結果
| 問題 | No.2243 Coaching Schedule |
| ユーザー |
👑  rin204
|
| 提出日時 | 2024-04-28 15:08:50 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 575 ms / 4,000 ms |
| コード長 | 25,561 bytes |
| コンパイル時間 | 4,342 ms |
| コンパイル使用メモリ | 281,112 KB |
| 実行使用メモリ | 9,684 KB |
| 最終ジャッジ日時 | 2024-11-17 07:58:17 |
| 合計ジャッジ時間 | 9,710 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
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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
6,820 KB |
| testcase_01 | AC | 2 ms
6,816 KB |
| testcase_02 | AC | 2 ms
6,816 KB |
| testcase_03 | AC | 2 ms
6,820 KB |
| testcase_04 | AC | 5 ms
6,816 KB |
| testcase_05 | AC | 50 ms
9,656 KB |
| testcase_06 | AC | 83 ms
9,536 KB |
| testcase_07 | AC | 83 ms
9,620 KB |
| testcase_08 | AC | 82 ms
9,576 KB |
| testcase_09 | AC | 111 ms
9,628 KB |
| testcase_10 | AC | 112 ms
9,536 KB |
| testcase_11 | AC | 113 ms
9,540 KB |
| testcase_12 | AC | 575 ms
9,684 KB |
| testcase_13 | AC | 435 ms
9,676 KB |
| testcase_14 | AC | 441 ms
9,680 KB |
| testcase_15 | AC | 435 ms
9,676 KB |
| testcase_16 | AC | 40 ms
9,532 KB |
| testcase_17 | AC | 24 ms
6,816 KB |
| testcase_18 | AC | 63 ms
8,816 KB |
| testcase_19 | AC | 99 ms
8,096 KB |
| testcase_20 | AC | 81 ms
6,816 KB |
| testcase_21 | AC | 37 ms
6,820 KB |
| testcase_22 | AC | 33 ms
6,816 KB |
| testcase_23 | AC | 7 ms
6,816 KB |
| testcase_24 | AC | 49 ms
6,820 KB |
| testcase_25 | AC | 9 ms
6,820 KB |
| testcase_26 | AC | 18 ms
6,816 KB |
| testcase_27 | AC | 54 ms
6,816 KB |
| testcase_28 | AC | 9 ms
6,820 KB |
| testcase_29 | AC | 75 ms
7,780 KB |
| testcase_30 | AC | 75 ms
8,972 KB |
| testcase_31 | AC | 78 ms
9,420 KB |
| testcase_32 | AC | 32 ms
6,816 KB |
| testcase_33 | AC | 20 ms
6,820 KB |
| testcase_34 | AC | 63 ms
8,260 KB |
| testcase_35 | AC | 78 ms
8,272 KB |
| testcase_36 | AC | 70 ms
9,148 KB |
ソースコード
// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
// #define INTERACTIVE
namespace templates {
// type
using ll = long long;
using ull = unsigned long long;
using Pii = pair<int, int>;
using Pil = pair<int, ll>;
using Pli = pair<ll, int>;
using Pll = pair<ll, ll>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using qp = priority_queue<T, vector<T>, greater<T>>;
// clang-format off
#define vec(T, A, ...) vector<T> A(__VA_ARGS__);
#define vvec(T, A, h, ...) vector<vector<T>> A(h, vector<T>(__VA_ARGS__));
#define vvvec(T, A, h1, h2, ...) vector<vector<vector<T>>> A(h1, vector<vector<T>>(h2, vector<T>(__VA_ARGS__)));
// clang-format on
// for loop
#define fori1(a) for (ll _ = 0; _ < (a); _++)
#define fori2(i, a) for (ll i = 0; i < (a); i++)
#define fori3(i, a, b) for (ll i = (a); i < (b); i++)
#define fori4(i, a, b, c) for (ll i = (a); ((c) > 0 || i > (b)) && ((c) < 0 || i < (b)); i += (c))
#define overload4(a, b, c, d, e, ...) e
#define fori(...) overload4(__VA_ARGS__, fori4, fori3, fori2, fori1)(__VA_ARGS__)
// declare and input
// clang-format off
#define INT(...) int __VA_ARGS__; inp(__VA_ARGS__);
#define LL(...) ll __VA_ARGS__; inp(__VA_ARGS__);
#define STRING(...) string __VA_ARGS__; inp(__VA_ARGS__);
