結果
問題 | No.2243 Coaching Schedule |
ユーザー |
|
提出日時 | 2023-03-10 22:44:26 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 496 ms / 4,000 ms |
コード長 | 21,931 bytes |
コンパイル時間 | 2,270 ms |
コンパイル使用メモリ | 213,492 KB |
最終ジャッジ日時 | 2025-02-11 08:52:39 |
ジャッジサーバーID (参考情報) |
judge4 / judge2 |
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ファイルパターン | 結果 |
---|---|
other | AC * 37 |
ソースコード
#include <bits/stdc++.h>using namespace std;#define rep(i, n) for (int i = 0; i < (n); i++)#define per(i, n) for (int i = (n)-1; i >= 0; i--)#define rep2(i, l, r) for (int i = (l); i < (r); i++)#define per2(i, l, r) for (int i = (r)-1; i >= (l); i--)#define each(e, v) for (auto &e : v)#define MM << " " <<#define pb push_back#define eb emplace_back#define all(x) begin(x), end(x)#define rall(x) rbegin(x), rend(x)#define sz(x) (int)x.size()using ll = long long;using pii = pair<int, int>;using pil = pair<int, ll>;using pli = pair<ll, int>;using pll = pair<ll, ll>;template <typename T>using minheap = priority_queue<T, vector<T>, greater<T>>;template <typename T>using maxheap = priority_queue<T>;template <typename T>bool chmax(T &x, const T &y) {return (x < y) ? (x = y, true) : false;}template <typename T>bool chmin(T &x, const T &y) {return (x > y) ? (x = y, true) : false;}template <typename T>int flg(T x, int i) {return (x >> i) & 1;}template <typename T>void print(const vector<T> &v, T x = 0) {int n = v.size();for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');if (v.empty()) cout << '\n';}template <typename T>void printn(const vector<T> &v, T x = 0) {int n = v.size();for (int i = 0; i < n; i++) cout << v[i] + x << '\n';}template <typename T>int lb(const vector<T> &v, T x) {return lower_bound(begin(v), end(v), x) - begin(v);}template <typename T>int ub(const vector<T> &v, T x) {return upper_bound(begin(v), end(v), x) - begin(v);}template <typename T>void rearrange(vector<T> &v) {sort(begin(v), end(v));v.erase(unique(begin(v), end(v)), end(v));}template <typename T>vector<int> id_sort(const vector<T> &v, bool greater = false) {int n = v.size();vector<int> ret(n);iota(begin(ret), end(ret), 0);sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });return ret;}template <typename S, typename T>pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {return make_pair(p.first + q.first, p.second + q.second);}template <typename S, typename T>pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {return make_pair(p.first - q.first, p.second - q.second);}template <typename S, typename T>istream &operator>>(istream &is, pair<S, T> &p) {S a;T b;is >> a >> b;p = make_pair(a, b);return is;}template <typename S, typename T>ostream &operator<<(ostream &os, const pair<S, T> &p) {return os << p.first << ' ' << p.second;}struct io_setup {io_setup() {ios_base::sync_with_stdio(false);cin.tie(NULL);cout << fixed << setprecision(15);}} io_setup;const int inf = (1 << 30) - 1;const ll INF = (1LL << 60) - 1;// const int MOD = 1000000007;const int MOD = 998244353;template <int mod>struct Mod_Int {int x;Mod_Int() : x(0) {}Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}static int get_mod() { return mod; }Mod_Int &operator+=(const Mod_Int &p) {if ((x += p.x) >= mod) x -= mod;return *this;}Mod_Int &operator-=(const Mod_Int &p) {if ((x += mod - p.x) >= mod) x -= mod;return *this;}Mod_Int &operator*=(const Mod_Int &p) {x = (int)(1LL * x * p.x % mod);return *this;}Mod_Int &operator/=(const