結果
| 問題 | No.2243 Coaching Schedule |
| ユーザー |
 satashun
|
| 提出日時 | 2023-05-16 09:37:40 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 1,809 ms / 4,000 ms |
| コード長 | 22,371 bytes |
| コンパイル時間 | 4,339 ms |
| コンパイル使用メモリ | 232,900 KB |
| 実行使用メモリ | 131,852 KB |
| 最終ジャッジ日時 | 2023-08-21 03:16:05 |
| 合計ジャッジ時間 | 47,973 ms |
|
ジャッジサーバーID （参考情報） |
judge11 / judge14 |
（要ログイン）
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 | 100 ms
112,748 KB |
| testcase_01 | AC | 104 ms
112,508 KB |
| testcase_02 | AC | 101 ms
112,596 KB |
| testcase_03 | AC | 105 ms
112,652 KB |
| testcase_04 | AC | 103 ms
112,972 KB |
| testcase_05 | AC | 1,794 ms
131,728 KB |
| testcase_06 | AC | 1,806 ms
131,556 KB |
| testcase_07 | AC | 1,800 ms
131,564 KB |
| testcase_08 | AC | 1,803 ms
131,500 KB |
| testcase_09 | AC | 1,797 ms
131,692 KB |
| testcase_10 | AC | 1,803 ms
131,608 KB |
| testcase_11 | AC | 1,806 ms
131,644 KB |
| testcase_12 | AC | 1,809 ms
131,352 KB |
| testcase_13 | AC | 1,799 ms
131,656 KB |
| testcase_14 | AC | 1,795 ms
131,344 KB |
| testcase_15 | AC | 1,794 ms
131,428 KB |
| testcase_16 | AC | 1,133 ms
131,852 KB |
| testcase_17 | AC | 447 ms
118,356 KB |
| testcase_18 | AC | 1,520 ms
128,928 KB |
| testcase_19 | AC | 1,702 ms
130,900 KB |
| testcase_20 | AC | 876 ms
124,008 KB |
| testcase_21 | AC | 830 ms
121,860 KB |
| testcase_22 | AC | 769 ms
120,724 KB |
| testcase_23 | AC | 166 ms
114,112 KB |
| testcase_24 | AC | 862 ms
123,604 KB |
| testcase_25 | AC | 226 ms
114,636 KB |
| testcase_26 | AC | 440 ms
117,372 KB |
| testcase_27 | AC | 884 ms
124,352 KB |
| testcase_28 | AC | 247 ms
114,992 KB |
| testcase_29 | AC | 1,528 ms
128,516 KB |
| testcase_30 | AC | 1,652 ms
130,476 KB |
| testcase_31 | AC | 1,717 ms
131,356 KB |
| testcase_32 | AC | 732 ms
120,640 KB |
| testcase_33 | AC | 428 ms
118,044 KB |
| testcase_34 | AC | 1,499 ms
128,292 KB |
| testcase_35 | AC | 1,616 ms
129,696 KB |
| testcase_36 | AC | 1,641 ms
129,668 KB |
ソースコード
#pragma region satashun
// #pragma GCC optimize("Ofast")
// #pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
using pii = pair<int, int>;
template <class T>
using V = vector<T>;
template <class T>
using VV = V<V<T>>;
template <class T>
V<T> make_vec(size_t a) {
return V<T>(a);
}
template <class T, class... Ts>
auto make_vec(size_t a, Ts... ts) {
return V<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...));
}
template <typename T, typename V>
void fill_vec(T& v, const V& val) {
v = val;
}
template <typename T, typename V>
void fill_vec(vector<T>& vec, const V& val) {
for (auto& v : vec) fill_vec(v, val);
}
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define rep(i, n) rep2(i, 0, n)
#define rep2(i, m, n) for (int i = m; i < (n); i++)
#define per(i, b) per2(i, 0, b)
#define per2(i, a, b) for (int i = int(b) - 1; i >= int(a); i--)
#define ALL(c) (c).begin(), (c).end()
#define SZ(x) ((int)(x).size())
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }
template <class T, class U>
void chmin(T& t, const U& u) {
if (t > u) t = u;
}
template <class T, class U>
void chmax(T& t, const U& u) {
if (t < u) t = u;
}
template <typename T>
int arglb(const V<T>& v, const T& x) {
return distance(v.begin(), lower_bound(ALL(v), x));
}
template <typename T>
int argub(const V<T>& v, const T& x) {
return distance(v.begin(), upper_bound(ALL(v), x));
}
template <class T>
void mkuni(vector<T>& v) {