#define CHAR(...) char __VA_ARGS__; inp(__VA_ARGS__);
#define DOUBLE(...) double __VA_ARGS__; STRING(str___); __VA_ARGS__ = stod(str___);
#define VEC(T, A, n) vector<T> A(n); inp(A);
#define VVEC(T, A, n, m) vector<vector<T>> A(n, vector<T>(m)); inp(A);
// clang-format on
// const value
const ll MOD1 = 1000000007;
const ll MOD9 = 998244353;
const double PI = acos(-1);
// other macro
#if !defined(RIN__LOCAL) && !defined(INTERACTIVE)
#define endl "\n"
#endif
#define spa ' '
#define len(A) ll(A.size())
#define all(A) begin(A), end(A)
// function
vector<char> stoc(string &S) {
int n = S.size();
vector<char> ret(n);
for (int i = 0; i < n; i++) ret[i] = S[i];
return ret;
}
string ctos(vector<char> &S) {
int n = S.size();
string ret = "";
for (int i = 0; i < n; i++) ret += S[i];
return ret;
}
template <class T>
auto min(const T &a) {
return *min_element(all(a));
}
template <class T>
auto max(const T &a) {
return *max_element(all(a));
}
template <class T, class S>
auto clamp(T &a, const S &l, const S &r) {
return (a > r ? r : a < l ? l : a);
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chclamp(T &a, const S &l, const S &r) {
auto b = clamp(a, l, r);
return (a != b ? a = b, 1 : 0);
}
template <typename T>
T sum(vector<T> &A) {
T tot = 0;
for (auto a : A) tot += a;
return tot;
}
template <typename T>
vector<T> compression(vector<T> X) {
sort(all(X));
X.erase(unique(all(X)), X.end());
return X;
}
// input and output
namespace io {
// __int128_t
std::ostream &operator<<(std::ostream &dest, __int128_t value) {
std::ostream::sentry s(dest);
if (s) {
__uint128_t tmp = value < 0 ? -value : value;
char buffer[128];
char *d = std::end(buffer);
do {
--d;
*d = "0123456789"[tmp % 10];
tmp /= 10;
} while (tmp != 0);
if (value < 0) {
--d;
*d = '-';
}
int len = std::end(buffer) - d;
if (dest.rdbuf()->sputn(d, len) != len) {
dest.setstate(std::ios_base::badbit);
}
}
return dest;
}
// vector<T>
template <typename T>
istream &operator>>(istream &is, vector<T> &A) {
for (auto &a : A) is >> a;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, vector<T> &A) {
for (size_t i = 0; i < A.size(); i++) {
os << A[i];
if (i != A.size() - 1) os << ' ';
}
return os;
}
// vector<vector<T>>
template <typename T>
istream &operator>>(istream &is, vector<vector<T>> &A) {
for (auto &a : A) is >> a;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, vector<vector<T>> &A) {
for (size_t i = 0; i < A.size(); i++) {
os << A[i];
if (i != A.size() - 1) os << endl;
}
return os;
}
// pair<S, T>
template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &A) {
is >> A.first >> A.second;
return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, pair<S, T> &A) {
os << A.first << ' ' << A.second;
return os;
}
// vector<pair<S, T>>
template <typename S, typename T>
istream &operator>>(istream &is, vector<pair<S, T>> &A) {
for (size_t i = 0; i < A.size(); i++) {
is >> A[i];
}
return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, vector<pair<S, T>> &A) {
for (size_t i = 0; i < A.size(); i++) {
os << A[i];
if (i != A.size() - 1) os << endl;
}
return os;
}
// tuple
template <typename T, size_t N>
