結果

問題 No.980 Fibonacci Convolution Hard
ユーザー square1001square1001
提出日時 2020-01-31 21:36:21
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
RE  
実行時間 -
コード長 6,192 bytes
コンパイル時間 1,285 ms
コンパイル使用メモリ 90,724 KB
実行使用メモリ 11,300 KB
最終ジャッジ日時 2023-10-17 08:53:31
合計ジャッジ時間 13,182 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge12
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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 TLE -
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ソースコード

diff # 

#ifndef CLASS_FAST_MODINT
#define CLASS_FAST_MODINT

#include <cstdint>

using singlebit = uint32_t;
using doublebit = uint64_t;
static constexpr int digit_level = 8 * sizeof(singlebit);

static constexpr singlebit find_inv(singlebit n, int d = 6, singlebit x = 1) {
    return d == 0 ? x : find_inv(n, d - 1, x * (2 - x * n));
}
template <singlebit mod> class fast_modint {
    // Fast Modulo Integer, Assertion: mod < 2^(bits of singlebit - 1) and mod is prime
private:
    singlebit n;
    static constexpr singlebit r2 = (((doublebit(1) << digit_level) % mod) << digit_level) % mod;
    static constexpr singlebit ninv = singlebit(-1) * find_inv(mod);
    singlebit reduce(doublebit x) const {
        singlebit res = (x + doublebit(singlebit(x) * ninv) * mod) >> digit_level;
        return res < mod ? res : res - mod;
    }
public:
    fast_modint() : n(0) {};
    fast_modint(singlebit n_) { n = reduce(doublebit(n_ % mod) * r2); };
    static constexpr singlebit get_mod() { return mod; }
    singlebit get() const { return reduce(n); }
    bool operator==(const fast_modint& x) const { return n == x.n; }
    bool operator!=(const fast_modint& x) const { return n != x.n; }
    fast_modint& operator+=(const fast_modint& x) { n += x.n; n -= (n < mod ? 0 : mod); return *this; }
    fast_modint& operator-=(const fast_modint& x) { n += mod - x.n; n -= (n < mod ? 0 : mod); return *this; }
    fast_modint& operator*=(const fast_modint& x) { n = reduce(doublebit(n) * x.n); return *this; }
    fast_modint operator+(const fast_modint& x) const { return fast_modint(*this) += x; }
    fast_modint operator-(const fast_modint& x) const { return fast_modint(*this) -= x; }
    fast_modint operator*(const fast_modint& x) const { return fast_modint(*this) *= x; }
    fast_modint inv() const { return binpow(mod - 2); }
    fast_modint binpow(singlebit b) const {
        fast_modint ans(1), cur(*this);
        while (b > 0) {
            if (b & 1) ans *= cur;
            cur *= cur;
            b >>= 1;
        }
        return ans;
    }
};

