結果
| 問題 |
No.2243 Coaching Schedule
|
| コンテスト | |
| ユーザー |
 Pachicobue
|
| 提出日時 | 2023-03-14 12:42:48 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 617 ms / 4,000 ms |
| コード長 | 29,431 bytes |
| コンパイル時間 | 4,353 ms |
| コンパイル使用メモリ | 257,664 KB |
| 最終ジャッジ日時 | 2025-02-11 11:06:43 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 37 |
ソースコード
#include <bits/stdc++.h>
using i32 = int;
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
using f64 = double;
using f80 = long double;
using f128 = __float128;
constexpr i32 operator"" _i32(u64 v) { return v; }
constexpr u32 operator"" _u32(u64 v) { return v; }
constexpr i64 operator"" _i64(u64 v) { return v; }
constexpr u64 operator"" _u64(u64 v) { return v; }
constexpr f64 operator"" _f64(f80 v) { return v; }
constexpr f80 operator"" _f80(f80 v) { return v; }
using Istream = std::istream;
using Ostream = std::ostream;
using Str = std::string;
template<typename T>
using Lt = std::less<T>;
template<typename T>
using Gt = std::greater<T>;
template<int n>
using BSet = std::bitset<n>;
template<typename T1, typename T2>
using Pair = std::pair<T1, T2>;
template<typename... Ts>
using Tup = std::tuple<Ts...>;
template<typename T, int N>
using Arr = std::array<T, N>;
template<typename... Ts>
using Deq = std::deque<Ts...>;
template<typename... Ts>
using Set = std::set<Ts...>;
template<typename... Ts>
using MSet = std::multiset<Ts...>;
template<typename... Ts>
using USet = std::unordered_set<Ts...>;
template<typename... Ts>
using UMSet = std::unordered_multiset<Ts...>;
template<typename... Ts>
using Map = std::map<Ts...>;
template<typename... Ts>
using MMap = std::multimap<Ts...>;
template<typename... Ts>
using UMap = std::unordered_map<Ts...>;
template<typename... Ts>
using UMMap = std::unordered_multimap<Ts...>;
template<typename... Ts>
using Vec = std::vector<Ts...>;
template<typename... Ts>
using Stack = std::stack<Ts...>;
template<typename... Ts>
using Queue = std::queue<Ts...>;
template<typename T>
using MaxHeap = std::priority_queue<T>;
template<typename T>
using MinHeap = std::priority_queue<T, Vec<T>, Gt<T>>;
constexpr bool LOCAL = false;
constexpr bool OJ = not LOCAL;
template<typename T>
static constexpr T OjLocal(T oj, T local)
{
return LOCAL ? local : oj;
}
template<typename T>
constexpr T LIMMIN = std::numeric_limits<T>::min();
template<typename T>
constexpr T LIMMAX = std::numeric_limits<T>::max();
template<typename T>
constexpr T INF = (LIMMAX<T> - 1) / 2;
template<typename T>
constexpr T PI = T{3.141592653589793238462643383279502884};
template<typename T = u64>
constexpr T TEN(int n)
{
return n == 0 ? T{1} : TEN<T>(n - 1) * T{10};
}
template<typename T>
constexpr bool chmin(T& a, const T& b)
{
return (a > b ? (a = b, true) : false);
}
template<typename T>
constexpr bool chmax(T& a, const T& b)
{
return (a < b ? (a = b, true) : false);
}
template<typename T>
constexpr T floorDiv(T x, T y)
{
assert(y != 0);
if (y < 0) { x = -x, y = -y; }
return x >= 0 ? x / y : (x - y + 1) / y;
}
template<typename T>
constexpr T ceilDiv(T x, T y)
{
assert(y != 0);
if (y < 0) { x = -x, y = -y; }
return x >= 0 ? (x + y - 1) / y : x / y;
}
template<typename T, typename I>
