結果

問題 No.980 Fibonacci Convolution Hard
ユーザー haruki_K
提出日時 2020-01-31 22:17:42
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
TLE  
(最新)
AC  
(最初)
実行時間 -
コード長 9,990 bytes
コンパイル時間 2,336 ms
コンパイル使用メモリ 193,548 KB
実行使用メモリ 168,136 KB
最終ジャッジ日時 2024-09-17 08:40:09
合計ジャッジ時間 40,509 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
other AC * 16 TLE * 1
権限があれば一括ダウンロードができます

ソースコード

diff # 

// >>> TEMPLATES
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
#define int ll
#define double ld
#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define rep1(i,n) for (int i = 1; i <= (int)(n); i++)
#define repR(i,n) for (int i = (int)(n)-1; i >= 0; i--)
#define rep1R(i,n) for (int i = (int)(n); i >= 1; i--)
#define loop(i,a,B) for (int i = a; i B; i++)
#define loopR(i,a,B) for (int i = a; i B; i--)
#define all(x) (x).begin(), (x).end()
#define allR(x) (x).rbegin(), (x).rend()
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fst first
#define snd second
#define INF (numeric_limits<int>::max()/2-1)
#ifdef LOCAL
#include "debug.hpp"
#define dump(...) cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] ", dump_impl(#__VA_ARGS__, __VA_ARGS__)
#define say(x) cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] " << x << endl
#define debug if (1)
#else
#define dump(...) (void)(0)
#define say(x) (void)(0)
#define debug if (0)
#endif
template <class T> using pque_max = priority_queue<T>;
template <class T> using pque_min = priority_queue<T, vector<T>, greater<T> >;
template <class T, class = typename T::iterator, class = typename enable_if<!is_same<T, string>::value>::type>
ostream& operator<<(ostream& os, T const& v) { bool f = true; for (auto const& x : v) os << (f ? "" : " ") << x, f = false; return os; }
template <class T, class = typename T::iterator, class = typename enable_if<!is_same<T, string>::value>::type>
istream& operator>>(istream& is, T &v) { for (auto& x : v) is >> x; return is; }
template <class T, class S> istream& operator>>(istream& is, pair<T,S>& p) { return is >> p.first >> p.second; }
struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup;
template <class F> struct FixPoint : private F {
    constexpr FixPoint(F&& f) : F(forward<F>(f)) {}
    template <class... T> constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward<T>(x)...); }
};
struct MakeFixPoint {
    template <class F> constexpr auto operator|(F&& f) const { return FixPoint<F>(forward<F>(f)); }
};
#define MFP MakeFixPoint()|
#define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__)
template <class T, size_t d> struct vec_impl {
    using type = vector<typename vec_impl<T,d-1>::type>;
    template <class... U> static type make_v(size_t n, U&&... x) { return type(n, vec_impl<T,d-1>::make_v(forward<U>(x)...)); }
};
template <class T> struct vec_impl<T,0> { using type = T; static type make_v(T const& x = {}) { return x; } };
template <class T, size_t d = 1> using vec = typename vec_impl<T,d>::type;
template <class T, size_t d = 1, class... Args> auto make_v(Args&&... args) { return vec_impl<T,d>::make_v(forward<Args>(args)...); }
template <class T> void quit(T const& x) { cout << x << endl; exit(0); }
template <class T> constexpr bool chmin(T& x, T const& y) { if (x > y) { x = y; return true; } return false; }
template <class T> constexpr bool chmax(T& x, T const& y) { if (x < y) { x = y; return true; } return false; }
template <class It> constexpr auto sumof(It b, It e) { return accumulate(b,e,typename iterator_traits<It>::value_type{}); }
template <class T> int sz(T const& x) { return x.size(); }
template <class C, class T> int lbd(C const& v, T const& x) {
    return lower_bound(v.begin(), v.end(), x)-v.begin();
}
template <class C, class T> int ubd(C const& v, T const& x) {
    return upper_bound(v.begin(), v.end(), x)-v.begin();
}
// <<<
// >>> NTT
template <class ModInt, int64_t g>
struct NTT {
    using modint = ModInt;
    static constexpr int64_t mod = ModInt::mod, gen = g, max_lg = __builtin_ctzll(mod-1);
    // mod:prime, g:primitive root
    static_assert(mod > 0 && g > 0 && max_lg > 0, "");

