結果

問題 No.980 Fibonacci Convolution Hard
ユーザー otamay6otamay6
提出日時 2020-01-31 22:37:11
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
MLE  
実行時間 -
コード長 6,510 bytes
コンパイル時間 3,867 ms
コンパイル使用メモリ 208,736 KB
実行使用メモリ 887,960 KB
最終ジャッジ日時 2023-10-17 10:55:29
合計ジャッジ時間 18,171 ms
ジャッジサーバーID
（参考情報） 		judge15 / judge14
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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 MLE -
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>
#define REP(i,n) for(int i=0,i##_len=int(n);i<i##_len;++i)
#define rep(i,a,b) for(int i=int(a);i<int(b);++i)
#define All(x) (x).begin(),(x).end()
#define rAll(x) (x).rbegin(),(x).rend()
using namespace std;
using ll = long long;
// MAX_N is max size of OUTPUT, DOUBLED INPUT
// MAX_RES_VALUE = MAX_VALUE^2 * MAX_N
// if MAX_N > 2^20, comment out primes!
// NTT {{{

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< 18, NTT::NTT_PRIMES[0][0], NTT::NTT_PRIMES[0][1] > nttBig;
NTT::Core< 18, 998244353, 5 > ntt;
using nttconv = NTT::ConvolutionWithGarner< 18 >;
// nttconv::conv< USE >(a, b, mod)
int main(){
    constexpr ll mod=1e9+7;
    ll p,Q;cin>>p>>Q;
    vector<int> query(Q);
    REP(i,Q){
        cin>>query[i];
    }
    int N=*max_element(All(query));
    vector<ll> A(N+1);
    A[2]=1;
    rep(i,3,N+1) (A[i]=p*A[i-1]+A[i-2])%=mod;
    nttconv c; 
    vector<ll> C = c.conv<18>(A,A,mod);
    REP(i,Q) cout<<C[query[i]]<<endl;
}
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