結果

問題 No.2369 Some Products
ユーザー Kak1_n0_taneKak1_n0_tane
提出日時 2023-06-25 14:48:14
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
TLE  
(最新)
AC  
(最初)
実行時間 -
コード長 14,612 bytes
コンパイル時間 5,005 ms
コンパイル使用メモリ 276,128 KB
実行使用メモリ 105,816 KB
最終ジャッジ日時 2023-09-21 14:19:57
合計ジャッジ時間 9,045 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge11
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 1 ms
4,380 KB
testcase_01 AC 2 ms
4,380 KB
testcase_02 TLE -
testcase_03 -- -
testcase_04 -- -
testcase_05 -- -
testcase_06 -- -
testcase_07 -- -
testcase_08 -- -
testcase_09 -- -
testcase_10 -- -
testcase_11 -- -
testcase_12 -- -
testcase_13 -- -
testcase_14 -- -
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 # 

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

istream &operator>>(istream &is, modint998244353 &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint998244353 &a) { return os << a.val(); }
istream &operator>>(istream &is, modint1000000007 &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint1000000007 &a) { return os << a.val(); }
template<int m> istream &operator>>(istream &is, static_modint<m> &a) { long long v; is >> v; a = v; return is; }
template<int m> istream &operator>>(istream &is, dynamic_modint<m> &a) { long long v; is >> v; a = v; return is; }
template<int m> ostream &operator<<(ostream &os, const static_modint<m> &a) { return os << a.val(); }
template<int m> ostream &operator<<(ostream &os, const dynamic_modint<m> &a) { return os << a.val(); }
#define rep_(i, a_, b_, a, b, ...) for (int i = (a), lim##i = (b); i < lim##i; ++i)
#define rep(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define drep_(i, a_, b_, a, b, ...) for (int i = (a)-1, lim##i = (b); i >= lim##i; --i)
#define drep(i, ...) drep_(i, __VA_ARGS__, __VA_ARGS__, __VA_ARGS__, 0)
using ll = long long;
template<class T> istream &operator>>(istream &is, vector<T> &v) { for (auto &e : v) is >> e; return is; }
template<class T> ostream &operator<<(ostream &os, const vector<T> &v) { for (auto &e : v) os << e << ' '; return os; }
struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;

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) {
        rep(i, 2, MAX+1) fac[i] = fac[i-1] * i;
        finv[MAX] /= fac[MAX];
        drep(i, MAX+1, 3) 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();
        rep(i, min(n, 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;
    }

    // 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;
        assert(d >= 0);
        *this = convolution(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); }

    // // naive
    // // O(n^2)
    // F &multiply_inplace(const F &g) {
    //     int n = this->size(), m = g.size();
    //     drep(i, n) {
    //       (*this)[i] *= g[0];
    //       rep(j, 1, min(i+1, m)) (*this)[i] += (*this)[i-j] * g[j];
    //     }
    //     return *this;
    // }
    // F multiply(const F &g) const { return F(*this).multiply_inplace(g); }
    // // O(n^2)
    // F &divide_inplace(const F &g) {
    //     assert(g[0] != T(0));
    //     T ig0 = g[0].inv();
    //     int n = this->size(), m = g.size();
    //     rep(i, n) {
    //       rep(j, 1, min(i+1, m)) (*this)[i] -= (*this)[i-j] * g[j];
    //       (*this)[i] *= ig0;
    //     }
    //     return *this;
    // }
    // F divide(const F &g) const { return F(*this).divide_inplace(g); }

    // 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;
        drep(i, n) {
            (*this)[i] *= c;
            for (auto &[j, b] : g) {
            if (j > i) break;
            (*this)[i] += (*this)[i-j] * 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)) drep(i, n-d) (*this)[i+d] += (*this)[i];
        else if (c == T(-1)) drep(i, n-d) (*this)[i+d] -= (*this)[i];
        else drep(i, n-d) (*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();
        rep(i, 2, n) inv[i] = - inv[p%i] * (p/i);
        rep(i, 2, n) (*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);
        rep(i, 2, n) (*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); }

    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; }
};

using fps = FormalPowerSeries<mint>;

int main(){
    // FILE *out = freopen("out1.txt", "w", stdout);
    int N;
    cin >> N;
    vector<ll> P(N);
    rep(i,N) cin >> P[i];

    // func[B][X] := 1以上B以下の整数からX個選び、積の総和
    vector<vector<mint>> func(N+1, vector<mint>(N+1, 0));
    rep(x,N+1){
        if(x==0) continue;
        rep(b,N){
            if(x==1){
                func[b+1][1] = func[b][1] + P[b];
            }
            else{
                func[b+1][x] = func[b][x] + P[b]*func[b][x-1];
            }
        }
    }

    // rep(i,N+1){
    //     rep(j,N+1){
    //         cout << func[i][j] << (j==N?'\n':' ');
    //     }
    // }

    int Q;
    cin >> Q;

    for(int i=0;i<Q;i++){
        ll A, B, X;
        cin >> A >> B >> X;
        fps keisuu(X+1);
        keisuu[0] = 1;
        rep(i,X) keisuu[i+1] = func[A-1][i+1];
        fps answer(X+1);
        answer[0] = 1;
        rep(i,X) answer[i+1] = func[B][i+1];
        
        // cout << keisuu << '\n';
        // cout << answer << '\n';
        
        fps func_abi(X+1);
        func_abi = convolution(answer, keisuu.inv());
        cout << func_abi[X] << '\n';
    }
}
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