constexpr T powerMonoid(T v, I n, const T& e)
{
assert(n >= 0);
if (n == 0) { return e; }
return (n % 2 == 1 ? v * powerMonoid(v, n - 1, e) : powerMonoid(v * v, n / 2, e));
}
template<typename T, typename I>
constexpr T powerInt(T v, I n)
{
return powerMonoid(v, n, T{1});
}
template<typename Vs, typename V>
constexpr void fillAll(Vs& arr, const V& v)
{
if constexpr (std::is_convertible<V, Vs>::value) {
arr = v;
} else {
for (auto& subarr : arr) { fillAll(subarr, v); }
}
}
template<typename Vs>
constexpr void sortAll(Vs& vs)
{
std::sort(std::begin(vs), std::end(vs));
}
template<typename Vs, typename C>
constexpr void sortAll(Vs& vs, C comp)
{
std::sort(std::begin(vs), std::end(vs), comp);
}
template<typename Vs>
constexpr void reverseAll(Vs& vs)
{
std::reverse(std::begin(vs), std::end(vs));
}
template<typename Vs>
constexpr Vs reversed(const Vs& vs)
{
auto rvs = vs;
reverseAll(rvs);
return rvs;
}
template<typename V, typename Vs>
constexpr V sumAll(const Vs& vs)
{
if constexpr (std::is_convertible<Vs, V>::value) {
return static_cast<V>(vs);
} else {
V ans = 0;
for (const auto& v : vs) { ans += sumAll<V>(v); }
return ans;
}
}
template<typename Vs>
constexpr int minInd(const Vs& vs)
{
return std::min_element(std::begin(vs), std::end(vs)) - std::begin(vs);
}
template<typename Vs>
constexpr int maxInd(const Vs& vs)
{
return std::max_element(std::begin(vs), std::end(vs)) - std::begin(vs);
}
template<typename Vs, typename V>
constexpr int lbInd(const Vs& vs, const V& v)
{
return std::lower_bound(std::begin(vs), std::end(vs), v) - std::begin(vs);
}
template<typename Vs, typename V>
constexpr int ubInd(const Vs& vs, const V& v)
{
return std::upper_bound(std::begin(vs), std::end(vs), v) - std::begin(vs);
}
template<typename Vs, typename V>
constexpr void plusAll(Vs& vs, const V& v)
{
for (auto& v_ : vs) { v_ += v; }
}
template<typename Vs>
constexpr void concat(Vs& vs1, const Vs& vs2)
{
std::copy(std::begin(vs2), std::end(vs2), std::back_inserter(vs1));
}
template<typename Vs>
constexpr void concatted(const Vs& vs1, const Vs& vs2)
{
auto vs = vs1;
concat(vs, vs2);
return vs;
}
template<typename T, typename F>
constexpr Vec<T> genVec(int n, F gen)
{
Vec<T> ans;
std::generate_n(std::back_inserter(ans), n, gen);
return ans;
}
template<typename T = int>
constexpr Vec<T> iotaVec(int n, T offset = 0)
{
Vec<T> ans(n);
std::iota(std::begin(ans), std::end(ans), offset);
return ans;
}
template<typename Vs>
constexpr void rearrange(Vs& vs, const Vec<int>& is)
{
auto vs_ = vs;
for (int i = 0; i < (int)is.size(); i++) { vs[i] = vs_[is[i]]; }
}
inline Vec<int> reversePerm(const Vec<int>& is)
{
auto ris = is;
for (int i = 0; i < (int)is.size(); i++) { ris[is[i]] = i; }
return ris;
}
inline Ostream& operator<<(Ostream& os, i128 v)
{
bool minus = false;
if (v < 0) { minus = true, v = -v; }
Str ans;
if (v == 0) { ans = "0"; }
while (v) { ans.push_back('0' + v % 10), v /= 10; }
std::reverse(ans.begin(), ans.end());
return os << (minus ? "-" : "") << ans;
}
inline Ostream& operator<<(Ostream& os, u128 v)
{
Str ans;
if (v == 0) { ans = "0"; }
while (v) { ans.push_back('0' + v % 10), v /= 10; }
std::reverse(ans.begin(), ans.end());
