#1007795 (C++17) No.2877 Gunegune Hyperion

提出ソース
結果

問題	No.2877 Gunegune Hyperion
ユーザー	fuppy_kyopro
提出日時	2024-09-06 22:42:24
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	1,050 ms / 6,000 ms
コード長	23,089 bytes
コンパイル時間	5,829 ms
コンパイル使用メモリ	296,732 KB
実行使用メモリ	23,272 KB
最終ジャッジ日時	2024-09-06 22:42:57
合計ジャッジ時間	24,967 ms
ジャッジサーバーID （参考情報）	judge5 / judge3
このコードへのチャレンジ
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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	AC	2 ms 6,812 KB
testcase_01	AC	2 ms 6,820 KB
testcase_02	AC	3 ms 6,944 KB
testcase_03	AC	206 ms 7,748 KB
testcase_04	AC	222 ms 7,776 KB
testcase_05	AC	490 ms 13,488 KB
testcase_06	AC	475 ms 16,740 KB
testcase_07	AC	517 ms 15,620 KB
testcase_08	AC	491 ms 14,656 KB
testcase_09	AC	451 ms 10,944 KB
testcase_10	AC	963 ms 18,788 KB
testcase_11	AC	475 ms 10,940 KB
testcase_12	AC	99 ms 6,944 KB
testcase_13	AC	207 ms 8,320 KB
testcase_14	AC	102 ms 6,944 KB
testcase_15	AC	448 ms 10,552 KB
testcase_16	AC	934 ms 20,884 KB
testcase_17	AC	994 ms 20,144 KB
testcase_18	AC	203 ms 7,360 KB
testcase_19	AC	224 ms 10,528 KB
testcase_20	AC	14 ms 6,940 KB
testcase_21	AC	955 ms 18,908 KB
testcase_22	AC	492 ms 13,536 KB
testcase_23	AC	1,006 ms 20,972 KB
testcase_24	AC	960 ms 19,800 KB
testcase_25	AC	1,037 ms 23,228 KB
testcase_26	AC	226 ms 8,216 KB
testcase_27	AC	484 ms 14,404 KB
testcase_28	AC	1,028 ms 23,252 KB
testcase_29	AC	1,026 ms 23,140 KB
testcase_30	AC	1,050 ms 23,272 KB
testcase_31	AC	1,046 ms 23,268 KB
testcase_32	AC	1,050 ms 23,264 KB
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

raw source code
/*
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
//*/

#include <atcoder/all>
// #include <atcoder/segtree>
#include <bits/stdc++.h>

using namespace std;
using namespace atcoder;

// #define _GLIBCXX_DEBUG

#define DEBUG(x) cerr << #x << ": " << x << endl;
#define DEBUG_VEC(v)                                        \
    cerr << #v << ":";                                      \
    for (int iiiiiiii = 0; iiiiiiii < v.size(); iiiiiiii++) \
        cerr << " " << v[iiiiiiii];                         \
    cerr << endl;
#define DEBUG_MAT(v)                                \
    cerr << #v << endl;                             \
    for (int iv = 0; iv < v.size(); iv++) {         \
        for (int jv = 0; jv < v[iv].size(); jv++) { \
            cerr << v[iv][jv] << " ";               \
        }                                           \
        cerr << endl;                               \
    }
typedef long long ll;
// #define int ll

