結果

問題 No.980 Fibonacci Convolution Hard
ユーザー emthrm
提出日時 2020-01-31 22:14:21
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
TLE  
実行時間 -
コード長 8,066 bytes
コンパイル時間 2,086 ms
コンパイル使用メモリ 202,948 KB
最終ジャッジ日時 2025-01-08 21:12:31
ジャッジサーバーID
（参考情報） 		judge1 / judge1
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ファイルパターン 結果
other TLE * 17
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ソースコード

diff # 

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
template <typename T> using posteriority_queue = priority_queue<T, vector<T>, greater<T> >;
const int INF = 0x3f3f3f3f;
const ll LINF = 0x3f3f3f3f3f3f3f3fLL;
const double EPS = 1e-8;
const int MOD = 1000000007;
// const int MOD = 998244353;
const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
const int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; }
template <typename T> void unique(vector<T> &a) { a.erase(unique(ALL(a)), a.end()); }
struct IOSetup {
  IOSetup() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  }
} iosetup;

int mod = MOD;
struct ModInt {
  unsigned val;
  ModInt(): val(0) {}
  ModInt(ll x) : val(x >= 0 ? x % mod : x % mod + mod) {}
  ModInt pow(ll exponent) {
    ModInt tmp = *this, res = 1;
    while (exponent > 0) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
      exponent >>= 1;
    }
    return res;
  }
  ModInt &operator+=(const ModInt &x) { if((val += x.val) >= mod) val -= mod; return *this; }
  ModInt &operator-=(const ModInt &x) { if((val += mod - x.val) >= mod) val -= mod; return *this; }
  ModInt &operator*=(const ModInt &x) { val = static_cast<unsigned long long>(val) * x.val % mod; return *this; }
  ModInt &operator/=(const ModInt &x) { return *this *= x.inv(); }
  bool operator==(const ModInt &x) const { return val == x.val; }
  bool operator!=(const ModInt &x) const { return val != x.val; }
  bool operator<(const ModInt &x) const { return val < x.val; }
  bool operator<=(const ModInt &x) const { return val <= x.val; }
  bool operator>(const ModInt &x) const { return val > x.val; }
  bool operator>=(const ModInt &x) const { return val >= x.val; }
  ModInt &operator++() { if (++val == mod) val = 0; return *this; }
  ModInt operator++(int) { ModInt res = *this; ++*this; return res; }
  ModInt &operator--() { val = (val == 0 ? mod : val) - 1; return *this; }
  ModInt operator--(int) { ModInt res = *this; --*this; return res; }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { return ModInt(val ? mod - val : 0); }
  ModInt operator+(const ModInt &x) const { return ModInt(*this) += x; }
  ModInt operator-(const ModInt &x) const { return ModInt(*this) -= x; }
  ModInt operator*(const ModInt &x) const { return ModInt(*this) *= x; }
  ModInt operator/(const ModInt &x) const { return ModInt(*this) /= x; }
  friend ostream &operator<<(ostream &os, const ModInt &x) { return os << x.val; }
  friend istream &operator>>(istream &is, ModInt &x) { ll val; is >> val; x = ModInt(val); return is; }
private:
  ModInt inv() const {
    // assert(__gcd(val, mod) == 1);
    unsigned a = val, b = mod; int x = 1, y = 0;
    while (b) {
      unsigned tmp = a / b;
      swap(a -= tmp * b, b);
      swap(x -= tmp * y, y);
    }
    return ModInt(x);
  }
};
ModInt abs(const ModInt &x) { return x; }
struct Combinatorics {
  int val; // "val!" and "mod" must be disjoint.
  vector<ModInt> fact, fact_inv, inv;
  Combinatorics(int val = 10000000) : val(val), fact(val + 1), fact_inv(val + 1), inv(val + 1) {
    fact[0] = 1;
    FOR(i, 1, val + 1) fact[i] = fact[i - 1] * i;
    fact_inv[val] = ModInt(1) / fact[val];
    for (int i = val; i > 0; --i) fact_inv[i - 1] = fact_inv[i] * i;
    FOR(i, 1, val + 1) inv[i] = fact[i - 1] * fact_inv[i];
  }
  ModInt nCk(int n, int k) {
    if (n < 0 || n < k || k < 0) return ModInt(0);
    // assert(n <= val && k <= val);
    return fact[n] * fact_inv[k] * fact_inv[n - k];
  }
  ModInt nPk(int n, int k) {
    if (n < 0 || n < k || k < 0) return ModInt(0);
    // assert(n <= val);
    return fact[n] * fact_inv[n - k];
  }
  ModInt nHk(int n, int k) {
    if (n < 0 || k < 0) return ModInt(0);
    return (k == 0 ? ModInt(1) : nCk(n + k - 1, k));
  }
};

// https://ei1333.github.io/algorithm/fft.html
struct NumberTheoreticTransform
{
  int mod;
  int primitiveroot;