sort(ALL(v));
v.erase(unique(ALL(v)), end(v));
}
template <class T>
vector<int> sort_by(const vector<T>& v, bool increasing = true) {
vector<int> res(v.size());
iota(res.begin(), res.end(), 0);
if (increasing) {
stable_sort(res.begin(), res.end(),
[&](int i, int j) { return v[i] < v[j]; });
} else {
stable_sort(res.begin(), res.end(),
[&](int i, int j) { return v[i] > v[j]; });
}
return res;
}
template <class T, class U>
istream& operator>>(istream& is, pair<T, U>& p) {
is >> p.first >> p.second;
return is;
}
template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
os << "(" << p.first << "," << p.second << ")";
return os;
}
template <class T>
istream& operator>>(istream& is, vector<T>& v) {
for (auto& x : v) {
is >> x;
}
return is;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
os << "{";
rep(i, v.size()) {
if (i) os << ",";
os << v[i];
}
os << "}";
return os;
}
template <class T>
ostream& operator<<(ostream& os, const set<T>& ST) {
os << "{";
for (auto it = ST.begin(); it != ST.end(); ++it) {
if (it != ST.begin()) os << ",";
os << *it;
}
os << "}";
return os;
}
template <class T>
ostream& operator<<(ostream& os, const multiset<T>& ST) {
os << "{";
for (auto it = ST.begin(); it != ST.end(); ++it) {
if (it != ST.begin()) os << ",";
os << *it;
}
os << "}";
return os;
}
template <class T, class U>
ostream& operator<<(ostream& os, const map<T, U>& MP) {
for (auto it = MP.begin(); it != MP.end(); ++it) {
os << "(" << it->first << ": " << it->second << ")";
}
return os;
}
string to_string(__int128_t x) {
if (x == 0) return "0";
string result;
if (x < 0) {
result += "-";
x *= -1;
}
string t;
while (x) {
t.push_back('0' + x % 10);
x /= 10;
}
reverse(t.begin(), t.end());
return result + t;
}
ostream& operator<<(ostream& o, __int128_t x) { return o << to_string(x); }
#ifdef LOCAL
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
cerr << " " << H;
debug_out(T...);
}
#define debug(...) \
cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif
template <class T>
V<T>& operator+=(V<T>& vec, const T& v) {
for (auto& x : vec) x += v;
return vec;
}
template <class T>
V<T>& operator-=(V<T>& vec, const T& v) {
for (auto& x : vec) x -= v;
return vec;
}
// suc : 1 = newline, 2 = space
template <class T>
void print(T x, int suc = 1) {
cout << x;
if (suc == 1)
cout << "\n";
else if (suc == 2)
cout << " ";
}
template <class T>
void print(const vector<T>& v, int suc = 1) {
for (int i = 0; i < v.size(); ++i)
print(v[i], i == int(v.size()) - 1 ? suc : 2);
}
template <class T>
void show(T x) {
print(x, 1);
}
template <typename Head, typename... Tail>
void show(Head H, Tail... T) {
print(H, 2);
show(T...);
}
int topbit(int t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int botbit(int a) { return a == 0 ? 32 : __builtin_ctz(a); }
int botbit(ll a) { return a == 0 ? 64 : __builtin_ctzll(a); }
int popcount(int t) { return __builtin_popcount(t); }
int popcount(ll t) { return __builtin_popcountll(t); }
int bit_parity(int t) { return __builtin_parity(t); }
int bit_parity(ll t) { return __builtin_parityll(t); }
struct prepare_io {
prepare_io() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(10);
}
} prep_io;
#pragma endregion satashun
template <unsigned int MOD>
struct ModInt {
using uint = unsigned int;
using ull = unsigned long long;
using M = ModInt;
uint v;
ModInt(ll _v = 0) { set_norm(_v % MOD + MOD); }