    using arr_t = array<ModInt,max_lg+1>;
    static arr_t ws,iws;
    static void init() {
        for (int i = 0; i <= max_lg; i++) {
            ws[i] = ModInt(g).pow((mod-1)>>i);
            iws[i] = ModInt(1)/ws[i];
        }
    }
    static void ntt(ModInt a[], int lg) {
        for (int b = lg-1; b >= 0; b--) {
            for (int i = 0; i < (1<<lg); i += 1<<(b+1)) {
                ModInt w = 1, r = ws[b+1];
                for (int j = i; j < (i|(1<<b)); j++, w *= r) {
                    const int k = j|(1<<b);
                    const auto x = a[j], y = a[k];
                    a[j] = x + y;
                    a[k] = w*(x - y);
                }
            }
        }
//        bit_reverse(a,1<<lg);
    }
    static void intt(ModInt a[], int lg) {
//        bit_reverse(a,1<<lg);
        for (int b = 0; b < lg; b++) {
            for (int i = 0; i < (1<<lg); i += 1<<(b+1)) {
                ModInt w = 1, r = iws[b+1];
                for (int j = i; j < (i|(1<<b)); j++, w *= r) {
                    const int k = j|(1<<b);
                    const auto x = a[j], y = a[k];
                    a[j] = x + y*w;
                    a[k] = x - y*w;
                }
            }
        }
    }
    static vector<int64_t> conv(vector<int64_t> const& a, vector<int64_t> const& b) {
        vector<ModInt> aa(a.size()), bb(b.size());
        rep (i,a.size()) aa[i] = a[i];
        rep (i,b.size()) bb[i] = b[i];
        auto cc = conv(move(aa), move(bb));
        vector<int64_t> c(cc.size());
        rep (i,c.size()) c[i] = cc[i].val();
        return c;
    }
    static vector<ModInt> conv(vector<ModInt> a, vector<ModInt> b) {
        if (a.empty() || b.empty()) return {};
        bool same = (a == b);
        init();
        const int s = a.size() + b.size() - 1, lg = __lg(2*s-1);
        assert(lg <= max_lg);
        a.resize(1<<lg); ntt(a.data(), lg);
        if (!same) { b.resize(1<<lg); ntt(b.data(), lg); }
        const auto x = ModInt(1)/ModInt(1<<lg);
        if (same) {
            rep (i,1<<lg) a[i] *= a[i]*x;
        } else {
            rep (i,1<<lg) a[i] *= b[i]*x;
        }
        intt(a.data(), lg); a.resize(s);
        return a;
    }
};
template <class ModInt, int64_t g>
typename NTT<ModInt,g>::arr_t NTT<ModInt,g>::ws;
template <class ModInt, int64_t g>
typename NTT<ModInt,g>::arr_t NTT<ModInt,g>::iws;
// <<<