struct TuplePrint {
static ostream &print(ostream &os, const T &t) {
TuplePrint<T, N - 1>::print(os, t);
os << ' ' << get<N - 1>(t);
return os;
}
};
template <typename T>
struct TuplePrint<T, 1> {
static ostream &print(ostream &os, const T &t) {
os << get<0>(t);
return os;
}
};
template <typename... Args>
ostream &operator<<(ostream &os, const tuple<Args...> &t) {
TuplePrint<decltype(t), sizeof...(Args)>::print(os, t);
return os;
}
// io functions
void FLUSH() {
cout << flush;
}
void print() {
cout << endl;
}
template <class Head, class... Tail>
void print(Head &&head, Tail &&...tail) {
cout << head;
if (sizeof...(Tail)) cout << spa;
print(std::forward<Tail>(tail)...);
}
template <typename T, typename S>
void prisep(vector<T> &A, S sep) {
int n = A.size();
for (int i = 0; i < n; i++) {
cout << A[i];
if (i != n - 1) cout << sep;
}
cout << endl;
}
template <typename T, typename S>
void priend(T A, S end) {
cout << A << end;
}
template <typename T>
void prispa(T A) {
priend(A, spa);
}
template <typename T, typename S>
bool printif(bool f, T A, S B) {
if (f)
print(A);
else
print(B);
return f;
}
template <class... T>
void inp(T &...a) {
(cin >> ... >> a);
}
} // namespace io
using namespace io;
// read graph
vector<vector<int>> read_edges(int n, int m, bool direct = false, int indexed = 1) {
vector<vector<int>> edges(n, vector<int>());
for (int i = 0; i < m; i++) {
INT(u, v);
u -= indexed;
v -= indexed;
edges[u].push_back(v);
if (!direct) edges[v].push_back(u);
}
return edges;
}
vector<vector<int>> read_tree(int n, int indexed = 1) {
return read_edges(n, n - 1, false, indexed);
}
template <typename T = long long>
vector<vector<pair<int, T>>> read_wedges(int n, int m, bool direct = false, int indexed = 1) {
vector<vector<pair<int, T>>> edges(n, vector<pair<int, T>>());
for (int i = 0; i < m; i++) {
INT(u, v);
T w;
inp(w);
u -= indexed;
v -= indexed;
edges[u].push_back({v, w});
if (!direct) edges[v].push_back({u, w});
}
return edges;
}
template <typename T = long long>
vector<vector<pair<int, T>>> read_wtree(int n, int indexed = 1) {
return read_wedges<T>(n, n - 1, false, indexed);
}
// yes / no
namespace yesno {
// yes
inline bool yes(bool f = true) {
cout << (f ? "yes" : "no") << endl;
return f;
}
inline bool Yes(bool f = true) {
cout << (f ? "Yes" : "No") << endl;
return f;
}
inline bool YES(bool f = true) {
cout << (f ? "YES" : "NO") << endl;
return f;
}
// no
inline bool no(bool f = true) {
cout << (!f ? "yes" : "no") << endl;
return f;
}
inline bool No(bool f = true) {
cout << (!f ? "Yes" : "No") << endl;
return f;
}
inline bool NO(bool f = true) {
cout << (!f ? "YES" : "NO") << endl;
return f;
}
// possible
inline bool possible(bool f = true) {
cout << (f ? "possible" : "impossible") << endl;
return f;
}
inline bool Possible(bool f = true) {
cout << (f ? "Possible" : "Impossible") << endl;
return f;
}
inline bool POSSIBLE(bool f = true) {
cout << (f ? "POSSIBLE" : "IMPOSSIBLE") << endl;
return f;
}
// impossible
inline bool impossible(bool f = true) {
cout << (!f ? "possible" : "impossible") << endl;
return f;
}
inline bool Impossible(bool f = true) {