return os << ans;
}
constexpr int popCount(u64 v) { return v ? __builtin_popcountll(v) : 0; }
constexpr int topBit(u64 v) { return v == 0 ? -1 : 63 - __builtin_clzll(v); }
constexpr int lowBit(u64 v) { return v == 0 ? 64 : __builtin_ctzll(v); }
constexpr int bitWidth(u64 v) { return topBit(v) + 1; }
constexpr u64 bitCeil(u64 v) { return v ? (1_u64 << bitWidth(v - 1)) : 1_u64; }
constexpr u64 bitFloor(u64 v) { return v ? (1_u64 << topBit(v)) : 0_u64; }
constexpr bool hasSingleBit(u64 v) { return (v > 0) and ((v & (v - 1)) == 0); }
constexpr bool isBitOn(u64 mask, int ind) { return (mask >> ind) & 1_u64; }
constexpr bool isBitOff(u64 mask, int ind) { return not isBitOn(mask, ind); }
constexpr u64 bitMask(int bitWidth) { return (bitWidth == 64 ? ~0_u64 : (1_u64 << bitWidth) - 1); }
constexpr u64 bitMask(int start, int end) { return bitMask(end - start) << start; }
template<typename F>
struct Fix : F
{
constexpr Fix(F&& f) : F{std::forward<F>(f)} {}
template<typename... Args>
constexpr auto operator()(Args&&... args) const
{
return F::operator()(*this, std::forward<Args>(args)...);
}
};
class irange
{
private:
struct itr
{
constexpr itr(i64 start = 0, i64 step = 1) : m_cnt{start}, m_step{step} {}
constexpr bool operator!=(const itr& it) const { return m_cnt != it.m_cnt; }
constexpr i64 operator*() { return m_cnt; }
constexpr itr& operator++() { return m_cnt += m_step, *this; }
i64 m_cnt, m_step;
};
i64 m_start, m_end, m_step;
public:
static constexpr i64 cnt(i64 start, i64 end, i64 step)
{
if (step == 0) { return -1; }
const i64 d = (step > 0 ? step : -step);
const i64 l = (step > 0 ? start : end);
const i64 r = (step > 0 ? end : start);
i64 n = (r - l) / d + ((r - l) % d ? 1 : 0);
if (l >= r) { n = 0; }
return n;
}
constexpr irange(i64 start, i64 end, i64 step = 1)
: m_start{start}, m_end{m_start + step * cnt(start, end, step)}, m_step{step}
{
assert(step != 0);
}
constexpr itr begin() const { return itr{m_start, m_step}; }
constexpr itr end() const { return itr{m_end, m_step}; }
};
constexpr irange rep(i64 end) { return irange(0, end, 1); }
constexpr irange per(i64 rend) { return irange(rend - 1, -1, -1); }
class Scanner
{
public:
Scanner(Istream& is = std::cin) : m_is{is} { m_is.tie(nullptr)->sync_with_stdio(false); }
template<typename T>
T val()
{
T v;
return m_is >> v, v;
}
template<typename T>
T val(T offset)
{
return val<T>() - offset;
}
template<typename T>
Vec<T> vec(int n)
{
return genVec<T>(n, [&]() { return val<T>(); });
}
template<typename T>
Vec<T> vec(int n, T offset)
{
return genVec<T>(n, [&]() { return val<T>(offset); });
}
template<typename T>
Vec<Vec<T>> vvec(int n, int m)
{
return genVec<Vec<T>>(n, [&]() { return vec<T>(m); });
}
template<typename T>
Vec<Vec<T>> vvec(int n, int m, const T offset)
{
return genVec<Vec<T>>(n, [&]() { return vec<T>(m, offset); });
}
template<typename... Args>
auto tup()
{
return Tup<Args...>{val<Args>()...};
}
template<typename... Args>
auto tup(const Args&... offsets)
{
return Tup<Args...>{val<Args>(offsets)...};
}
private:
Istream& m_is;
};
inline Scanner in;
class Printer
{
public:
Printer(Ostream& os = std::cout) : m_os{os} { m_os << std::fixed << std::setprecision(15); }