#define vi vector<int>
#define vl vector<ll>
#define vii vector<vector<int>>
#define vll vector<vector<ll>>
#define pii pair<int, int>
#define pis pair<int, string>
#define psi pair<string, int>
#define pll pair<ll, ll>
template <class S, class T>
pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) {
    return pair<S, T>(s.first + t.first, s.second + t.second);
}
template <class S, class T>
pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first - t.first, s.second - t.second); }
template <class S, class T>
ostream &operator<<(ostream &os, pair<S, T> p) {
    os << "(" << p.first << ", " << p.second << ")";
    return os;
}
#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 rrep(i, n) for (int i = (int)(n) - 1; i >= 0; i--)
#define rrep1(i, n) for (int i = (int)(n); i > 0; i--)
#define REP(i, a, b) for (int i = a; i < b; i++)
#define in(x, a, b) (a <= x && x < b)
#define all(c) c.begin(), c.end()
void YES(bool t = true) {
    cout << (t ? "YES" : "NO") << endl;
}
void Yes(bool t = true) { cout << (t ? "Yes" : "No") << endl; }
void yes(bool t = true) { cout << (t ? "yes" : "no") << endl; }
void NO(bool t = true) { cout << (t ? "NO" : "YES") << endl; }
void No(bool t = true) { cout << (t ? "No" : "Yes") << endl; }
void no(bool t = true) { cout << (t ? "no" : "yes") << endl; }
template <class T>
bool chmax(T &a, const T &b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
bool chmin(T &a, const T &b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T, class U>
T ceil_div(T a, U b) {
    return (a + b - 1) / b;
}
template <class T>
T safe_mul(T a, T b) {
    if (a == 0 || b == 0) return 0;
    if (numeric_limits<T>::max() / a < b) return numeric_limits<T>::max();
    return a * b;
}
#define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end());
const ll inf = 1000000001;
const ll INF = (ll)1e18 + 1;
const long double pi = 3.1415926535897932384626433832795028841971L;
int popcount(ll t) { return __builtin_popcountll(t); }
vector<int> gen_perm(int n) {
    vector<int> ret(n);
    iota(all(ret), 0);
    return ret;
}
// int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
// int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 };
vi dx = {0, 0, -1, 1}, dy = {-1, 1, 0, 0};
vi dx2 = {1, 1, 0, -1, -1, -1, 0, 1}, dy2 = {0, 1, 1, 1, 0, -1, -1, -1};
struct Setup_io {
    Setup_io() {
        ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
        cout << fixed << setprecision(25);
        cerr << fixed << setprecision(25);
    }
} setup_io;
// constexpr ll MOD = 1000000007;
constexpr ll MOD = 998244353;
// #define mp make_pair

#include <bits/stdc++.h>
using namespace std;

// https://web.archive.org/web/20220903140644/https://opt-cp.com/fps-fast-algorithms/
using mint = modint998244353;
template <typename T>
struct Factorial {
    int MAX;
    vector<T> fac, finv;
    Factorial(int m = 0) : MAX(m), fac(m + 1, 1), finv(m + 1, 1) {
        for (int i = 2; i < MAX + 1; i++) {
            fac[i] = fac[i - 1] * i;
        }
        finv[MAX] /= fac[MAX];
        for (int i = MAX; i >= 3; i--) {
            finv[i - 1] = finv[i] * i;
        }
    }
    T binom(int n, int k) {
        if (k < 0 || n < k) return 0;
        return fac[n] * finv[k] * finv[n - k];
    }
    T perm(int n, int k) {
        if (k < 0 || n < k) return 0;
        return fac[n] * finv[n - k];
    }
};
Factorial<mint> fc;

template <class T>
struct FormalPowerSeries : vector<T> {
    using vector<T>::vector;
    using vector<T>::operator=;
    using F = FormalPowerSeries;

    F operator-() const {
        F res(*this);
        for (auto &e : res)
            e = -e;
        return res;
    }
    F &operator*=(const T &g) {
        for (auto &e : *this)
            e *= g;
        return *this;
    }
    F &operator/=(const T &g) {
        assert(g != T(0));
        *this *= g.inv();
        return *this;
    }
    F &operator+=(const F &g) {
        int n = this->size(), m = g.size();
        this->resize(max(n, m), T(0));
        rep(i, m)(*this)[i] += g[i];
        return *this;
    }
    F &operator-=(const F &g) {
        int n = this->size(), m = g.size();
        rep(i, min(n, m))(*this)[i] -= g[i];
        return *this;
    }
    F &operator<<=(const int d) {
        int n = this->size();
        if (d >= n) *this = F(n);
        this->insert(this->begin(), d, 0);
        this->resize(n);
        return *this;
    }
    F &operator>>=(const int d) {
        int n = this->size();
        this->erase(this->begin(), this->begin() + min(n, d));
        this->resize(n);
        return *this;
    }