cout << (!f ? "Possible" : "Impossible") << endl;
return f;
}
inline bool IMPOSSIBLE(bool f = true) {
cout << (!f ? "POSSIBLE" : "IMPOSSIBLE") << endl;
return f;
}
// Alice Bob
inline bool Alice(bool f = true) {
cout << (f ? "Alice" : "Bob") << endl;
return f;
}
inline bool Bob(bool f = true) {
cout << (f ? "Bob" : "Alice") << endl;
return f;
}
// Takahashi Aoki
inline bool Takahashi(bool f = true) {
cout << (f ? "Takahashi" : "Aoki") << endl;
return f;
}
inline bool Aoki(bool f = true) {
cout << (f ? "Aoki" : "Takahashi") << endl;
return f;
}
} // namespace yesno
using namespace yesno;
} // namespace templates
using namespace templates;
template <int MOD>
struct Modint {
int x;
Modint() : x(0) {}
Modint(int64_t y) {
if (y >= 0)
x = y % MOD;
else
x = (y % MOD + MOD) % MOD;
}
Modint &operator+=(const Modint &p) {
x += p.x;
if (x >= MOD) x -= MOD;
return *this;
}
Modint &operator-=(const Modint &p) {
x -= p.x;
if (x < 0) x += MOD;
return *this;
}
Modint &operator*=(const Modint &p) {
x = int(1LL * x * p.x % MOD);
return *this;
}
Modint &operator/=(const Modint &p) {
*this *= p.inverse();
return *this;
}
Modint &operator%=(const Modint &p) {
assert(p.x == 0);
return *this;
}
Modint operator-() const {
return Modint(-x);
}
Modint &operator++() {
x++;
if (x == MOD) x = 0;
return *this;
}
Modint &operator--() {
if (x == 0) x = MOD;
x--;
return *this;
}
Modint operator++(int) {
Modint result = *this;
++*this;
return result;
}
Modint operator--(int) {
Modint result = *this;
--*this;
return result;
}
friend Modint operator+(const Modint &lhs, const Modint &rhs) {
return Modint(lhs) += rhs;
}
friend Modint operator-(const Modint &lhs, const Modint &rhs) {
return Modint(lhs) -= rhs;
}
friend Modint operator*(const Modint &lhs, const Modint &rhs) {
return Modint(lhs) *= rhs;
}
friend Modint operator/(const Modint &lhs, const Modint &rhs) {
return Modint(lhs) /= rhs;
}
friend Modint operator%(const Modint &lhs, const Modint &rhs) {
assert(rhs.x == 0);
return Modint(lhs);
}
bool operator==(const Modint &p) const {
return x == p.x;
}
bool operator!=(const Modint &p) const {
return x != p.x;
}
bool operator<(const Modint &rhs) const {
return x < rhs.x;
}
bool operator<=(const Modint &rhs) const {
return x <= rhs.x;
}
bool operator>(const Modint &rhs) const {
return x > rhs.x;
}
bool operator>=(const Modint &rhs) const {
return x >= rhs.x;
}
Modint inverse() const {
int a = x, b = MOD, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
a -= t * b;
u -= t * v;
std::swap(a, b);
std::swap(u, v);
}
return Modint(u);
}
Modint pow(int64_t k) const {
Modint ret(1);
Modint y(x);
while (k > 0) {
if (k & 1) ret *= y;
y *= y;
k >>= 1;
}
return ret;
}
friend std::ostream &operator<<(std::ostream &os, const Modint &p) {
return os << p.x;
}
friend std::istream &operator>>(std::istream &is, Modint &p) {
int64_t y;
is >> y;
p = Modint<MOD>(y);
return (is);
}
static int get_mod() {
return MOD;
}
};
struct Arbitrary_Modint {
int x;
static int MOD;
static void set_mod(int mod) {
MOD = mod;
}
Arbitrary_Modint() : x(0) {}
Arbitrary_Modint(int64_t y) {
if (y >= 0)
x = y % MOD;
