(int j = 0; j < k; j++) {
          Mint z = a[i + j + k] * rts[j + k];
          a[i + j + k] = a[i + j] - z;
          a[i + j] = a[i + j] + z;
        }
      }
    }
  }


  void intt(vector< Mint > &a) {
    const int n = (int) a.size();
    ntt(a);
    reverse(a.begin() + 1, a.end());
    Mint inv_sz = Mint(1) / n;
    for(int i = 0; i < n; i++) a[i] *= inv_sz;
  }

  vector< Mint > multiply(vector< Mint > a) {
    int need = a.size() + a.size() - 1;
    int nbase = 1;
    while((1 << nbase) < need) nbase++;
    ensure_base(nbase);
    int sz = 1 << nbase;
    a.resize(sz, 0);
    ntt(a);
    Mint inv_sz = Mint(1) / sz;
    for(int i = 0; i < sz; i++) {
      a[i] *= a[i] * inv_sz;
    }
    reverse(a.begin() + 1, a.end());
    ntt(a);
    a.resize(need);
    return a;
  }
};

// http://math314.hateblo.jp/entry/2015/05/07/014908
inline int add(unsigned x, int y, int mod) {
  x += y;
  if(x >= mod) x -= mod;
  return (x);
}


template< int mod >
vector< int > AnyModNTTMultiply(vector< int > &a) {
  using mint = ModInt< mod >;
  using mint1 = ModInt< 167772161 >;
  using mint2 = ModInt< 469762049 >;
  using mint3 = ModInt< 595591169 >;
  NumberTheoreticTransformFriendlyModInt< mint1 > ntt1;
  NumberTheoreticTransformFriendlyModInt< mint2 > ntt2;
  NumberTheoreticTransformFriendlyModInt< mint3 > ntt3;
  vector< mint1 > a1(begin(a), end(a));
  vector< mint2 > a2(begin(a), end(a));
  vector< mint3 > a3(begin(a), end(a));
  auto x = ntt1.multiply(a1);
  auto y = ntt2.multiply(a2);
  auto z = ntt3.multiply(a3);
  const int m1 = 167772161, m2 = 469762049, m3 = 595591169;
  const auto m1_inv_m2 = mint2(m1).inverse().get();
  const auto m12_inv_m3 = (mint3(m1) * m2).inverse().get();
  const auto m12_mod = (mint(m1) * m2).get();
  vector< int > ret(x.size());
  for(int i = 0; i < x.size(); i++) {
    auto v1 = ((mint2(y[i]) + m2 - x[i].get()) * m1_inv_m2).get();
    auto v2 = ((z[i] + m3 - x[i].get() - mint3(m1) * v1) * m12_inv_m3).get();
    ret[i] = (mint(x[i].get()) + mint(m1) * v1 + mint(m12_mod) * v2).get();
  }
  return ret;
}


int main() {
  int P;
  cin >> P;
  vector< int > S(2000000);
  S[1] = 0;
  S[2] = 1;
  for(int i = 3; i < 2000000; i++) {
    S[i] = (1LL * S[i - 1] * P + S[i - 2]) % mod;
  }
  S = AnyModNTTMultiply< mod >(S);
  int Q;
  cin >> Q;
  while(Q--) {
    int64 q;
    cin >> q;
    cout << S[q] << "\n";
  }
}
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