#endif // CLASS_FAST_MODINT

#ifndef CLASS_POLYNOMIAL_NTT
#define CLASS_POLYNOMIAL_NTT

#include <vector>
#include <algorithm>

template<singlebit mod, singlebit depth, singlebit primroot>
class polynomial_ntt {
public:
    using modulo = fast_modint<mod>;
    static void fourier_transform(std::vector<modulo>& v, bool inverse) {
        std::size_t s = v.size();
        for (std::size_t i = 0, j = 1; j < s - 1; ++j) {
            for (std::size_t k = s >> 1; k > (i ^= k); k >>= 1);
            if (i < j) std::swap(v[i], v[j]);
        }
        std::size_t sc = 0, sz = 1;
        while (sz < s) sz *= 2, ++sc;
        modulo root = modulo(primroot).binpow((mod - 1) >> sc);
        std::vector<modulo> pw(s + 1); pw[0] = 1;
        for (std::size_t i = 1; i <= s; i++) pw[i] = pw[i - 1] * root;
        std::size_t qs = s;
        for (std::size_t b = 1; b < s; b <<= 1) {
            qs >>= 1;
            for (std::size_t i = 0; i < s; i += b * 2) {
                for (std::size_t j = i; j < i + b; ++j) {
                    modulo delta = pw[(inverse ? b * 2 - j + i : j - i) * qs] * v[j + b];
                    v[j + b] = v[j] - delta;
                    v[j] += delta;
                }
            }
        }
        if (!inverse) return;
        modulo powinv = modulo((mod + 1) / 2).binpow(sc);
        for (std::size_t i = 0; i < s; ++i) {
            v[i] = v[i] * powinv;
        }
    }
    static std::vector<modulo> convolve(std::vector<modulo> v1, std::vector<modulo> v2) {
        std::size_t s1 = v1.size(), s2 = v2.size(), s = 1;
        while (s < s1 || s < s2) s *= 2;
        v1.resize(s * 2); fourier_transform(v1, false);
        v2.resize(s * 2); fourier_transform(v2, false);
        for (singlebit i = 0; i < s * 2; ++i) v1[i] *= v2[i];
        fourier_transform(v1, true);
        v1.resize(s1 + s2 - 1);
        return v1;
    }
};

#endif // CLASS_POLYNOMIAL_NTT

#include <vector>
#include <algorithm>
using namespace std;
using ntt1 = polynomial_ntt<469762049, 26, 3>; using modulo1 = ntt1::modulo;
using ntt2 = polynomial_ntt<167772161, 25, 3>; using modulo2 = ntt2::modulo;
using ntt3 = polynomial_ntt<998244353, 23, 3>; using modulo3 = ntt3::modulo;
using modulo = fast_modint<1000000007>;
const modulo2 inv21 = modulo2(modulo1::get_mod()).inv();
const modulo3 inv31 = modulo3(modulo1::get_mod()).inv();
const modulo3 inv32 = modulo3(modulo2::get_mod()).inv();
const modulo1 inv1b = modulo1(modulo::get_mod()).inv();
const modulo2 inv2b = modulo2(modulo::get_mod()).inv();
const modulo3 inv3b = modulo3(modulo::get_mod()).inv();
template<class modulox>
std::vector<modulox> get_modvector(std::vector<modulo> v) {
    std::vector<modulox> ans(v.size());
    for (std::size_t i = 0; i < v.size(); ++i) {
        ans[i] = modulox(v[i].get());
    }
    return ans;
}
vector<modulo> convolve(vector<modulo> v1, vector<modulo> v2) {
    vector<modulo1> res1 = ntt1::convolve(get_modvector<modulo1>(v1), get_modvector<modulo1>(v2));
    vector<modulo2> res2 = ntt2::convolve(get_modvector<modulo2>(v1), get_modvector<modulo2>(v2));
    vector<modulo3> res3 = ntt3::convolve(get_modvector<modulo3>(v1), get_modvector<modulo3>(v2));
    vector<modulo> res(v1.size() + v2.size() - 1);
    for (int i = 0; i < v1.size() + v2.size() - 1; ++i) {
        modulo1 m1 = res1[i];
        modulo2 m2 = (res2[i] - m1.get()) * inv21;
        modulo3 m3 = ((res3[i] - m1.get()) * inv31 - m2.get()) * inv32;
        singlebit m4 = ((m1.get() + doublebit(m2.get()) * modulo1::get_mod()) % modulo::get_mod() + doublebit(m3.get()) * modulo1::get_mod() % modulo::get_mod() * modulo2::get_mod()) % modulo::get_mod();
        res[i] = m4;
    }
    return res;
}

#include <vector>
#include <iostream>
using namespace std;
int main() {
    int N, P, Q;
    cin >> N >> P >> Q;
    vector<modulo> seq(2000001);
    seq[0] = 0;
    if (N >= 2) seq[1] = 1;
    for (int i = 2; i < N; ++i) {
        seq[i] = seq[i - 1] * P + seq[i - 2];
    }
    vector<modulo> ans = convolve(seq, seq);
    for (int i = 0; i < Q; ++i) {
        int x;
        cin >> x; x -= 2;
        cout << ans[i].get() << '\n';
    }
    return 0;
}
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