else
x = (y % MOD + MOD) % MOD;
}
Arbitrary_Modint &operator+=(const Arbitrary_Modint &p) {
x += p.x;
if (x >= MOD) x -= MOD;
return *this;
}
Arbitrary_Modint &operator-=(const Arbitrary_Modint &p) {
x -= p.x;
if (x < 0) x += MOD;
return *this;
}
Arbitrary_Modint &operator*=(const Arbitrary_Modint &p) {
x = int(1LL * x * p.x % MOD);
return *this;
}
Arbitrary_Modint &operator/=(const Arbitrary_Modint &p) {
*this *= p.inverse();
return *this;
}
Arbitrary_Modint &operator%=(const Arbitrary_Modint &p) {
assert(p.x == 0);
return *this;
}
Arbitrary_Modint operator-() const {
return Arbitrary_Modint(-x);
}
Arbitrary_Modint &operator++() {
x++;
if (x == MOD) x = 0;
return *this;
}
Arbitrary_Modint &operator--() {
if (x == 0) x = MOD;
x--;
return *this;
}
Arbitrary_Modint operator++(int) {
Arbitrary_Modint result = *this;
++*this;
return result;
}
Arbitrary_Modint operator--(int) {
Arbitrary_Modint result = *this;
--*this;
return result;
}
friend Arbitrary_Modint operator+(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
return Arbitrary_Modint(lhs) += rhs;
}
friend Arbitrary_Modint operator-(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
return Arbitrary_Modint(lhs) -= rhs;
}
friend Arbitrary_Modint operator*(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
return Arbitrary_Modint(lhs) *= rhs;
}
friend Arbitrary_Modint operator/(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
return Arbitrary_Modint(lhs) /= rhs;
}
friend Arbitrary_Modint operator%(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {
assert(rhs.x == 0);
return Arbitrary_Modint(lhs);
}
bool operator==(const Arbitrary_Modint &p) const {
return x == p.x;
}
bool operator!=(const Arbitrary_Modint &p) const {
return x != p.x;
}
bool operator<(const Arbitrary_Modint &rhs) {
return x < rhs.x;
}
bool operator<=(const Arbitrary_Modint &rhs) {
return x <= rhs.x;
}
bool operator>(const Arbitrary_Modint &rhs) {
return x > rhs.x;
}
bool operator>=(const Arbitrary_Modint &rhs) {
return x >= rhs.x;
}
Arbitrary_Modint inverse() const {
int a = x, b = MOD, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
a -= t * b;
u -= t * v;
std::swap(a, b);
std::swap(u, v);
}
return Arbitrary_Modint(u);
}
Arbitrary_Modint pow(int64_t k) const {
Arbitrary_Modint ret(1);
Arbitrary_Modint y(x);
while (k > 0) {
if (k & 1) ret *= y;
y *= y;
k >>= 1;
}
return ret;
}
friend std::ostream &operator<<(std::ostream &os, const Arbitrary_Modint &p) {
return os << p.x;
}
friend std::istream &operator>>(std::istream &is, Arbitrary_Modint &p) {
int64_t y;
is >> y;
p = Arbitrary_Modint(y);
return (is);
}
static int get_mod() {
return MOD;
}
};
int Arbitrary_Modint::MOD = 998244353;
using modint9 = Modint<998244353>;
using modint1 = Modint<1000000007>;
using modint = Arbitrary_Modint;
using mint = modint9;
template <typename mint>
struct NumberTheoreticTransform {
static std::vector<mint> roots, iroots, rate3, irate3;
static int max_base;
NumberTheoreticTransform() = default;
static void init() {
if (!roots.empty()) return;
const unsigned mod = mint::get_mod();
auto tmp = mod - 1;
max_base = 0;
while (tmp % 2 == 0) {
