結果

問題 No.2243 Coaching Schedule
ユーザー tokusakurai
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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(要ログイン)
ファイルパターン 結果
other AC * 37
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ソースコード

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プレゼンテーションモードにする

#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 k
static T H(int n, int k) {
if (n < 0 || k < 0) return 0;
return k == 0 ? 1 : C(n + k - 1, k);
}
// n k 1
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 k
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 2^(i+2)
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^n
Formal_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) g(x)
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) g(x)
Formal_Power_Series &operator%=(const Formal_Power_Series &g) { return *this -= (*this / g) * g; }
// f(x)/x^k
Formal_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^k
Formal_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/dx
Formal_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)dx
Formal_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^n
Formal_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 ()
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';
}
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0