// >>> modint
template <int32_t md>
class modint {
    static_assert(md > 0, "");
    using M = modint;
    using ll = int64_t;
    int32_t x;
public:
    static constexpr int32_t mod = md;
    constexpr modint(ll x = 0) : x((x%=mod) < 0 ? x+mod : x) { }
    constexpr ll val() const { return x; }
    constexpr bool operator==(M const& r) const { return x == r.x; }
    constexpr bool operator!=(M const& r) const { return x != r.x; }
    constexpr M operator+() const { return *this; }
    constexpr M operator-() const { return M()-*this; }
    constexpr M& operator+=(M const& r) { ll t = ll(x) + r.x; if (t >= mod) t -= mod; x = t; return *this; }
    constexpr M& operator-=(M const& r) { ll t = ll(x) + mod-r.x; if (t >= mod) t -= mod; x = t; return *this; }
    constexpr M& operator*=(M const& r) { return *this = *this * r; }
    constexpr M operator*(M const& r) const { M t; t.x = (ll(x)*r.x) % mod; return t; }
    constexpr M& operator/=(M const& r) { return *this *= r.inv(); }
    constexpr M operator+(M const& r) const { return M(*this) += r; }
    constexpr M operator-(M const& r) const { return M(*this) -= r; }
    constexpr M operator/(M const& r) const { return M(*this) /= r; }
    friend constexpr M operator+(ll x, M const& y) { return M(x)+y; }
    friend constexpr M operator-(ll x, M const& y) { return M(x)-y; }
    friend constexpr M operator*(ll x, M const& y) { return M(x)*y; }
    friend constexpr M operator/(ll x, M const& y) { return M(x)/y; }
    constexpr M pow(ll n) const {
        if (n < 0) return inv().pow(-n);
        M v = *this, r = 1;
        for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v;
        return r;
    }
    constexpr M inv() const {
        assert(x > 0);
        ll t = 1, v = x, q = 0, r = 0;
        while (v != 1) {
            q = mod / v; r = mod % v;
            if (r * 2 < v) {
                t *= -q; t %= mod; v = r;
            } else {
                t *= q + 1; t %= mod; v -= r;
            }
        }
        if (t < 0) t += mod;
        M y; y.x = t; return y;
    }
};
#ifdef LOCAL
template <int32_t MOD> string to_s(modint<MOD> const& r) { return to_s(r.val(), MOD); }
#endif
template <int32_t MOD> ostream& operator<<(ostream& os, modint<MOD> const& r) { return os << r.val(); }
template <int32_t MOD> istream& operator>>(istream& is, modint<MOD> &r) { int64_t x; is >> x; r = x; return is; }
// <<<
constexpr int64_t MOD = 1e9+7;
using mint = modint<(int32_t)MOD>;

using ntt1 = NTT<modint< 167772161>, 3>; // mod-1 =  5<<25
using ntt2 = NTT<modint< 469762049>, 3>; // mod-1 =  7<<26
using ntt3 = NTT<modint<1224736769>, 3>; // mod-1 = 73<<24
//using ntt3 = NTT<modint<998244353>, 3>; // mod-1 = 119<<23

// https://math314.hateblo.jp/entry/2015/05/07/014908
template <class ModInt>
vector<ModInt> conv(vector<ModInt> const& a, vector<ModInt> const& b) {
    vector<int64_t> aa(a.size()), bb(b.size());
    rep (i,a.size()) aa[i] = a[i].val();
    rep (i,b.size()) bb[i] = b[i].val();
    auto x = ntt1::conv(aa, bb);
    auto y = ntt2::conv(aa, bb);
    auto z = ntt3::conv(aa, bb);
    constexpr int64_t m1 = ntt1::mod, m2 = ntt2::mod;
	constexpr auto m1_inv_m2 = ntt2::modint(m1).inv();
	constexpr auto m12_inv_m3 = ntt3::modint(m1 * m2).inv();
	constexpr auto m12_mod = ModInt(m1 * m2);
	vector<ModInt> ret(x.size());
	rep (i,x.size()) {
		auto v1 = (y[i] - x[i]) * m1_inv_m2;
		auto v2 = (z[i] - (x[i] + m1 * v1.val())) * m12_inv_m3;
		ret[i] = x[i] + m1 * v1.val() + m12_mod * v2.val();
	}
    return ret;
}

int32_t main() {
    int p; cin >> p;

    const int NN = 2e6 + 10;
    vector<mint> a(NN);
    a[0] = 0, a[1] = 1;
    rep (i,NN-2) a[i+2] = p*a[i+1] + a[i];

    auto aa = conv(a,a);

    int Q; cin >> Q;
    while (Q--) {
        int q; cin >> q;
        cout << aa[q-2] << "\n";
    }

}
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