Mod_Int &p) {*this *= p.inverse();return *this;}Mod_Int &operator++() { return *this += Mod_Int(1); }Mod_Int operator++(int) {Mod_Int tmp = *this;++*this;return tmp;}Mod_Int &operator--() { return *this -= Mod_Int(1); }Mod_Int operator--(int) {Mod_Int tmp = *this;--*this;return tmp;}Mod_Int operator-() const { return Mod_Int(-x); }Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; }Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; }Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; }Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; }bool operator==(const Mod_Int &p) const { return x == p.x; }bool operator!=(const Mod_Int &p) const { return x != p.x; }Mod_Int inverse() const {assert(*this != Mod_Int(0));return pow(mod - 2);}Mod_Int pow(long long k) const {Mod_Int now = *this, ret = 1;for (; k > 0; k >>= 1, now *= now) {if (k & 1) ret *= now;}return ret;}friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; }friend istream &operator>>(istream &is, Mod_Int &p) {long long a;is >> a;p = Mod_Int<mod>(a);return is;}};using mint = Mod_Int<MOD>;template <typename T>struct Combination {static vector<T> _fac, _ifac;Combination() {}static void init(int n) {_fac.resize(n + 1), _ifac.resize(n + 1);_fac[0] = 1;for (int i = 1; i <= n; i++) _fac[i] = _fac[i - 1] * i;_ifac[n] = _fac[n].inverse();for (int i = n; i >= 1; i--) _ifac[i - 1] = _ifac[i] * i;}static T fac(int k) { return _fac[k]; }static T ifac(int k) { return _ifac[k]; }static T inv(int k) { return fac(k - 1) * ifac(k); }static T P(int n, int k) {if (k < 0 || n < k) return 0;return fac(n) * ifac(n - k);}static T C(int n, int k) {if (k < 0 || n < k) return 0;return fac(n) * ifac(n - k) * ifac(k);}// n 個の区別できる箱に、k 個の区別できない玉を入れる場合の数static T H(int n, int k) {if (n < 0 || k < 0) return 0;return k == 0 ? 1 : C(n + k - 1, k);}// n 個の区別できる玉を、k 個の区別しない箱に、各箱に 1 個以上玉が入るように入れる場合の数static T second_stirling_number(int n, int k) {T ret = 0;for (int i = 0; i <= k; i++) {T tmp = C(k, i) * T(i).pow(n);ret += ((k - i) & 1) ? -tmp : tmp;}return ret * ifac(k);}// n 個の区別できる玉を、k 個の区別しない箱に入れる場合の数static T bell_number(int n, int k) {if (n == 0) return 1;k = min(k, n);vector<T> pref(k + 1);pref[0] = 1;for (int i = 1; i <= k; i++) {if (i & 1) {pref[i] = pref[i - 1] - ifac(i);} else {pref[i] = pref[i - 1] + ifac(i);}}T ret = 0;for (int i = 1; i <= k; i++) ret += T(i).pow(n) * ifac(i) * pref[k - i];return ret;}};template <typename T>vector<T> Combination<T>::_fac = vector<T>();template <typename T>vector<T> Combination<T>::_ifac = vector<T>();using comb = Combination<mint>;template <typename T>struct Number_Theoretic_Transform {static int max_base;static T root;static vector<T> r, ir;Number_Theoretic_Transform() {}static void init() {if (!r.empty()) return;int mod = T::get_mod();int tmp = mod - 1;root = 2;while (root.pow(tmp >> 1) == 1) root++;max_base = 0;while (tmp % 2 == 0) tmp >>= 1, max_base++;r.resize(max_base), ir.resize(max_base);for (int i = 0; i < max_base; i++) {r[i] = -root.pow((mod - 1) >> (i + 2)); // r[i] := 1 の 2^(i+2) 乗根ir[i] = r[i].inverse(); // ir[i] := 1/r[i]}}static void ntt(vector<T> &a) {init();int n = a.size();assert((n & (n - 1)) == 0);assert(n <= (1 << max_base));for (int k = n; k >>= 1;) {T w = 1;for (int s = 0, t = 0; s < n; s += 2 * k) {for (int i = s, j = s + k; i < s + k; i++, j++) {T x = a[i], y = w * a[j];a[i] = x + y, a[j] = x - y;}w *= r[__builtin_ctz(++t)];}}}static void