    F operator*(const T &g) const { return F(*this) *= g; }
    F operator/(const T &g) const { return F(*this) /= g; }
    F operator+(const F &g) const { return F(*this) += g; }
    F operator-(const F &g) const { return F(*this) -= g; }
    F operator<<(const int d) const { return F(*this) <<= d; }
    F operator>>(const int d) const { return F(*this) >>= d; }

    F pre(int sz) const {
        return F(begin(*this), begin(*this) + min((int)this->size(), sz));
    }
    F rev() const {
        F ret(*this);
        reverse(begin(ret), end(ret));
        return ret;
    }
    void shrink() {
        while (this->size() && this->back() == T(0)) {
            this->pop_back();
        }
    }

    // O(n log n)
    F inv(int d = -1) const {
        int n = this->size();
        assert(n != 0 && (*this)[0] != 0);
        if (d == -1) d = n;
        assert(d >= 0);
        F res{(*this)[0].inv()};
        for (int m = 1; m < d; m *= 2) {
            F f(this->begin(), this->begin() + min(n, 2 * m));
            F g(res);
            f.resize(2 * m), internal::butterfly(f);
            g.resize(2 * m), internal::butterfly(g);
            rep(i, 2 * m) f[i] *= g[i];
            internal::butterfly_inv(f);
            f.erase(f.begin(), f.begin() + m);
            f.resize(2 * m), internal::butterfly(f);
            rep(i, 2 * m) f[i] *= g[i];
            internal::butterfly_inv(f);
            T iz = T(2 * m).inv();
            iz *= -iz;
            rep(i, m) f[i] *= iz;
            res.insert(res.end(), f.begin(), f.begin() + m);
        }
        res.resize(d);
        return res;
    }

    // fast: FMT-friendly modulus only
    // O(n log n)
    F &multiply_inplace(const F &g, int d = -1) {
        int n = this->size();
        if (d == -1) d = n + g.size() - 1;
        assert(d >= 0);
        *this = convolution(std::move(*this), g);
        this->resize(d);
        return *this;
    }
    F multiply(const F &g, const int d = -1) const {
        return F(*this).multiply_inplace(g, d);
    }
    // O(n log n)
    F &divide_inplace(const F &g, int d = -1) {
        int n = this->size();
        if (d == -1) d = n;
        assert(d >= 0);
        *this = convolution(move(*this), g.inv(d));
        this->resize(d);
        return *this;
    }
    F divide(const F &g, const int d = -1) const { return F(*this).divide_inplace(g, d); }

    F divide_polynomial_inplace(F g) {
        // https://qiita.com/hotman78/items/f0e6d2265badd84d429a#4%E5%A4%9A%E9%A0%85%E5%BC%8F%E3%81%A8%E3%81%97%E3%81%A6%E3%81%AE%E5%95%86%E4%BD%99%E3%82%8A
        // 実装は Nyaan さんのものをほぼコピーしている
        if (this->size() < g.size()) {
            this->clear();
            return *this;
        }
        int n = (int)this->size() - (int)g.size() + 1;
        if ((int)g.size() <= 64) {
            // g が小さい時は愚直の方が早い
            F f(*this);
            g.shrink();
            mint coeff = g.back().inv();
            for (auto &x : g)
                x *= coeff;
            int deg = (int)f.size() - (int)g.size() + 1;
            int gs = g.size();
            F quo(deg);
            for (int i = deg - 1; i >= 0; i--) {
                quo[i] = f[i + gs - 1];
                for (int j = 0; j < gs; j++)
                    f[i + j] -= quo[i] * g[j];
            }
            *this = quo * coeff;
            this->resize(n, T(0));
            return *this;
        }
        // rev が x に x^-1 を代入する行為とほぼ等しい
        return *this = ((*this).rev().pre(n).multiply(g.rev().inv(n))).pre(n).rev();
    }
    F divide_polynomial(const F &g) const {
        // 高校で習うような多項式の割り算という意味での divide
        return F(*this).divide_polynomial_inplace(g);
    }
    F remainder_polynomial(const F &g) const {
        // 高校で習うような多項式の割り算という意味での remainder
        auto p = this->divide_polynomial(g);
        auto q = *this - p.multiply(g);
        q.shrink();
        return q;
    }

