結果

問題 No.980 Fibonacci Convolution Hard
ユーザー finefine
提出日時 2020-01-31 22:45:37
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
TLE  
実行時間 -
コード長 6,473 bytes
コンパイル時間 3,301 ms
コンパイル使用メモリ 181,564 KB
実行使用メモリ 356,204 KB
最終ジャッジ日時 2023-10-17 11:21:59
合計ジャッジ時間 9,516 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge11
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 TLE -
testcase_01 -- -
testcase_02 -- -
testcase_03 -- -
testcase_04 -- -
testcase_05 -- -
testcase_06 -- -
testcase_07 -- -
testcase_08 -- -
testcase_09 -- -
testcase_10 -- -
testcase_11 -- -
testcase_12 -- -
testcase_13 -- -
testcase_14 -- -
testcase_15 -- -
testcase_16 -- -
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ソースコード

diff # 

#include <bits/stdc++.h>

using namespace std;

using ll = long long;

namespace NTT {
using uint = uint_fast32_t;

// NTT_PRIMES {{{
constexpr ll NTT_PRIMES[][2] = {
    {1224736769, 3}, // 2^24 * 73 + 1,
    //{1053818881, 7}, // 2^20 * 3 * 5 * 67 + 1
    //{1051721729, 6}, // 2^20 * 17 * 59 + 1
    //{1045430273, 3}, // 2^20 * 997 + 1
    //{1012924417, 5}, // 2^21 * 3 * 7 * 23 + 1
    //{1007681537, 3}, // 2^20 * 31^2 + 1
    //{1004535809, 3}, // 2^21 * 479 + 1
    {998244353, 3},  // 2^23 * 7 * 17 + 1
    //{985661441, 3},  // 2^22 * 5 * 47 + 1
    //{976224257, 3},  // 2^20 * 7^2 * 19 + 1
    //{975175681, 17}, // 2^21 * 3 * 5 * 31 + 1
    //{962592769, 7},  // 2^21 * 3^3 * 17 + 1
    //{950009857, 7},  // 2^21 * 4 * 151 + 1
    //{943718401, 7},  // 2^22 * 3^2 * 5^2 + 1
    //{935329793, 3},  // 2^22 * 223 + 1
    //{924844033, 5},  // 2^21 * 3^2 * 7^2 + 1
    {469762049, 3},  // 2^26 * 7 + 1
    {167772161, 3},  // 2^25 * 5 + 1
};
// }}}

// general math {{{
ll extgcd(ll a, ll b, ll &x, ll &y) {
  ll d;
  return b == 0 ? (x = a < 0 ? -1 : 1, y = 0, a < 0 ? -a : a)
                : (d = extgcd(b, a % b, y, x), y -= a / b * x, d);
}
ll modinv(ll a, ll mod) {
  ll x, y;
  extgcd(a, mod, x, y);
  x %= mod;
  return x < 0 ? x + mod : x;
}
ll modpow(ll a, ll b, ll mod) {
  ll r = 1;
  a %= mod;
  while(b) {
    if(b & 1) r = r * a % mod;
    a = a * a % mod;
    b >>= 1;
  }
  return r;
}
// }}}

// NTT Core {{{
template < int MAX_H >
struct Pool {
  static ll *tmp, *A, *B;
};
template < int MAX_H >
ll *Pool< MAX_H >::tmp = new ll[1 << MAX_H];
template < int MAX_H >
ll *Pool< MAX_H >::A = new ll[1 << MAX_H];
template < int MAX_H >
ll *Pool< MAX_H >::B = new ll[1 << MAX_H];