tmp >>= 1;
max_base++;
}
mint root = 2;
while (root.pow((mod - 1) >> 1) == 1) root++;
roots.resize(max_base + 1);
iroots.resize(max_base + 1);
rate3.resize(max_base + 1);
irate3.resize(max_base + 1);
roots[max_base] = root.pow((mod - 1) >> max_base);
iroots[max_base] = mint(1) / roots[max_base];
for (int i = max_base - 1; i >= 0; i--) {
roots[i] = roots[i + 1] * roots[i + 1];
iroots[i] = iroots[i + 1] * iroots[i + 1];
}
mint prod = 1, iprod = 1;
for (int i = 0; i <= max_base - 3; i++) {
rate3[i] = roots[i + 3] * prod;
irate3[i] = iroots[i + 3] * iprod;
prod *= iroots[i + 3];
iprod *= roots[i + 3];
}
}
static void ntt(std::vector<mint> &A) {
init();
int n = int(A.size());
int h = __builtin_ctz(n);
int le = 0;
mint imag = roots[2];
if (h & 1) {
int p = 1 << (h - 1);
for (int i = 0; i < p; i++) {
auto r = A[i + p];
A[i + p] = A[i] - r;
A[i] += r;
}
le++;
}
for (; le + 1 < h; le += 2) {
int p = 1 << (h - le - 2);
for (int i = 0; i < p; i++) {
auto a0 = A[i];
auto a1 = A[i + p];
auto a2 = A[i + 2 * p];
auto a3 = A[i + 3 * p];
auto a1na3imag = (a1 - a3) * imag;
A[i] = a0 + a2 + a1 + a3;
A[i + p] = a0 + a2 - (a1 + a3);
A[i + 2 * p] = a0 - a2 + a1na3imag;
A[i + 3 * p] = a0 - a2 - a1na3imag;
}
mint rot = rate3[0];
for (int s = 1; s < (1 << le); s++) {
int offset = s << (h - le);
mint rot2 = rot * rot;
mint rot3 = rot2 * rot;
for (int i = 0; i < p; i++) {
auto a0 = A[i + offset];
auto a1 = A[i + offset + p] * rot;
auto a2 = A[i + offset + 2 * p] * rot2;
auto a3 = A[i + offset + 3 * p] * rot3;
auto a1na3imag = (a1 - a3) * imag;
A[i + offset] = a0 + a2 + a1 + a3;
A[i + offset + p] = a0 + a2 - (a1 + a3);
A[i + offset + 2 * p] = a0 - a2 + a1na3imag;
A[i + offset + 3 * p] = a0 - a2 - a1na3imag;
}
rot *= rate3[__builtin_ctz(~s)];
}
}
}
static void intt(std::vector<mint> &A, bool f = true) {
init();
int n = int(A.size());
int h = __builtin_ctz(n);
int le = h;
mint iimag = iroots[2];
for (; le > 1; le -= 2) {
int p = 1 << (h - le);
for (int i = 0; i < p; i++) {
auto a0 = A[i];
auto a1 = A[i + p];
auto a2 = A[i + 2 * p];
auto a3 = A[i + 3 * p];
auto a2na3iimag = (a2 - a3) * iimag;
A[i] = a0 + a1 + a2 + a3;
A[i + p] = a0 - a1 + a2na3iimag;
A[i + 2 * p] = a0 + a1 - (a2 + a3);
A[i + 3 * p] = a0 - a1 - a2na3iimag;
}
mint irot = irate3[0];
for (int s = 1; s < (1 << (le - 2)); s++) {
int offset = s << (h - le + 2);
mint irot2 = irot * irot;
mint irot3 = irot2 * irot;
for (int i = 0; i < p; i++) {
auto a0 = A[i + offset];
auto a1 = A[i + offset + p];
auto a2 = A[i + offset + 2 * p];
auto a3 = A[i + offset + 3 * p];
auto a2na3iimag = (a2 - a3) * iimag;
A[i + offset] = a0 + a1 + a2 + a3;
A[i + offset + p] = (a0 - a1 + a2na3iimag) * irot;
A[i + offset + 2 * p] = (a0 + a1 - (a2 + a3)) * irot2;
A[i + offset + 3 * p] = (a0 - a1 - a2na3iimag) * irot3;
}
irot *= irate3[__builtin_ctz(~s)];
}
}
if (le >= 1) {
int p = 1 << (h - 1);
for (int i = 0; i < p; i++) {
auto ajp = A[i] - A[i + p];
A[i] += A[i + p];
A[i + p] = ajp;
}
}
if (f) {
mint inv = mint(1) / n;
for (int i = 0; i < n; i++) {
A[i] *= inv;
}
}
}
static std::vector<mint> multiply(std::vector<mint> A, std::vector<mint> B) {