template<typename... Args>
int operator()(const Args&... args)
{
return dump(args...), 0;
}
template<typename... Args>
int ln(const Args&... args)
{
return dump(args...), m_os << '\n', 0;
}
template<typename... Args>
int el(const Args&... args)
{
return dump(args...), m_os << std::endl, 0;
}
int YES(bool b = true) { return ln(b ? "YES" : "NO"); }
int NO(bool b = true) { return YES(not b); }
int Yes(bool b = true) { return ln(b ? "Yes" : "No"); }
int No(bool b = true) { return Yes(not b); }
private:
template<typename T>
void dump(const T& v)
{
m_os << v;
}
template<typename T>
void dump(const Vec<T>& vs)
{
for (int i : rep(vs.size())) { m_os << (i ? " " : ""), dump(vs[i]); }
}
template<typename T>
void dump(const Vec<Vec<T>>& vss)
{
for (int i : rep(vss.size())) { m_os << (i ? "\n" : ""), dump(vss[i]); }
}
template<typename T, typename... Ts>
int dump(const T& v, const Ts&... args)
{
return dump(v), m_os << ' ', dump(args...), 0;
}
Ostream& m_os;
};
inline Printer out;
template<typename T, int n, int i = 0>
auto ndVec(int const (&szs)[n], const T x = T{})
{
if constexpr (i == n) {
return x;
} else {
return std::vector(szs[i], ndVec<T, n, i + 1>(szs, x));
}
}
template<typename T, typename F>
inline T binSearch(T ng, T ok, F check)
{
while (std::abs(ok - ng) > 1) {
const T mid = (ok + ng) / 2;
(check(mid) ? ok : ng) = mid;
}
return ok;
}
template<typename T>
constexpr Pair<T, T> extgcd(const T a, const T b) // [x,y] -> ax+by=gcd(a,b)
{
static_assert(std::is_signed_v<T>, "Signed integer is allowed.");
assert(a != 0 or b != 0);
if (a >= 0 and b >= 0) {
if (a < b) {
const auto [y, x] = extgcd(b, a);
return {x, y};
}
if (b == 0) { return {1, 0}; }
const auto [x, y] = extgcd(b, a % b);
return {y, x - (a / b) * y};
} else {
auto [x, y] = extgcd(std::abs(a), std::abs(b));
if (a < 0) { x = -x; }
if (b < 0) { y = -y; }
return {x, y};
}
}
template<typename T>
constexpr T inverse(const T a, const T mod) // ax=gcd(a,M) (mod M)
{
assert(a > 0 and mod > 0);
auto [x, y] = extgcd(a, mod);
if (x <= 0) { x += mod; }
return x;
}
template<u32 mod_, u32 root_, u32 max2p_>
class modint
{
template<typename U = u32&>
static U modRef()
{
static u32 s_mod = 0;
return s_mod;
}
template<typename U = u32&>
static U rootRef()
{
static u32 s_root = 0;
return s_root;
}
template<typename U = u32&>
static U max2pRef()
{
static u32 s_max2p = 0;
return s_max2p;
}
public:
static_assert(mod_ <= LIMMAX<i32>, "mod(signed int size) only supported!");
static constexpr bool isDynamic() { return (mod_ == 0); }
template<typename U = const u32>
static constexpr std::enable_if_t<mod_ != 0, U> mod()
{
return mod_;
}
template<typename U = const u32>
static std::enable_if_t<mod_ == 0, U> mod()
{
return modRef();
}
template<typename U = const u32>
static constexpr std::enable_if_t<mod_ != 0, U> root()
{
return root_;
}
template<typename U = const u32>
static std::enable_if_t<mod_ == 0, U> root()
{
return rootRef();
}
template<typename U = const u32>
static constexpr std::enable_if_t<mod_ != 0, U> max2p()
{
return max2p_;
}
template<typename U = const u32>
static std::enable_if_t<mod_ == 0, U> max2p()
{
return max2pRef();