M& set_norm(uint _v) { //[0, MOD * 2)->[0, MOD)
v = (_v < MOD) ? _v : _v - MOD;
return *this;
}
explicit operator bool() const { return v != 0; }
explicit operator int() const { return v; }
M operator+(const M& a) const { return M().set_norm(v + a.v); }
M operator-(const M& a) const { return M().set_norm(v + MOD - a.v); }
M operator*(const M& a) const { return M().set_norm(ull(v) * a.v % MOD); }
M operator/(const M& a) const { return *this * a.inv(); }
M& operator+=(const M& a) { return *this = *this + a; }
M& operator-=(const M& a) { return *this = *this - a; }
M& operator*=(const M& a) { return *this = *this * a; }
M& operator/=(const M& a) { return *this = *this / a; }
M operator-() const { return M() - *this; }
M& operator++(int) { return *this = *this + 1; }
M& operator--(int) { return *this = *this - 1; }
M pow(ll n) const {
if (n < 0) return inv().pow(-n);
M x = *this, res = 1;
while (n) {
if (n & 1) res *= x;
x *= x;
n >>= 1;
}
return res;
}
M inv() const {
ll a = v, b = MOD, p = 1, q = 0, t;
while (b != 0) {
t = a / b;
swap(a -= t * b, b);
swap(p -= t * q, q);
}
return M(p);
}
friend ostream& operator<<(ostream& os, const M& a) { return os << a.v; }
friend istream& operator>>(istream& in, M& x) {
ll v_;
in >> v_;
x = M(v_);
return in;
}
bool operator<(const M& r) const { return v < r.v; }
bool operator>(const M& r) const { return v < *this; }
bool operator<=(const M& r) const { return !(r < *this); }
bool operator>=(const M& r) const { return !(*this < r); }
bool operator==(const M& a) const { return v == a.v; }
bool operator!=(const M& a) const { return v != a.v; }
static uint get_mod() { return MOD; }
};
// using Mint = ModInt<1000000007>;
using Mint = ModInt<998244353>;
V<Mint> fact, ifact, inv;
VV<Mint> small_comb;
void mod_init() {
const int maxv = 1000010;
const int maxvv = 5000;
fact.resize(maxv);
ifact.resize(maxv);
inv.resize(maxv);
small_comb = make_vec<Mint>(maxvv, maxvv);
fact[0] = 1;
for (int i = 1; i < maxv; ++i) {
fact[i] = fact[i - 1] * i;
}
ifact[maxv - 1] = fact[maxv - 1].inv();
for (int i = maxv - 2; i >= 0; --i) {
ifact[i] = ifact[i + 1] * (i + 1);
}
for (int i = 1; i < maxv; ++i) {
inv[i] = ifact[i] * fact[i - 1];
}
for (int i = 0; i < maxvv; ++i) {
small_comb[i][0] = small_comb[i][i] = 1;
for (int j = 1; j < i; ++j) {
small_comb[i][j] = small_comb[i - 1][j] + small_comb[i - 1][j - 1];
}
}
}
Mint comb(int n, int r) {
if (n < 0 || r < 0 || r > n) return Mint(0);
if (n < small_comb.size()) return small_comb[n][r];
return fact[n] * ifact[r] * ifact[n - r];
}
Mint inv_comb(int n, int r) {
if (n < 0 || r < 0 || r > n) return Mint(0);
return ifact[n] * fact[r] * fact[n - r];
}
// O(k)
Mint comb_slow(ll n, ll k) {
if (n < 0 || k < 0 || k > n) return Mint(0);
Mint res = ifact[k];
for (int i = 0; i < k; ++i) {
res = res * (n - i);
}
return res;
}
// line up
// a 'o' + b 'x'
Mint comb2(int a, int b) {
if (a < 0 || b < 0) return 0;
return comb(a + b, a);
}
// divide a into b groups
Mint nhr(int a, int b) {
if (b == 0) return Mint(a == 0);
return comb(a + b - 1, a);
}
// O(p + log_p n)
Mint lucas(ll n, ll k, int p) {
if (n < 0 || k < 0 || k > n) return Mint(0);
Mint res = 1;
while (n > 0) {
res *= comb(n % p, k % p);
n /= p;
k /= p;
}
return res;
}
struct ModPrepare {
ModPrepare() { mod_init(); }
} prep_mod;
/**
* @docs docs/ntt.md
*/
template <class D>
struct NumberTheoreticTransform {
D root;