int need = int(A.size() + B.size()) - 1;
if (std::min(A.size(), B.size()) < 60u) {
std::vector<mint> C(need, 0);
for (size_t i = 0; i < A.size(); i++)
for (size_t j = 0; j < B.size(); j++) {
C[i + j] += A[i] * B[j];
}
return C;
}
int sz = 1;
while (sz < need) sz <<= 1;
A.resize(sz, 0);
B.resize(sz, 0);
ntt(A);
ntt(B);
mint inv = mint(1) / sz;
for (int i = 0; i < sz; i++) A[i] *= B[i] * inv;
intt(A, false);
A.resize(need);
return A;
}
};
template <typename mint>
std::vector<mint> NumberTheoreticTransform<mint>::roots = std::vector<mint>();
template <typename mint>
std::vector<mint> NumberTheoreticTransform<mint>::iroots = std::vector<mint>();
template <typename mint>
std::vector<mint> NumberTheoreticTransform<mint>::rate3 = std::vector<mint>();
template <typename mint>
std::vector<mint> NumberTheoreticTransform<mint>::irate3 = std::vector<mint>();
template <typename mint>
int NumberTheoreticTransform<mint>::max_base = 0;
template <typename T>
struct Combination {
int N;
std::vector<T> fact, invfact;
Combination(int N) : N(N) {
fact.resize(N + 1);
invfact.resize(N + 1);
fact[0] = 1;
for (int i = 1; i <= N; i++) {
fact[i] = fact[i - 1] * i;
}
invfact[N] = T(1) / fact[N];
for (int i = N - 1; i >= 0; i--) {
invfact[i] = invfact[i + 1] * (i + 1);
}
}
void extend(int n) {
int le = fact.size();
fact.resize(n + 1);
invfact.resize(n + 1);
for (int i = le; i <= n; i++) {
fact[i] = fact[i - 1] * i;
}
invfact[n] = T(1) / fact[n];
for (int i = n - 1; i >= le; i--) {
invfact[i] = invfact[i + 1] * (i + 1);
}
}
T nCk(int n, int k) {
if (k > n || k < 0) return T(0);
if (n >= int(fact.size())) extend(n);
return fact[n] * invfact[k] * invfact[n - k];
}
T nPk(int n, int k) {
if (k > n || k < 0) return T(0);
if (n >= int(fact.size())) extend(n);
return fact[n] * invfact[n - k];
}
T nHk(int n, int k) {
if (n == 0 && k == 0) return T(1);
return nCk(n + k - 1, k);
}
T Catalan(int n) {
return nCk(2 * n, n) - nCk(2 * n, n + 1);
}
// n 個の +1, m 個の -1, 累積和が常にk以下
T Catalan(int n, int m, int k) {
if (n > m + k || k < 0)
return T(0);
else
return nCk(n + m, n) - nCk(n + m, m + k + 1);
}
T Narayana(int n, int k) {
return nCk(n, k) * nCk(n, k - 1) / n;
}
T inv(int n) {
assert(n >= 1);
if (n >= int(fact.size())) extend(n);
return invfact[n] * fact[n - 1];
}
};
using NTT = NumberTheoreticTransform<mint>;
void solve() {
LL(m, n);
Combination<mint> Comb(n + m + 10);
VEC(ll, A, n);
for (auto &a : A) a--;
vec(ll, C, m, 0);
for (auto a : A) C[a]++;
vec(mint, dp, n + 1, 0);
ll ma = max(C);
map<ll, ll> cnt;
for (auto c : C) {
if (c != 0) cnt[c]++;
}
fori(d, ma, n + 1) {
mint prod = 1;
for (auto [k, v] : cnt) {
prod *= Comb.nPk(d, k).pow(v);
}
dp[d] = prod;
}
fori(i, ma, n + 1) {
dp[i] *= Comb.invfact[i];
}
vec(mint, invs, n + 1, 0);
fori(i, n + 1) {
invs[i] = Comb.invfact[i] * (i % 2 == 0 ? 1 : -1);
}
auto dp2 = NTT::multiply(dp, invs);
dp2.resize(n + 1);
fori(i, n + 1) {
dp2[i] *= Comb.fact[i];
}
print(sum(dp2));
}
int main() {
#ifndef INTERACTIVE
cin.tie(0)->sync_with_stdio(0);
#endif
// cout << fixed << setprecision(12);
int t;
t = 1;
// cin >> t;
while (t--) solve();
return 0;
}