}
template<typename U = u32>
static void setMod(std::enable_if_t<mod_ == 0, U> m)
{
assert(1 <= m and m <= LIMMAX<i32>);
modRef() = m;
sinvRef() = {1, 1};
factRef() = {1, 1};
ifactRef() = {1, 1};
}
template<typename U = u32>
static void setRoot(std::enable_if_t<mod_ == 0, U> r)
{
rootRef() = r;
}
template<typename U = u32>
static void setMax2p(std::enable_if_t<mod_ == 0, U> m)
{
max2pRef() = m;
}
constexpr modint() : m_val{0} {}
constexpr modint(i64 v) : m_val{normll(v)} {}
constexpr void setRaw(u32 v) { m_val = v; }
constexpr modint operator-() const { return modint{0} - (*this); }
constexpr modint& operator+=(const modint& m)
{
m_val = norm(m_val + m.val());
return *this;
}
constexpr modint& operator-=(const modint& m)
{
m_val = norm(m_val + mod() - m.val());
return *this;
}
constexpr modint& operator*=(const modint& m)
{
m_val = normll((i64)m_val * (i64)m.val() % (i64)mod());
return *this;
}
constexpr modint& operator/=(const modint& m) { return *this *= m.inv(); }
constexpr modint operator+(const modint& m) const
{
auto v = *this;
return v += m;
}
constexpr modint operator-(const modint& m) const
{
auto v = *this;
return v -= m;
}
constexpr modint operator*(const modint& m) const
{
auto v = *this;
return v *= m;
}
constexpr modint operator/(const modint& m) const
{
auto v = *this;
return v /= m;
}
constexpr bool operator==(const modint& m) const { return m_val == m.val(); }
constexpr bool operator!=(const modint& m) const { return not(*this == m); }
friend Istream& operator>>(Istream& is, modint& m)
{
i64 v;
return is >> v, m = v, is;
}
friend Ostream& operator<<(Ostream& os, const modint& m) { return os << m.val(); }
constexpr u32 val() const { return m_val; }
template<typename I>
constexpr modint pow(I n) const
{
return powerInt(*this, n);
}
constexpr modint inv() const { return inverse<i32>(m_val, mod()); }
static modint sinv(u32 n)
{
auto& is = sinvRef();
for (u32 i = (u32)is.size(); i <= n; i++) { is.push_back(-is[mod() % i] * (mod() / i)); }
return is[n];
}
static modint fact(u32 n)
{
auto& fs = factRef();
for (u32 i = (u32)fs.size(); i <= n; i++) { fs.push_back(fs.back() * i); }
return fs[n];
}
static modint ifact(u32 n)
{
auto& ifs = ifactRef();
for (u32 i = (u32)ifs.size(); i <= n; i++) { ifs.push_back(ifs.back() * sinv(i)); }
return ifs[n];
}
static modint perm(int n, int k) { return k > n or k < 0 ? modint{0} : fact(n) * ifact(n - k); }
static modint comb(int n, int k)
{
return k > n or k < 0 ? modint{0} : fact(n) * ifact(n - k) * ifact(k);
}
private:
static Vec<modint>& sinvRef()
{
static Vec<modint> is{1, 1};
return is;
}
static Vec<modint>& factRef()
{
static Vec<modint> fs{1, 1};
return fs;
}
static Vec<modint>& ifactRef()
{
static Vec<modint> ifs{1, 1};
return ifs;
}
static constexpr u32 norm(u32 x) { return x < mod() ? x : x - mod(); }
static constexpr u32 normll(i64 x) { return norm(u32(x % (i64)mod() + (i64)mod())); }
u32 m_val;
};
using modint_1000000007 = modint<1000000007, 5, 1>;
using modint_998244353 = modint<998244353, 3, 23>;
template<int id>
using modint_dynamic = modint<0, 0, id>;
template<typename T = int>
class Graph
{
struct Edge
{
Edge() = default;
