#748070 (C++17) No.1771 A DELETEQ

提出ソース

結果

問題	No.1771 A DELETEQ
ユーザー	Ricky_pon
提出日時	2022-03-24 22:45:31
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	34 ms / 3,500 ms
コード長	19,544 bytes
コンパイル時間	5,421 ms
コンパイル使用メモリ	265,744 KB
実行使用メモリ	5,376 KB
最終ジャッジ日時	2024-04-21 07:42:33
合計ジャッジ時間	23,677 ms
ジャッジサーバーID （参考情報）	judge4 / judge5

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 5,248 KB
testcase_01	AC	2 ms 5,248 KB
testcase_02	AC	34 ms 5,248 KB
testcase_03	AC	2 ms 5,248 KB
testcase_04	AC	34 ms 5,376 KB
testcase_05	AC	33 ms 5,376 KB
testcase_06	AC	2 ms 5,376 KB
testcase_07	AC	2 ms 5,376 KB
testcase_08	AC	2 ms 5,376 KB
testcase_09	AC	9 ms 5,376 KB
testcase_10	AC	9 ms 5,376 KB
testcase_11	AC	9 ms 5,376 KB
testcase_12	AC	9 ms 5,376 KB
testcase_13	AC	9 ms 5,376 KB
testcase_14	AC	18 ms 5,376 KB
testcase_15	AC	33 ms 5,376 KB
testcase_16	AC	33 ms 5,376 KB
testcase_17	AC	4 ms 5,376 KB
testcase_18	AC	10 ms 5,376 KB
testcase_19	AC	2 ms 5,376 KB
testcase_20	AC	17 ms 5,376 KB
testcase_21	AC	5 ms 5,376 KB
testcase_22	AC	17 ms 5,376 KB
testcase_23	AC	17 ms 5,376 KB
testcase_24	AC	9 ms 5,376 KB
testcase_25	AC	6 ms 5,376 KB
testcase_26	AC	17 ms 5,376 KB
testcase_27	AC	9 ms 5,376 KB
testcase_28	AC	5 ms 5,376 KB
evil_hand_1.txt	AC	2,568 ms 20,788 KB
evil_hand_2.txt	AC	2 ms 5,376 KB
evil_hand_3.txt	AC	2 ms 5,376 KB
evil_random_1.txt	AC	563 ms 7,336 KB
evil_random_2.txt	AC	937 ms 11,196 KB
evil_random_3.txt	AC	1,157 ms 11,076 KB
evil_random_4.txt	AC	2,401 ms 18,328 KB
evil_random_5.txt	AC	1,200 ms 11,840 KB
evil_random_6.txt	AC	535 ms 7,428 KB
evil_random_7.txt	AC	2,562 ms 19,924 KB
evil_random_8.txt	AC	2,210 ms 19,952 KB
evil_random_9.txt	AC	2,414 ms 19,680 KB

権限があれば一括ダウンロードができます

コンパイルメッセージ

main.cpp:125: warning: "rep" redefined
  125 | #define rep(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
      | 
main.cpp:69: note: this is the location of the previous definition
   69 | #define rep(i, n) For(i, 0, n)
      |

ソースコード

raw source code

#include <bits/stdc++.h>

#include <atcoder/convolution>
#include <atcoder/modint>

#include <algorithm>
#include <cassert>
#include <vector>

template <class T>
bool chmax(T &a, const T &b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template <class T>
bool chmin(T &a, const T &b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

template <class T>
T div_floor(T a, T b) {
    if (b < 0) a *= -1, b *= -1;
    return a >= 0 ? a / b : (a + 1) / b - 1;
}

template <class T>
T div_ceil(T a, T b) {
    if (b < 0) a *= -1, b *= -1;
    return a > 0 ? (a - 1) / b + 1 : a / b;
}

template <typename T>
struct CoordComp {
    std::vector<T> v;
    bool sorted;

    CoordComp() : sorted(false) {}

    int size() { return v.size(); }

    void add(T x) { v.push_back(x); }

    void build() {
        std::sort(v.begin(), v.end());

        v.erase(std::unique(v.begin(), v.end()), v.end());
        sorted = true;
    }

    int get_idx(T x) {
        assert(sorted);
        return lower_bound(v.begin(), v.end(), x) - v.begin();
    }

    T &operator[](int i) { return v[i]; }
};


#define For(i, a, b) for (int i = (int)(a); (i) < (int)(b); ++(i))
#define rFor(i, a, b) for (int i = (int)(a)-1; (i) >= (int)(b); --(i))
#define rep(i, n) For(i, 0, n)
#define rrep(i, n) rFor(i, n, 0)
#define fi first
#define se second

using namespace std;

using lint = long long;
using pii = pair<int, int>;
using pll = pair<lint, lint>;

using mint = atcoder::modint998244353;

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_;

