結果

問題 No.980 Fibonacci Convolution Hard
ユーザー otamay6otamay6
提出日時 2020-01-31 22:57:31
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
RE  
実行時間 -
コード長 7,248 bytes
コンパイル時間 2,154 ms
コンパイル使用メモリ 184,320 KB
実行使用メモリ 216,456 KB
最終ジャッジ日時 2024-09-17 09:59:48
合計ジャッジ時間 29,677 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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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 RE -
testcase_01 RE -
testcase_02 RE -
testcase_03 RE -
testcase_04 RE -
testcase_05 RE -
testcase_06 RE -
testcase_07 RE -
testcase_08 RE -
testcase_09 RE -
testcase_10 RE -
testcase_11 RE -
testcase_12 RE -
testcase_13 RE -
testcase_14 RE -
testcase_15 RE -
testcase_16 RE -
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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;

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
    };
    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();
        }
    };

} 
// 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<4>(A,A,mod);
    REP(i,Q) cout<<C[query[i]]<<endl;
}
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