Edge(int i, int t, T c) : id{i}, to{t}, cost{c} {}
int id;
int to;
T cost;
operator int() const { return to; }
};
public:
Graph(int n) : m_v{n}, m_edges(n) {}
void addEdge(int u, int v, bool bi = false)
{
assert(0 <= u and u < m_v);
assert(0 <= v and v < m_v);
m_edges[u].emplace_back(m_e, v, 1);
if (bi) { m_edges[v].emplace_back(m_e, u, 1); }
m_e++;
}
void addEdge(int u, int v, const T& c, bool bi = false)
{
assert(0 <= u and u < m_v);
assert(0 <= v and v < m_v);
m_edges[u].emplace_back(m_e, v, c);
if (bi) { m_edges[v].emplace_back(m_e, u, c); }
m_e++;
}
const Vec<Edge>& operator[](const int u) const
{
assert(0 <= u and u < m_v);
return m_edges[u];
}
Vec<Edge>& operator[](const int u)
{
assert(0 <= u and u < m_v);
return m_edges[u];
}
int v() const { return m_v; }
int e() const { return m_e; }
friend Ostream& operator<<(Ostream& os, const Graph& g)
{
for (int u : rep(g.v())) {
for (const auto& [id, v, c] : g[u]) {
os << "[" << id << "]: ";
os << u << "->" << v << "(" << c << ")\n";
}
}
return os;
}
Vec<T> sizes(int root = 0) const
{
const int N = v();
assert(0 <= root and root < N);
Vec<T> ss(N, 1);
Fix([&](auto dfs, int u, int p) -> void {
for ([[maybe_unused]] const auto& [_temp_name_0, v, c] : m_edges[u]) {
if (v == p) { continue; }
dfs(v, u);
ss[u] += ss[v];
}
})(root, -1);
return ss;
}
Vec<T> depths(int root = 0) const
{
const int N = v();
assert(0 <= root and root < N);
Vec<T> ds(N, 0);
Fix([&](auto dfs, int u, int p) -> void {
for ([[maybe_unused]] const auto& [_temp_name_1, v, c] : m_edges[u]) {
if (v == p) { continue; }
ds[v] = ds[u] + c;
dfs(v, u);
}
})(root, -1);
return ds;
}
Vec<int> parents(int root = 0) const
{
const int N = v();
assert(0 <= root and root < N);
Vec<int> ps(N, -1);
Fix([&](auto dfs, int u, int p) -> void {
for ([[maybe_unused]] const auto& [_temp_name_2, v, c] : m_edges[u]) {
if (v == p) { continue; }
ps[v] = u;
dfs(v, u);
}
})(root, -1);
return ps;
}
private:
int m_v;
int m_e = 0;
Vec<Vec<Edge>> m_edges;
};
template<typename mint>
class NumberTheoriticTransform
{
// DynamicModint 非対応
static_assert(not mint::isDynamic(), "class NTT: Not support dynamic modint.");
private:
static constexpr u32 MOD = mint::mod();
static constexpr u32 ROOT = mint::root();
static constexpr u32 L_MAX = mint::max2p();
static constexpr int N_MAX = (1 << L_MAX);
public:
static Vec<mint> convolute(Vec<mint> as, Vec<mint> bs)
{
const int AN = as.size();
const int BN = bs.size();
const int CN = AN + BN - 1;
const int N = bitCeil(CN);
as.resize(N, 0), bs.resize(N, 0);
transform(as, false), transform(bs, false);
for (int i : rep(N)) { as[i] *= bs[i]; }
transform(as, true);
as.resize(CN);
return as;
}
static void transform(Vec<mint>& as, bool rev)
{
const int N = as.size();
assert(hasSingleBit(N));
if (N == 1) { return; }
const int L = topBit(N);
const auto l_range = (rev ? irange(1, L + 1, 1) : irange(L, 0, -1));
for (int l : l_range) {
const int H = 1 << l;
const int B = N / H;
for (int b : rep(B)) {
const mint W = zeta(l, rev);
mint W_h = 1;
for (int h : rep(H / 2)) {
const int y1 = H * b + h;
const int y2 = y1 + H / 2;
const mint a1 = as[y1];
const mint a2 = as[y2];
const mint na1 = (rev ? a1 + a2 * W_h : a1 + a2);