    // sparse
    // O(nk)
    F &multiply_inplace(vector<pair<int, T>> g) {
        int n = this->size();
        auto [d, c] = g.front();
        if (d == 0)
            g.erase(g.begin());
        else
            c = 0;

        for (int i = n - 1; i >= 0; i--) {
            mint ori = (*this)[i];
            (*this)[i] *= c;
            for (auto &[j, b] : g) {
                while (this->size() <= i + j)
                    this->push_back(0);

                (*this)[i + j] += ori * b;
            }
        }
        return *this;
    }
    F multiply(const vector<pair<int, T>> &g) const { return F(*this).multiply_inplace(g); }
    // O(nk)
    F &divide_inplace(vector<pair<int, T>> g) {
        int n = this->size();
        auto [d, c] = g.front();
        assert(d == 0 && c != T(0));
        T ic = c.inv();
        g.erase(g.begin());
        rep(i, n) {
            for (auto &[j, b] : g) {
                if (j > i) break;
                (*this)[i] -= (*this)[i - j] * b;
            }
            (*this)[i] *= ic;
        }
        return *this;
    }
    F divide(const vector<pair<int, T>> &g) const { return F(*this).divide_inplace(g); }

    // multiply and divide (1 + cz^d)
    // O(n)
    void multiply_inplace(const int d, const T c) {
        int n = this->size();
        if (c == T(1))
            for (int i = n - d - 1; i >= 0; i--)
                (*this)[i + d] += (*this)[i];
        else if (c == T(-1))
            for (int i = n - d - 1; i >= 0; i--)
                (*this)[i + d] -= (*this)[i];
        else
            for (int i = n - d - 1; i >= 0; i--)
                (*this)[i + d] += (*this)[i] * c;
    }
    // O(n)
    void divide_inplace(const int d, const T c) {
        int n = this->size();
        if (c == T(1))
            rep(i, n - d)(*this)[i + d] -= (*this)[i];
        else if (c == T(-1))
            rep(i, n - d)(*this)[i + d] += (*this)[i];
        else
            rep(i, n - d)(*this)[i + d] -= (*this)[i] * c;
    }

    // O(n)
    T eval(const T &a) const {
        T x(1), res(0);
        for (auto e : *this)
            res += e * x, x *= a;
        return res;
    }

    // O(n)
    F &integral_inplace() {
        int n = this->size();
        assert(n > 0);
        if (n == 1) return *this = F{0};
        this->insert(this->begin(), 0);
        this->pop_back();
        vector<T> inv(n);
        inv[1] = 1;
        int p = T::mod();
        for (int i = 2; i < n; i++) {
            inv[i] = -inv[p % i] * (p / i);
        }
        for (int i = 2; i < n; i++) {
            (*this)[i] *= inv[i];
        }
        return *this;
    }
    F integral() const { return F(*this).integral_inplace(); }

    // O(n)
    F &derivative_inplace() {
        int n = this->size();
        assert(n > 0);
        for (int i = 2; i < n; i++) {
            (*this)[i] *= i;
        }
        this->erase(this->begin());
        this->push_back(0);
        return *this;
    }
    F derivative() const { return F(*this).derivative_inplace(); }