template < int MAX_H, ll mod, ll primitive >
class Core {
public:
  static_assert((mod & ((1 << MAX_H) - 1)) == 1, "mod is too small; comment out");
  // ord zetaList[i] = 2^(i + 1)
  ll zetaList[MAX_H], zetaInvList[MAX_H];
  // constexpr
  Core() {
    zetaList[MAX_H - 1] = modpow(primitive, (mod - 1) / (1 << MAX_H), mod);
    zetaInvList[MAX_H - 1] = modinv(zetaList[MAX_H - 1], mod);
    for(int ih = MAX_H - 2; ih >= 0; --ih) {
      zetaList[ih] = zetaList[ih + 1] * zetaList[ih + 1] % mod;
      zetaInvList[ih] = zetaInvList[ih + 1] * zetaInvList[ih + 1] % mod;
    }
  }
  void fft(ll *a, uint n, uint nh, bool inverse) const {
    ll *tmp = Pool< MAX_H >::tmp;
    uint mask = n - 1;
    for(uint i = n >> 1, ih = nh - 1; i >= 1; i >>= 1, --ih) {
      ll zeta = inverse ? zetaInvList[nh - 1 - ih] : zetaList[nh - 1 - ih];
      ll powZeta = 1;
      for(uint j = 0; j < n; j += i) {
        for(uint k = 0; k < i; ++k) {
          tmp[j | k] =
              (a[((j << 1) & mask) | k] + powZeta * a[(((j << 1) | i) & mask) | k]) % mod;
        }
        powZeta = powZeta * zeta % mod;
      }
      swap(a, tmp);
    }
    if(nh & 1) {
      swap(a, tmp);
      for(uint i = 0; i < n; ++i) a[i] = tmp[i];
    }
    if(inverse) {
      ll invN = modinv(n, mod);
      for(uint i = 0; i < n; ++i) a[i] = a[i] * invN % mod;
    }
  }
  vector< ll > conv(const vector< ll > &a, const vector< ll > &b) const {
    uint t = a.size() + b.size() - 1;
    uint n = 1, nh = 0;
    while(n < t) n <<= 1, ++nh;
    return convStrict(a, b, n, nh);
  }
  vector< ll > convStrict(const vector< ll > &a, const vector< ll > &b, uint n,
                          uint nh) const {
    ll *A = Pool< MAX_H >::A, *B = Pool< MAX_H >::B;
    for(uint i = 0; i < n; ++i) A[i] = B[i] = 0;
    copy(a.begin(), a.end(), A);
    copy(b.begin(), b.end(), B);
    fft(A, n, nh, 0), fft(B, n, nh, 0);
    for(uint i = 0; i < n; ++i) A[i] = A[i] * B[i] % mod;
    fft(A, n, nh, 1);
    return vector< ll >(A, A + n);
  }
};
// }}}

// Convolution With Garner {{{
template < int MAX_H, int I >
class ConvolutionWithGarnerCore {
public:
  static void conv_for(uint n, uint nh, const vector< ll > &a, const vector< ll > &b,
                       vector< ll > &mods, vector< ll > &coeffs,
                       vector< vector< ll > > &constants) {
    static const Core< MAX_H, NTT_PRIMES[I][0], NTT_PRIMES[I][1] > ntt;
    auto c = ntt.convStrict(a, b, n, nh);
    mods[I] = NTT_PRIMES[I][0];
    ConvolutionWithGarnerCore< MAX_H, I - 1 >::conv_for(
        n, nh, a, b, mods, coeffs, constants);
    // garner
    for(size_t i = 0; i < c.size(); ++i) {
      ll v = (c[i] - constants[I][i]) * modinv(coeffs[I], mods[I]) % mods[I];
      if(v < 0) v += mods[I];
      for(size_t j = I + 1; j < mods.size(); ++j) {
        constants[j][i] = (constants[j][i] + coeffs[j] * v) % mods[j];
      }
    }
    for(size_t j = I + 1; j < mods.size(); ++j) {
      coeffs[j] = (coeffs[j] * mods[I]) % mods[j];
    }
  }
};

template < int MAX_H >
class ConvolutionWithGarnerCore< MAX_H, -1 > {
public:
  static void conv_for(uint, uint, const vector< ll > &, const vector< ll > &,
                       vector< ll > &, vector< ll > &, vector< vector< ll > > &) {}
};

template < int MAX_H >
class ConvolutionWithGarner {
public:
  template < int USE >
  static vector< ll > conv(const vector< ll > &a, const vector< ll > &b, ll mod) {
    static_assert(USE >= 1, "USE must be positive");
    static_assert(USE <= sizeof(NTT_PRIMES) / sizeof(*NTT_PRIMES), "USE is too big");
    uint nt = a.size() + b.size() - 1;
    uint n = 1, nh = 0;
    while(n < nt) n <<= 1, ++nh;
    vector< ll > coeffs(USE + 1, 1);
    vector< vector< ll > > constants(USE + 1, vector< ll >(n));
    vector< ll > mods(USE + 1, mod);
    ConvolutionWithGarnerCore< MAX_H, USE - 1 >::conv_for(
        n, nh, a, b, mods, coeffs, constants);
    return constants.back();
  }
};

// }}}

} // namespace NTT
// }}}

// 1st param is MAX_H
NTT::Core< 22, NTT::NTT_PRIMES[0][0], NTT::NTT_PRIMES[0][1] > nttBig;
NTT::Core< 22, 998244353, 5 > ntt;
using nttconv = NTT::ConvolutionWithGarner< 22 >;
// nttconv::conv< USE >(a, b, mod)

constexpr int MOD = 1000000007;

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    ll p;
    cin >> p;

    int q;
    cin >> q;
    vector<int> ks(q);
    int maxk = 0;
    for (int i = 0; i < q; ++i) {
        cin >> ks[i];
        ks[i] -= 2;
        maxk = max(maxk, ks[i]);
    }

    vector<ll> a(maxk + 1, 0);
    a[1] = 1;
    for (int i = 2; i <= maxk; ++i) {
        a[i] = (a[i - 1] * p % MOD + a[i - 2]) % MOD;
    }
    
    vector<ll> ans = nttconv::conv<3>(a, a, MOD);
    for (int i = 0; i < q; ++i) {
        cout << ans[ks[i]] << "\n";
    }
    return 0;
}
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