intt(vector<T> &a) {init();int n = a.size();assert((n & (n - 1)) == 0);assert(n <= (1 << max_base));for (int k = 1; k < n; k <<= 1) {T w = 1;for (int s = 0, t = 0; s < n; s += 2 * k) {for (int i = s, j = s + k; i < s + k; i++, j++) {T x = a[i], y = a[j];a[i] = x + y, a[j] = w * (x - y);}w *= ir[__builtin_ctz(++t)];}}T inv = T(n).inverse();for (auto &e : a) e *= inv;}static vector<T> convolve(vector<T> a, vector<T> b) {if (a.empty() || b.empty()) return {};int k = (int)a.size() + (int)b.size() - 1, n = 1;while (n < k) n <<= 1;a.resize(n), b.resize(n);ntt(a), ntt(b);for (int i = 0; i < n; i++) a[i] *= b[i];intt(a), a.resize(k);return a;}};template <typename T>int Number_Theoretic_Transform<T>::max_base = 0;template <typename T>T Number_Theoretic_Transform<T>::root = T();template <typename T>vector<T> Number_Theoretic_Transform<T>::r = vector<T>();template <typename T>vector<T> Number_Theoretic_Transform<T>::ir = vector<T>();using NTT = Number_Theoretic_Transform<mint>;template <typename T>struct Formal_Power_Series : vector<T> {using NTT_ = Number_Theoretic_Transform<T>;using vector<T>::vector;Formal_Power_Series(const vector<T> &f) : vector<T>(f) {}// f(x) mod x^nFormal_Power_Series pre(int n) const {Formal_Power_Series ret(begin(*this), begin(*this) + min((int)this->size(), n));ret.resize(n, 0);return ret;}// f(1/x)x^{n-1}Formal_Power_Series rev(int n = -1) const {Formal_Power_Series ret = *this;if (n != -1) ret.resize(n, 0);reverse(begin(ret), end(ret));return ret;}void normalize() {while (!this->empty() && this->back() == 0) this->pop_back();}Formal_Power_Series operator-() const {Formal_Power_Series ret = *this;for (int i = 0; i < (int)ret.size(); i++) ret[i] = -ret[i];return ret;}Formal_Power_Series &operator+=(const T &t) {if (this->empty()) this->resize(1, 0);(*this)[0] += t;return *this;}Formal_Power_Series &operator+=(const Formal_Power_Series &g) {if (g.size() > this->size()) this->resize(g.size());for (int i = 0; i < (int)g.size(); i++) (*this)[i] += g[i];this->normalize();return *this;}Formal_Power_Series &operator-=(const T &t) {if (this->empty()) this->resize(1, 0);*this[0] -= t;return *this;}Formal_Power_Series &operator-=(const Formal_Power_Series &g) {if (g.size() > this->size()) this->resize(g.size());for (int i = 0; i < (int)g.size(); i++) (*this)[i] -= g[i];this->normalize();return *this;}Formal_Power_Series &operator*=(const T &t) {for (int i = 0; i < (int)this->size(); i++) (*this)[i] *= t;return *this;}Formal_Power_Series &operator*=(const Formal_Power_Series &g) {if (empty(*this) || empty(g)) {this->clear();return *this;}return *this = NTT_::convolve(*this, g);}Formal_Power_Series &operator/=(const T &t) {assert(t != 0);T inv = t.inverse();return *this *= inv;}// f(x) を g(x) で割った商Formal_Power_Series &operator/=(const Formal_Power_Series &g) {if (g.size() > this->size()) {this->clear();return *this;}int n = this->size(), m = g.size();return *this = (rev() * g.rev().inv(n - m + 1)).pre(n - m + 1).rev();}// f(x) を g(x) で割った余りFormal_Power_Series &operator%=(const Formal_Power_Series &g) { return *this -= (*this / g) * g; }// f(x)/x^kFormal_Power_Series &operator<<=(int k) {Formal_Power_Series ret(k, 0);ret.insert(end(ret), begin(*this), end(*this));return *this = ret;}// f(x)x^kFormal_Power_Series &operator>>=(int k) {Formal_Power_Series ret;ret.insert(end(ret), begin(*this) + k, end(*this));return *this = ret;}Formal_Power_Series operator+(const