// verified by:
// https://judge.yosupo.jp/problem/convolution_mod
// https://judge.yosupo.jp/problem/inv_of_formal_power_series
// https://judge.yosupo.jp/problem/log_of_formal_power_series
// https://judge.yosupo.jp/problem/exp_of_formal_power_series
// https://judge.yosupo.jp/problem/pow_of_formal_power_series
// https://judge.yosupo.jp/problem/polynomial_taylor_shift
// https://judge.yosupo.jp/problem/bernoulli_number
// https://judge.yosupo.jp/problem/sharp_p_subset_sum

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>;

// https://judge.yosupo.jp/problem/inv_of_formal_power_series
void yosupo_inv() {
    int n;
    cin >> n;
    fps a(n);
    cin >> a;
    cout << a.inv() << '\n';
}

// https://judge.yosupo.jp/problem/log_of_formal_power_series
void yosupo_log() {
    int n;
    cin >> n;
    fps a(n);
    cin >> a;
    cout << a.log_inplace() << '\n';
}

// https://judge.yosupo.jp/problem/exp_of_formal_power_series
void yosupo_exp() {
    int n;
    cin >> n;
    fps a(n);
    cin >> a;
    cout << a.exp_inplace() << '\n';
}

// https://judge.yosupo.jp/problem/pow_of_formal_power_series
void yosupo_pow() {
    int n, m;
    cin >> n >> m;
    fps a(n);
    cin >> a;
    cout << a.pow_inplace(m) << '\n';
}

// https://judge.yosupo.jp/problem/polynomial_taylor_shift
void yosupo_shift() {
    int n, c;
    cin >> n >> c;
    fps a(n);
    cin >> a;
    cout << a.shift_inplace(c) << '\n';
}

// https://judge.yosupo.jp/problem/bernoulli_number
void yosupo_bernoulli() {
    int n;
    cin >> n;
    ++n;
    fc = Factorial<mint>(n);
    fps f((fc.finv).begin() + 1, (fc.finv).end());
    f = f.inv();
    rep(i, n) f[i] *= fc.fac[i];
    cout << f << '\n';
}

// https://judge.yosupo.jp/problem/sharp_p_subset_sum
void yosupo_count_subset_sum() {
    int n, t;
    cin >> n >> t;
    ++t;
    vector<int> c(t);
    rep(i, n) {
        int s;
        cin >> s;
        ++c[s];
    }

    vector<mint> inv(t);
    inv[1] = 1;
    int p = mint::mod();
    rep(i, 2, t) inv[i] = -inv[p % i] * (p / i);

    fps f(t);
    rep(i, t) {
        if (c[i] == 0) continue;
        for (int j = 1, d = i; d < t; ++j, d += i) {
            if (j & 1)
                f[d] += c[i] * inv[j];
            else
                f[d] -= c[i] * inv[j];
        }
    }
    f.exp_inplace();
    f.erase(f.begin());
    cout << f << '\n';
}

template <class T>
struct bostan_mori {
    vector<T> p, q;
    bostan_mori(vector<T> a, vector<T> c) : p(move(a)), q(move(c)) {
        assert(p.size() == q.size());
        int d = q.size();
        q.resize(d + 1);
        drep(i, d) q[i + 1] = -q[i];
        q[0] = 1;
        p = convolution(move(p), q);
        p.resize(d);
    }
    void rev(vector<T> &f) const {
        int d = f.size();
        rep(i, d) if (i & 1) f[i] = -f[i];
    }
    void even(vector<T> &f) const {
        int d = (f.size() + 1) >> 1;
        rep(i, d) f[i] = f[i << 1];
        f.resize(d);
    }
    void odd(vector<T> &f) const {
        int d = f.size() >> 1;
        rep(i, d) f[i] = f[i << 1 | 1];
        f.resize(d);
    }
    T operator[](ll n) const {
        vector<T> _p(p), _q(q), _q_rev(q);
        rev(_q_rev);
        for (; n; n >>= 1) {
            _p = convolution(move(_p), _q_rev);
            if (n & 1)
                odd(_p);
            else
                even(_p);
            _q = convolution(move(_q), move(_q_rev));
            even(_q);
            _q_rev = _q;
            rev(_q_rev);
        }
        return _p[0] / _q[0];
    }
};

int main() {
    int n, m;
    scanf("%d%d", &n, &m);
    if (n > m) swap(n, m);

    fps a(2 * n + 3), b(2 * n + 3), c(n + 4), d = {1, 1, 1};
    a[0] = 1;
    a[1] = 2;
    b[1] = 1;
    b[2] = -mint(1);
    a = a.pow(n + 1) - b.pow(n + 1);

    c[0] = 1;
    c[1] = -mint(1);
    c = c.pow(n + 1).multiply(d);

    // cout << a << endl;
    // cout << c << endl;

    a = a.divide(c);
    c >>= 1;
    c *= -mint(1);
    c.resize(a.size());

    bostan_mori bm(a, c);
    printf("%u\n", bm[m].val());
}

yukicoder

結果

テストケース

コンパイルメッセージ

ソースコード