  NumberTheoreticTransform(int mod, int root) : mod(mod), primitiveroot(root) {}

  inline int mod_pow(int x, int n)
  {
    int ret = 1;
    while(n > 0) {
      if(n & 1) ret = mul(ret, x);
      x = mul(x, x);
      n >>= 1;
    }
    return ret;
  }

  inline int inverse(int x)
  {
    return (mod_pow(x, mod - 2));
  }

  inline int add(unsigned x, int y)
  {
    x += y;
    if(x >= mod) x -= mod;
    return (x);
  }

  inline int mul(int a, int b)
  {
    unsigned long long x = (long long) a * b;
    unsigned xh = (unsigned) (x >> 32), xl = (unsigned) x, d, m;
    asm("divl %4; \n\t" : "=a" (d), "=d" (m) : "d" (xh), "a" (xl), "r" (mod));
    return (m);
  }

  void DiscreteFourierTransform(vector< int > &F, bool rev)
  {
    const int N = (int) F.size();
    for(int i = 0, j = 1; j + 1 < N; j++) {
      for(int k = N >> 1; k > (i ^= k); k >>= 1);
      if(i > j) swap(F[i], F[j]);
    }
    int w, wn, s, t;
    for(int i = 1; i < N; i <<= 1) {
      w = mod_pow(primitiveroot, (mod - 1) / (i * 2));
      if(rev) w = inverse(w);
      for(int k = 0; k < i; k++) {
        wn = mod_pow(w, k);
        for(int j = 0; j < N; j += i * 2) {
          s = F[j + k], t = mul(F[j + k + i], wn);
          F[j + k] = add(s, t), F[j + k + i] = add(s, mod - t);
        }
      }
    }
    if(rev) {
      int temp = inverse(N);
      for(int i = 0; i < N; i++) F[i] = mul(F[i], temp);
    }
  }

  vector< int > Multiply(const vector< int > &A, const vector< int > &B)
  {
    int sz = 1;
    while(sz < A.size() + B.size() - 1) sz <<= 1;
    vector< int > F(sz), G(sz);
    for(int i = 0; i < A.size(); i++) F[i] = A[i];
    for(int i = 0; i < B.size(); i++) G[i] = B[i];
    DiscreteFourierTransform(F, false);
    DiscreteFourierTransform(G, false);
    for(int i = 0; i < sz; i++) F[i] = mul(F[i], G[i]);
    DiscreteFourierTransform(F, true);
    F.resize(A.size() + B.size() - 1);
    return (F);
  }
};

inline int add(unsigned x, int y, int mod)
{
  x += y;
  if(x >= mod) x -= mod;
  return (x);
}

inline int mul(int a, int b, int mod)
{
  unsigned long long x = (long long) a * b;
  unsigned xh = (unsigned) (x >> 32), xl = (unsigned) x, d, m;
  asm("divl %4; \n\t" : "=a" (d), "=d" (m) : "d" (xh), "a" (xl), "r" (mod));
  return (m);
}

inline int mod_pow(int x, int n, int mod)
{
  int ret = 1;
  while(n > 0) {
    if(n & 1) ret = mul(ret, x, mod);
    x = mul(x, x, mod);
    n >>= 1;
  }
  return ret;
}

inline int inverse(int x, int mod)
{
  return (mod_pow(x, mod - 2, mod));
}

vector< int > AnyModNTTMultiply(vector< int >& a, vector< int >& b, int mod)
{
  for(auto &x : a) x %= mod;
  for(auto &x : b) x %= mod;
  NumberTheoreticTransform ntt1(167772161, 3);
  NumberTheoreticTransform ntt2(469762049, 3);
  NumberTheoreticTransform ntt3(1224736769, 3);
  auto x = ntt1.Multiply(a, b);
  auto y = ntt2.Multiply(a, b);
  auto z = ntt3.Multiply(a, b);
  const int m1 = ntt1.mod, m2 = ntt2.mod, m3 = ntt3.mod;
  const int m1_inv_m2 = inverse(m1, m2);
  const int m12_inv_m3 = inverse(mul(m1, m2, m3), m3);
  const int m12_mod = mul(m1, m2, mod);
  vector< int > ret(x.size());
  for(int i = 0; i < x.size(); i++) {
    int v1 = mul(add(y[i], m2 - x[i], m2), m1_inv_m2, m2);
    int v2 = mul(add(z[i], m3 - add(x[i], mul(m1, v1, m3), m3), m3), m12_inv_m3, m3);
    ret[i] = add(x[i], add(mul(m1, v1, mod), mul(m12_mod, v2, mod), mod), mod);
  }
  return ret;
}

int main() {
  const int N = 2000000;
  int p; cin >> p;
  vector<ModInt> a(N + 1, 0);
  a[2] = 1;
  FOR(i, 3, N + 1) a[i] = a[i - 1] * p + a[i - 2];
  vector<int> A(N + 1), B(N + 1);
  REP(i, N + 1) A[i] = B[i] = a[i].val;
  vector<int> ans = AnyModNTTMultiply(A, B, 1000000007);
  int q; cin >> q;
  while (q--) {
    int q; cin >> q;
    cout << ans[q] << '\n';
  }
  return 0;
}
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