const mint na2 = (rev ? a1 - a2 * W_h : (a1 - a2) * W_h);
as[y1] = na1;
as[y2] = na2;
W_h *= W;
}
}
}
if (rev) {
const mint iN = mint::sinv(N);
for (auto& a : as) { a *= iN; }
}
}
private:
static mint zeta(int i, bool rev)
{
static Vec<mint> zs; // zs[i] = 1の2^i乗根
static Vec<mint> izs; // izs[i] = zs[i]の逆元
if (zs.empty()) {
zs.resize(L_MAX + 1, 1);
izs.resize(L_MAX + 1, 1);
zs[L_MAX] = mint(ROOT).pow((MOD - 1) / (1 << L_MAX));
izs[L_MAX] = zs[L_MAX].inv();
for (int l : per(L_MAX)) {
zs[l] = zs[l + 1] * zs[l + 1];
izs[l] = izs[l + 1] * izs[l + 1];
}
}
return (rev ? izs[i] : zs[i]);
}
};
class Garner
{
public:
template<typename mint, typename mint1, typename mint2>
static mint restore_mod(const mint1& x1, const mint2& x2)
{
constexpr auto m1 = mint1::mod();
const auto [y0, y1] = coeff(x1, x2);
return mint(y0.val()) + mint(y1.val()) * m1;
}
template<typename mint, typename mint1, typename mint2, typename mint3>
static mint restore_mod(const mint1& x1, const mint2& x2, const mint3& x3)
{
constexpr auto m1 = mint1::mod();
constexpr auto m2 = mint2::mod();
const auto [y0, y1, y2] = coeff(x1, x2, x3);
return mint(y0.val()) + mint(y1.val()) * m1 + mint(y2.val()) * m1 * m2;
}
template<typename mint1, typename mint2>
static i64 restore_i64(const mint1& x1, const mint2& x2)
{
constexpr u32 m1 = mint1::mod();
constexpr u32 m2 = mint2::mod();
const auto [y0, y1] = coeff(x1, x2);
constexpr u64 MAX = 1_u64 << 63;
const i128 M = (i128)m1 * m2;
i128 S = i128(y0.val()) + i128(y1.val()) * m1;
if (S >= MAX) { S -= M; }
return (i64)S;
}
template<typename mint1, typename mint2, typename mint3>
static i64 restore_i64(const mint1& x1, const mint2& x2, const mint3& x3)
{
constexpr u32 m1 = mint1::mod();
constexpr u32 m2 = mint2::mod();
constexpr u32 m3 = mint3::mod();
const auto [y0, y1, y2] = coeff(x1, x2, x3);
constexpr u64 MAX = 1_u64 << 63;
const i128 M = (i128)m1 * m2 * m3;
i128 S = i128(y0.val()) + i128(y1.val()) * m1 + i128(y2.val()) * m1 * m2;
if (S >= MAX) { S -= M; }
return (i64)S;
}
private:
template<typename mint1, typename mint2>
static Pair<mint1, mint2> coeff(const mint1& x1, const mint2& x2)
{
constexpr auto m1 = mint1::mod();
constexpr mint2 m1_inv = mint2(m1).inv();
const mint1 y0 = x1;
const mint2 y1 = (x2 - mint2(y0.val())) * m1_inv;
return {y0, y1};
}
template<typename mint1, typename mint2, typename mint3>
static Tup<mint1, mint2, mint3> coeff(const mint1& x1, const mint2& x2, const mint3& x3)
{
constexpr auto m1 = mint1::mod();
constexpr auto m2 = mint2::mod();
constexpr mint2 m1_inv = mint2(m1).inv();
constexpr mint3 m1m2_inv = (mint3(m1) * mint3(m2)).inv();
const mint1 y0 = x1;
const mint2 y1 = (x2 - mint2(y0.val())) * m1_inv;
const mint3 y2 = (x3 - mint3(y0.val()) - mint3(y1.val()) * m1) * m1m2_inv;
return {y0, y1, y2};
}
};
template<typename mint>
Vec<mint> convolute_mod(const Vec<mint>& as, const Vec<mint>& bs)
{
constexpr u32 L_MAX = mint::max2p();
constexpr int N_MAX = (1 << L_MAX);
const int AN = as.size();
const int BN = bs.size();
if (AN == 0 or BN == 0) { return {}; }
if (AN > BN) { return convolute_mod(bs, as); }
const int N = AN + BN - 1;
if (AN * 2 <= BN) {
Vec<mint> cs(N, 0);