V<D> roots = {0, 1};
V<int> rev = {0, 1};
int base = 1, max_base = -1;
void init() {
int mod = D::get_mod();
int tmp = mod - 1;
max_base = 0;
while (tmp % 2 == 0) {
tmp /= 2;
max_base++;
}
root = 2;
while (true) {
if (root.pow(1 << max_base).v == 1) {
if (root.pow(1 << (max_base - 1)).v != 1) {
break;
}
}
root++;
}
}
void ensure_base(int nbase) {
if (max_base == -1) init();
if (nbase <= base) return;
assert(nbase <= max_base);
rev.resize(1 << nbase);
for (int i = 0; i < (1 << nbase); ++i) {
rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
}
roots.resize(1 << nbase);
while (base < nbase) {
D z = root.pow(1 << (max_base - 1 - base));
for (int i = 1 << (base - 1); i < (1 << base); ++i) {
roots[i << 1] = roots[i];
roots[(i << 1) + 1] = roots[i] * z;
}
++base;
}
}
void ntt(V<D>& a, bool inv = false) {
int n = a.size();
// assert((n & (n - 1)) == 0);
int zeros = __builtin_ctz(n);
ensure_base(zeros);
int shift = base - zeros;
for (int i = 0; i < n; i++) {
if (i < (rev[i] >> shift)) {
swap(a[i], a[rev[i] >> shift]);
}
}
for (int k = 1; k < n; k <<= 1) {
for (int i = 0; i < n; i += 2 * k) {
for (int j = 0; j < k; j++) {
D x = a[i + j];
D y = a[i + j + k] * roots[j + k];
a[i + j] = x + y;
a[i + j + k] = x - y;
}
}
}
int v = D(n).inv().v;
if (inv) {
reverse(a.begin() + 1, a.end());
for (int i = 0; i < n; i++) {
a[i] *= v;
}
}
}
V<D> mul(V<D> a, V<D> b) {
if (a.size() == 0 && b.size() == 0) return {};
int s = a.size() + b.size() - 1;
int nbase = 1;
while ((1 << nbase) < s) nbase++;
int sz = 1 << nbase;
if (sz <= 16) {
V<D> ret(s);
for (int i = 0; i < a.size(); i++) {
for (int j = 0; j < b.size(); j++) ret[i + j] += a[i] * b[j];
}
return ret;
}
a.resize(sz);
b.resize(sz);
ntt(a);
ntt(b);
for (int i = 0; i < sz; i++) {
a[i] *= b[i];
}
ntt(a, true);
a.resize(s);
return a;
}
};
// T : modint
template <class T>
void ntt_2d(VV<T>& a, bool rev) {
if (a.size() == 0 || a[0].size() == 0) return;
int h = a.size(), w = a[0].size();
NumberTheoreticTransform<T> fft;
fft.init();
for (auto& v : a) {
fft.ntt(v, rev);
}
rep(j, w) {
V<T> vh(h);
rep(i, h) { vh[i] = a[i][j]; }
fft.ntt(vh, rev);
rep(i, h) { a[i][j] = vh[i]; }
}
}
// depends on FFT libs
// work only with NTT-friendly mod
NumberTheoreticTransform<Mint> ntt;
struct prepare_FPS {
prepare_FPS() { ntt.init(); }
} prep_FPS;
template <class D>
struct Poly : public V<D> {
template <class... Args>
Poly(Args... args) : V<D>(args...) {}
Poly(initializer_list<D> init) : V<D>(init.begin(), init.end()) {}
int size() const { return V<D>::size(); }
D at(int p) const { return (p < this->size() ? (*this)[p] : D(0)); }
void shrink() {
while (this->size() > 0 && this->back() == D(0)) this->pop_back();
}
// first len terms
Poly pref(int len) const {
return Poly(this->begin(), this->begin() + min(this->size(), len));
}
// for polynomial division
Poly rev() const {
Poly res = *this;
reverse(res.begin(), res.end());
return res;
}
Poly shiftr(int d) const {
int n = max(size() + d, 0);
Poly res(n);
for (int i = 0; i < size(); ++i) {
if (i + d >= 0) {
res[i + d] = at(i);
}
}
return res;
}
Poly operator+(const Poly& r) const {
auto n = max(size(), r.size());
V<D> tmp(n);
for (int i = 0; i < n; ++i) {
tmp[i] = at(i) + r.at(i);
}
return tmp;
}
Poly operator-(const Poly& r) const {
auto n = max(size(), r.size());
V<D> tmp(n);
for (int i = 0; i < n; ++i) {
tmp[i] = at(i) - r.at(i);
}
return tmp;
}
// scalar