    // O(n log n)
    F &log_inplace(int d = -1) {
        int n = this->size();
        assert(n > 0 && (*this)[0] == 1);
        if (d == -1) d = n;
        assert(d >= 0);
        if (d < n) this->resize(d);
        F f_inv = this->inv();
        this->derivative_inplace();
        this->multiply_inplace(f_inv);
        this->integral_inplace();
        return *this;
    }
    F log(const int d = -1) const { return F(*this).log_inplace(d); }

    // O(n log n)
    // https://arxiv.org/abs/1301.5804 (Figure 1, right)
    F &exp_inplace(int d = -1) {
        int n = this->size();
        assert(n > 0 && (*this)[0] == 0);
        if (d == -1) d = n;
        assert(d >= 0);
        F g{1}, g_fft{1, 1};
        (*this)[0] = 1;
        this->resize(d);
        F h_drv(this->derivative());
        for (int m = 2; m < d; m *= 2) {
            // prepare
            F f_fft(this->begin(), this->begin() + m);
            f_fft.resize(2 * m), internal::butterfly(f_fft);

            // Step 2.a'
            {
                F _g(m);
                rep(i, m) _g[i] = f_fft[i] * g_fft[i];
                internal::butterfly_inv(_g);
                _g.erase(_g.begin(), _g.begin() + m / 2);
                _g.resize(m), internal::butterfly(_g);
                rep(i, m) _g[i] *= g_fft[i];
                internal::butterfly_inv(_g);
                _g.resize(m / 2);
                _g /= T(-m) * m;
                g.insert(g.end(), _g.begin(), _g.begin() + m / 2);
            }

            // Step 2.b'--d'
            F t(this->begin(), this->begin() + m);
            t.derivative_inplace();
            {
                // Step 2.b'
                F r{h_drv.begin(), h_drv.begin() + m - 1};
                // Step 2.c'
                r.resize(m);
                internal::butterfly(r);
                rep(i, m) r[i] *= f_fft[i];
                internal::butterfly_inv(r);
                r /= -m;
                // Step 2.d'
                t += r;
                t.insert(t.begin(), t.back());
                t.pop_back();
            }

            // Step 2.e'
            if (2 * m < d) {
                t.resize(2 * m);
                internal::butterfly(t);
                g_fft = g;
                g_fft.resize(2 * m);
                internal::butterfly(g_fft);
                rep(i, 2 * m) t[i] *= g_fft[i];
                internal::butterfly_inv(t);
                t.resize(m);
                t /= 2 * m;
            } else { // この場合分けをしても数パーセントしか速くならない
                F g1(g.begin() + m / 2, g.end());
                F s1(t.begin() + m / 2, t.end());
                t.resize(m / 2);
                g1.resize(m), internal::butterfly(g1);
                t.resize(m), internal::butterfly(t);
                s1.resize(m), internal::butterfly(s1);
                rep(i, m) s1[i] = g_fft[i] * s1[i] + g1[i] * t[i];
                rep(i, m) t[i] *= g_fft[i];
                internal::butterfly_inv(t);
                internal::butterfly_inv(s1);
                rep(i, m / 2) t[i + m / 2] += s1[i];
                t /= m;
            }

            // Step 2.f'
            F v(this->begin() + m, this->begin() + min<int>(d, 2 * m));
            v.resize(m);
            t.insert(t.begin(), m - 1, 0);
            t.push_back(0);
            t.integral_inplace();
            rep(i, m) v[i] -= t[m + i];

            // Step 2.g'
            v.resize(2 * m);
            internal::butterfly(v);
            rep(i, 2 * m) v[i] *= f_fft[i];
            internal::butterfly_inv(v);
            v.resize(m);
            v /= 2 * m;

            // Step 2.h'
            rep(i, min(d - m, m))(*this)[m + i] = v[i];
        }
        return *this;
    }
    F exp(const int d = -1) const { return F(*this).exp_inplace(d); }