for (int sj : irange(0, BN, AN)) {
const int tj = std::min(BN, sj + AN);
const auto bbs = Vec<mint>(std::begin(bs) + sj, std::begin(bs) + tj);
const auto bcs = convolute_mod(as, bbs);
for (int dj : rep(bcs.size())) { cs[sj + dj] += bcs[dj]; }
}
return cs;
}
if (N <= N_MAX) {
// mintはNTT Friendlyなのでそのまま畳み込み
return NumberTheoriticTransform<mint>::convolute(as, bs);
} else {
assert(N <= (1 << 24));
using submint1 = modint<469762049, 3, 26>;
using submint2 = modint<167772161, 3, 25>;
using submint3 = modint<754974721, 11, 24>;
// mod 3つでGarner復元
Vec<submint1> as1(AN), bs1(BN);
Vec<submint2> as2(AN), bs2(BN);
Vec<submint3> as3(AN), bs3(BN);
for (int i : rep(AN)) { as1[i] = as[i].val(), as2[i] = as[i].val(), as3[i] = as[i].val(); }
for (int i : rep(BN)) { bs1[i] = bs[i].val(), bs2[i] = bs[i].val(), bs3[i] = bs[i].val(); }
const auto cs1 = NumberTheoriticTransform<submint1>::convolute(as1, bs1);
const auto cs2 = NumberTheoriticTransform<submint2>::convolute(as2, bs2);
const auto cs3 = NumberTheoriticTransform<submint3>::convolute(as3, bs3);
Vec<mint> cs(N);
for (int i : rep(N)) { cs[i] = Garner::restore_mod<mint>(cs1[i], cs2[i], cs3[i]); }
return cs;
}
}
template<typename I>
Vec<i64> convolute_i64(const Vec<I>& as, const Vec<I>& bs)
{
const int AN = as.size();
const int BN = bs.size();
if (AN == 0 or BN == 0) { return {}; }
if (AN > BN) { return convolute_i64<I>(bs, as); }
const int N = AN + BN - 1;
assert(N <= (1 << 24));
if (AN * 2 <= BN) {
Vec<i64> cs(N, 0);
for (int sj : irange(0, BN, AN)) {
const int tj = std::min(BN, sj + AN);
const auto bbs = Vec<I>(std::begin(bs) + sj, std::begin(bs) + tj);
const auto bcs = convolute_i64<I>(as, bbs);
for (int dj : rep(bcs.size())) { cs[sj + dj] += bcs[dj]; }
}
return cs;
}
using submint1 = modint<469762049, 3, 26>;
using submint2 = modint<167772161, 3, 25>;
using submint3 = modint<754974721, 11, 24>;
// mod 3つでGarner復元
Vec<submint1> as1(AN), bs1(BN);
Vec<submint2> as2(AN), bs2(BN);
Vec<submint3> as3(AN), bs3(BN);
for (int i : rep(AN)) { as1[i] = as[i], as2[i] = as[i], as3[i] = as[i]; }
for (int i : rep(BN)) { bs1[i] = bs[i], bs2[i] = bs[i], bs3[i] = bs[i]; }
const auto cs1 = NumberTheoriticTransform<submint1>::convolute(as1, bs1);
const auto cs2 = NumberTheoriticTransform<submint2>::convolute(as2, bs2);
const auto cs3 = NumberTheoriticTransform<submint3>::convolute(as3, bs3);
Vec<i64> cs(N);
for (int i : rep(N)) { cs[i] = Garner::restore_i64(cs1[i], cs2[i], cs3[i]); }
return cs;
}
int main()
{
using mint = modint_998244353;
const auto [M, N] = in.tup<int, int>();
const auto As = in.vec<int>(N, 1);
Vec<int> ns(M, 0);
for (int A : As) {
ns[A]++;
}
Map<int, int> Ns;
for (int i : rep(M)) {
Ns[ns[i]]++;
}
const int K = ns.size();
Vec<mint> f(N + 1);
for (int i : rep(N + 1)) {
f[i] = mint::ifact(i) * (i % 2 == 0 ? 1 : -1);
}
Vec<mint> g(N + 1, 1);
for (int i : rep(N + 1)) {
g[i] *= mint::fact(i).pow(K - 1);
for (const auto& [n, cnt] : Ns) {
if (i < n) {
g[i] *= 0;
} else {
g[i] *= mint::ifact(i - n).pow(cnt);
}
}
}
auto h = convolute_mod(f, g);
for (int i : rep(h.size())) {
h[i] *= mint::fact(i);
}
mint ans = 0;
for (int i : rep(N + 1)) {
ans += h[i];
}
out.ln(ans);
return 0;
}