T &t) const { return Formal_Power_Series(*this) += t; }Formal_Power_Series operator+(const Formal_Power_Series &g) const { return Formal_Power_Series(*this) += g; }Formal_Power_Series operator-(const T &t) const { return Formal_Power_Series(*this) -= t; }Formal_Power_Series operator-(const Formal_Power_Series &g) const { return Formal_Power_Series(*this) -= g; }Formal_Power_Series operator*(const T &t) const { return Formal_Power_Series(*this) *= t; }Formal_Power_Series operator*(const Formal_Power_Series &g) const { return Formal_Power_Series(*this) *= g; }Formal_Power_Series operator/(const T &t) const { return Formal_Power_Series(*this) /= t; }Formal_Power_Series operator/(const Formal_Power_Series &g) const { return Formal_Power_Series(*this) /= g; }Formal_Power_Series operator%(const Formal_Power_Series &g) const { return Formal_Power_Series(*this) %= g; }Formal_Power_Series operator<<(int k) const { return Formal_Power_Series(*this) <<= k; }Formal_Power_Series operator>>(int k) const { return Formal_Power_Series(*this) >>= k; }// f(c)T val(const T &c) const {T ret = 0;for (int i = (int)this->size() - 1; i >= 0; i--) ret *= c, ret += (*this)[i];return ret;}// df/dxFormal_Power_Series derivative() const {if (empty(*this)) return *this;int n = this->size();Formal_Power_Series ret(n - 1);for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * i;return ret;}// ∫f(x)dxFormal_Power_Series integral() const {if (empty(*this)) return *this;int n = this->size();vector<T> inv(n + 1, 0);inv[1] = 1;int mod = T::get_mod();for (int i = 2; i <= n; i++) inv[i] = -inv[mod % i] * T(mod / i);Formal_Power_Series ret(n + 1, 0);for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] * inv[i + 1];return ret;}// 1/f(x) mod x^n (f[0] != 0)Formal_Power_Series inv(int n = -1) const {assert((*this)[0] != 0);if (n == -1) n = this->size();Formal_Power_Series ret(1, (*this)[0].inverse());for (int m = 1; m < n; m <<= 1) {Formal_Power_Series f = pre(2 * m), g = ret;f.resize(2 * m), g.resize(2 * m);NTT_::ntt(f), NTT_::ntt(g);Formal_Power_Series h(2 * m);for (int i = 0; i < 2 * m; i++) h[i] = f[i] * g[i];NTT_::intt(h);for (int i = 0; i < m; i++) h[i] = 0;NTT_::ntt(h);for (int i = 0; i < 2 * m; i++) h[i] *= g[i];NTT_::intt(h);for (int i = 0; i < m; i++) h[i] = 0;ret -= h;}ret.resize(n);return ret;}// log(f(x)) mod x^n (f[0] = 1)Formal_Power_Series log(int n = -1) const {assert((*this)[0] == 1);if (n == -1) n = this->size();Formal_Power_Series ret = (derivative() * inv(n)).pre(n - 1).integral();ret.resize(n);return ret;}// exp(f(x)) mod x^n (f[0] = 0)Formal_Power_Series exp(int n = -1) const {assert((*this)[0] == 0);if (n == -1) n = this->size();vector<T> inv(2 * n + 1, 0);inv[1] = 1;int mod = T::get_mod();for (int i = 2; i <= 2 * n; i++) inv[i] = -inv[mod % i] * T(mod / i);auto inplace_integral = [inv](Formal_Power_Series &f) {if (empty(f)) return;int n = f.size();f.insert(begin(f), 0);for (int i = 1; i <= n; i++) f[i] *= inv[i];};auto inplace_derivative = [](Formal_Power_Series &f) {if (empty(f)) return;int n = f.size();f.erase(begin(f));for (int i = 0; i < n - 1; i++) f[i] *= T(i + 1);};Formal_Power_Series ret{1, this->size() > 1 ? (*this)[1] : 0}, c{1}, z1, z2{1, 1};for (int m = 2; m < n; m *= 2) {auto y = ret;y.resize(2 * m);NTT_::ntt(y);z1 = z2;Formal_Power_Series z(m);for (int i = 0; i < m; i++) z[i] = y[i] * z1[i];NTT_::intt(z);fill(begin(z), begin(z) + m / 2, 