    // O(n log n)
    F &pow_inplace(const ll k, int d = -1) {
        int n = this->size();
        if (d == -1) d = n;
        assert(d >= 0 && k >= 0);
        if (d == 0) return *this = F(0);
        if (k == 0) {
            *this = F(d);
            (*this)[0] = 1;
            return *this;
        }
        int l = 0;
        while (l < n && (*this)[l] == 0)
            ++l;
        if (l == n || l > (d - 1) / k) return *this = F(d);
        T c{(*this)[l]};
        this->erase(this->begin(), this->begin() + l);
        *this /= c;
        this->log_inplace(d - l * k);
        *this *= k;
        this->exp_inplace();
        *this *= c.pow(k);
        this->insert(this->begin(), l * k, 0);
        return *this;
    }
    F pow(const ll k, const int d = -1) const { return F(*this).pow_inplace(k, d); }

    // O(n log n)
    F &shift_inplace(const T c) {
        int n = this->size();
        fc = Factorial<T>(n);
        rep(i, n)(*this)[i] *= fc.fac[i];
        reverse(this->begin(), this->end());
        F g(n);
        T cp = 1;
        rep(i, n) g[i] = cp * fc.finv[i], cp *= c;
        this->multiply_inplace(g, n);
        reverse(this->begin(), this->end());
        rep(i, n)(*this)[i] *= fc.finv[i];
        return *this;
    }
    F shift(const T c) const { return F(*this).shift_inplace(c); }

    vector<T> multipoint_evaluate(vector<T> const &xs) const {
        // xs の各要素に対しての f(xs) を返す
        // https://rsk0315.hatenablog.com/entry/2020/04/05/190941#fn-ab0dfd97
        // verify: https://judge.yosupo.jp/submission/220213

        int m = xs.size();
        // m 以上の最小の 2 べき
        int m2 = 1;
        while (m2 < m) {
            m2 <<= 1;
        }
        // セグ木のように (x - xs[i]) の積を構築する
        vector<F> g(m2 + m2, {1});
        for (int i = 0; i < m; ++i) {
            g[m2 + i] = {-xs[i], 1}; // (x - xi)
        }
        for (int i = m2 - 1; i > 0; i--) {
            g[i] = g[i << 1 | 0].multiply(g[i << 1 | 1]);
        }

        // g[1] (根) を this を g[1] で割った余りにする
        // g[i] は親を g[i] で割った余りにする
        // 最終的に g[m2 + i] は f を (x - xs[i]) で割った余りになり、剰余の定理よりそれが求める答えとなる
        g[1] = this->remainder_polynomial(g[1]);
        for (int i = 2; i < m2 + m; i++) {
            g[i] = g[i >> 1].remainder_polynomial(g[i]);
        }
        std::vector<T> ys(m);
        for (int i = 0; i < m; i++) {
            ys[i] = g[m2 + i][0];
        }
        return ys;
    }

    static F multiply_sequence(const vector<F> &fs) {
        if (fs.size() == 0) {
            return {1};
        }
        // fs を全て掛け合わせる
        queue<F> qu;
        for (const auto &f : fs) {
            qu.push(f);
        }

        while (qu.size() > 1) {
            F f1 = qu.front();
            qu.pop();
            F f2 = qu.front();
            qu.pop();
            qu.push(f1.multiply(f2, f1.size() + f2.size() - 1));
        }
        return qu.front();
    }
};

using fps = FormalPowerSeries<mint>;

fps interpolate(const vector<mint> &xs, const vector<mint> &ys) {
    // https://rsk0315.hatenablog.com/entry/2020/04/05/203210
    // https://ferin-tech.hatenablog.com/entry/2019/08/11/%E3%83%A9%E3%82%B0%E3%83%A9%E3%83%B3%E3%82%B8%E3%83%A5%E8%A3%9C%E9%96%93 も参考になる
    // n 次多項式 y = f(x) において、n + 1 個の点 (x_i, y_i) が与えられたとき、
    // 係数 a_0, a_1, ..., a_n を求める

    int n = xs.size();
    // n 以上の最小の 2 べき
    int n2 = 1;
    while (n2 < n) {
        n2 <<= 1;
    }

    // セグ木のように (x - xs[i]) の積を構築する
    vector<fps> mul(n2 + n2, {1});
    for (int i = 0; i < n; ++i) {
        mul[n2 + i] = {-xs[i], 1}; // (x - xi)
    }
    for (int i = n2 - 1; i > 0; i--) {
        mul[i] = mul[i << 1 | 0].multiply(mul[i << 1 | 1]);
    }

    // mul[1] が全ての積になる
    // mul[1] の微分を d としたとき a_i = y_i / d(x_i) を計算したい
    // d(x_i) は剰余の定理を使って計算できる（multipoint_evaluate 参照）
    auto d = mul[1].derivative();

    vector<fps> g(n2 + n2);
    g[1] = d.remainder_polynomial(mul[1]);
    for (int i = 2; i < n2 + n; i++) {
        g[i] = g[i >> 1].remainder_polynomial(mul[i]);
    }
    // これ以降 g の意味は \sum_{l <= j < r} (a_j \mul{l <= i < r, i != j} (x - x_i)) とする
    // [l, r) はセグ木の区間
    for (int i = 0; i < n; i++) {
        g[n2 + i] = {ys[i] / g[n2 + i][0]};
    }
    for (int i = n2 - 1; i >= 1; i--) {
        int lch = i << 1 | 0, rch = i << 1 | 1;
        g[i] = g[lch].multiply(mul[rch]) + g[rch].multiply(mul[lch]);
    }

    return g[1];
}

using V = array<array<fps, 3>, 3>;

mint inv2 = mint(2).inv();
mint inv3 = mint(3).inv();

V e0, e1;

V mul(const V &a, const V &b) {
    V c;
    rep(i, 3) rep(j, 3) c[i][j] = fps{0};

    rep(i, 3) rep(j, 3) rep(k, 3) {
        c[i][j] += a[i][k].multiply(b[k][j]);
    }
    return c;
}

V pow(int k) {
    if (k == 0) {
        return e0;
    }
    if (k == 1) {
        return e1;
    }

    V res = e0;
    if (k & 1) {
        res = e1;
        k--;
    }

    V tmp = pow(k / 2);
    return mul(res, mul(tmp, tmp));
}

signed main() {
    int n, h;
    cin >> n >> h;

    for (int i = 0; i < 3; i++) {
        for (int j = 0; j < 3; j++) {
            if (i == j) {
                e0[i][j] = fps{1};
            } else {
                e0[i][j] = fps{0};
            }
        }
    }

    rep(i, 3) rep(j, 3) {
        e1[i][j] = fps{0};
    }

    rep(from, 3) {
        if (from == 0) {
            e1[from][0] = fps{inv2};
            e1[from][1] = fps{0, inv2};
        } else if (from == 1) {
            e1[from][0] = fps{inv3};
            e1[from][1] = fps{0, inv3};
            e1[from][2] = fps{0, inv3};
        } else {
            e1[from][1] = fps{0, inv3 * 2};
            e1[from][2] = fps{0, inv3};
        }
    }

    array<fps, 3> ini;
    ini[0] = fps{mint(2) / 5};
    ini[1] = fps{0, mint(2) / 5};
    ini[2] = fps{0, mint(1) / 5};

    V An = pow(n - 1);

    fps ret;
    rep(from, 3) rep(to, 3) {
        ret += ini[from].multiply(An[from][to]);
    }

    mint ans = 0;
    for (int i = h; i < ret.size(); i++) {
        ans += ret[i];
    }

    cout << ans.val() << endl;
}
yukicoder

結果

テストケース

ソースコード