0);NTT_::ntt(z);for (int i = 0; i < m; i++) z[i] *= -z1[i];NTT_::intt(z);c.insert(end(c), begin(z) + m / 2, end(z));z2 = c, z2.resize(2 * m);NTT_::ntt(z2);Formal_Power_Series x(begin(*this), begin(*this) + min((int)this->size(), m));inplace_derivative(x);x.resize(m, 0);NTT_::ntt(x);for (int i = 0; i < m; i++) x[i] *= y[i];NTT_::intt(x);x -= ret.derivative(), x.resize(2 * m);for (int i = 0; i < m - 1; i++) x[m + i] = x[i], x[i] = 0;NTT_::ntt(x);for (int i = 0; i < 2 * m; i++) x[i] *= z2[i];NTT_::intt(x);x.pop_back();inplace_integral(x);for (int i = m; i < min((int)this->size(), 2 * m); i++) x[i] += (*this)[i];fill(begin(x), begin(x) + m, 0);NTT_::ntt(x);for (int i = 0; i < 2 * m; i++) x[i] *= y[i];NTT_::intt(x);ret.insert(end(ret), begin(x) + m, end(x));}ret.resize(n);return ret;}// f(x)^k mod x^nFormal_Power_Series pow(long long k, int n = -1) const {if (n == -1) n = this->size();int m = this->size();for (int i = 0; i < m; i++) {if ((*this)[i] == 0) continue;T inv = (*this)[i].inverse();Formal_Power_Series g(m - i, 0);for (int j = i; j < m; j++) g[j - i] = (*this)[j] * inv;g = (g.log(n) * k).exp(n) * ((*this)[i].pow(k));Formal_Power_Series ret(n, 0);if (i > 0 && k > n / i) return ret;long long d = i * k;for (int j = 0; j + d < n && j < g.size(); j++) ret[j + d] = g[j];return ret;}Formal_Power_Series ret(n, 0);if (k == 0) ret[0] = 1;return ret;}// √f(x) mod x^n (存在しなければ空)Formal_Power_Series sqrt(int n = -1) const {if (n == -1) n = this->size();int mod = T::get_mod();auto sqrt_mod = [mod](const T &a) {if (mod == 2) return a;int s = mod - 1, t = 0;while (s % 2 == 0) s /= 2, t++;T root = 2;while (root.pow((mod - 1) / 2) == 1) root++;T x = a.pow((s + 1) / 2);T u = root.pow(s);T y = x * x * a.inverse();while (y != 1) {int k = 0;T z = y;while (z != 1) k++, z *= z;for (int i = 0; i < t - k - 1; i++) u *= u;x *= u, u *= u, y *= u;t = k;}return x;};if ((*this)[0] == 0) {for (int i = 1; i < (int)this->size(); i++) {if ((*this)[i] != 0) {if (i & 1) return {};if ((*this)[i].pow((mod - 1) / 2) != 1) return {};if (n <= i / 2) break;return ((*this) >> i).sqrt(n - i / 2) << (i / 2);}}return Formal_Power_Series(n, 0);}if ((*this)[0].pow((mod - 1) / 2) != 1) return {};T tw = T(2).inverse();Formal_Power_Series ret{sqrt_mod((*this)[0])};for (int m = 1; m < n; m *= 2) {Formal_Power_Series g = (*this).pre(m * 2) * ret.inv(m * 2);g.resize(2 * m);ret = (ret + g) * tw;}ret.resize(n);return ret;}// f(x+c)Formal_Power_Series Taylor_shift(T c) const {int n = this->size();vector<T> ifac(n, 1);Formal_Power_Series f(n), g(n);for (int i = 0; i < n; i++) {f[n - 1 - i] = (*this)[i] * ifac[n - 1];if (i < n - 1) ifac[n - 1] *= i + 1;}ifac[n - 1] = ifac[n - 1].inverse();for (int i = n - 1; i > 0; i--) ifac[i - 1] = ifac[i] * i;T pw = 1;for (int i = 0; i < n; i++) {g[i] = pw * ifac[i];pw *= c;}f *= g;Formal_Power_Series b(n);for (int i = 0; i < n; i++) b[i] = f[n - 1 - i] * ifac[i];return b;}};using fps = Formal_Power_Series<mint>;int main() {int M, N;cin >> M >> N;comb::init(1000000);vector<int> c(M, 0);rep(i, N) {int x;cin >> x;x--;c[x]++;}vector<int> cnt(N + 1, 0);rep(i, M) cnt[c[i]]++;vector<int> cs;rep(i, N + 1) {if (cnt[i] > 0) cs.eb(i);}fps f(N + 1, 1);rep(k, N + 1) {each(e, cs) {f[k] *= comb::P(k, e).pow(cnt[e]); //}f[k] *= comb::ifac(k);}fps h(N + 1, 0);rep(i, N + 1) h[i] = comb::ifac(i);auto g = f * h.inv();mint ans = 0;rep2(k, 1, N + 1) ans += g[k] * comb::fac(k);cout << ans << '\n';}