Poly operator*(const D& k) const {
int n = size();
V<D> tmp(n);
for (int i = 0; i < n; ++i) {
tmp[i] = at(i) * k;
}
return tmp;
}
Poly operator*(const Poly& r) const {
Poly a = *this;
Poly b = r;
auto v = ntt.mul(a, b);
return v;
}
// scalar
Poly operator/(const D& k) const { return *this * k.inv(); }
Poly operator/(const Poly& r) const {
if (size() < r.size()) {
return {{}};
}
int d = size() - r.size() + 1;
return (rev().pref(d) * r.rev().inv(d)).pref(d).rev();
}
Poly operator%(const Poly& r) const {
auto res = *this - *this / r * r;
res.shrink();
return res;
}
Poly diff() const {
V<D> res(max(0, size() - 1));
for (int i = 1; i < size(); ++i) {
res[i - 1] = at(i) * i;
}
return res;
}
Poly inte() const {
V<D> res(size() + 1);
for (int i = 0; i < size(); ++i) {
res[i + 1] = at(i) / (D)(i + 1);
}
return res;
}
// f * f.inv(m) === 1 mod (x^m)
// f_0 ^ -1 must exist
Poly inv(int m) const {
Poly res = Poly({D(1) / at(0)});
for (int i = 1; i < m; i *= 2) {
res = (res * D(2) - res * res * pref(i * 2)).pref(i * 2);
}
return res.pref(m);
}
// f_0 = 1 must hold
Poly log(int n) const {
auto f = pref(n);
return (f.diff() * f.inv(n - 1)).pref(n - 1).inte();
}
// f_0 = 0 must hold
Poly exp(int n) const {
auto h = diff();
Poly f({1}), g({1});
for (int m = 1; m < n; m *= 2) {
g = (g * D(2) - f * g * g).pref(m);
auto q = h.pref(m - 1);
auto w = (q + g * (f.diff() - f * q)).pref(m * 2 - 1);
f = (f + f * (*this - w.inte()).pref(m * 2)).pref(m * 2);
}
return f.pref(n);
}
// front n elements of f(x)^k
// be careful when k = 0
Poly pow(ll k, int n) const {
int zero = 0;
while (zero < size() && at(zero) == 0) {
zero++;
}
if (zero == size() || zero * k >= n) {
Poly res(n);
if (n > 0 && k == 0) res[0] = 1;
return res;
}
Poly h(this->begin() + zero, this->end());
D a = h[0], ra = D(1) / a;
h *= ra;
h = h.log(n - zero * k) * D(k);
h = h.exp(n - zero * k);
h = h.shiftr(zero * k) * a.pow(k);
return h;
}
// f_0 = 1 must hold (use it with modular sqrt)
// CF250E
Poly sqrt(int n) const {
Poly f = pref(n);
Poly g({1});
for (int i = 1; i < n; i *= 2) {
g = (g + f.pref(i * 2) * g.inv(i * 2)) * D(2).inv();
}
return g.pref(n);
}
D eval(D x) const {
D res = 0, c = 1;
for (auto a : *this) {
res += a * c;
c *= x;
}
return res;
}
Poly powmod(ll k, const Poly& md) {
auto v = *this % md;
Poly res{1};
while (k) {
if (k & 1) {
res = res * v % md;
}
v = v * v % md;
k /= 2;
}
return res;
}
Poly& operator+=(const Poly& r) { return *this = *this + r; }
Poly& operator-=(const Poly& r) { return *this = *this - r; }
Poly& operator*=(const D& r) { return *this = *this * r; }
Poly& operator*=(const Poly& r) { return *this = *this * r; }
Poly& operator/=(const Poly& r) { return *this = *this / r; }
Poly& operator/=(const D& r) { return *this = *this / r; }
Poly& operator%=(const Poly& r) { return *this = *this % r; }
friend ostream& operator<<(ostream& os, const Poly& pl) {
if (pl.size() == 0) return os << "0";
for (int i = 0; i < pl.size(); ++i) {
if (pl[i]) {
os << pl[i] << "x^" << i;
if (i + 1 != pl.size()) os << ",";
}
}
return os;
}
explicit operator bool() const {
bool f = false;
for (int i = 0; i < size(); ++i) {
if (at(i)) {
f = true;
}
}
return f;
}
};
// calculate characteristic polynomial
// c_0 * s_i + c_1 * s_{i+1} + ... + c_k * s_{i+k} = 0
// c_k = -1
template <class T>
Poly<T> berlekamp_massey(const V<T>& s) {
int n = int(s.size());
V<T> b = {T(-1)}, c = {T(-1)};
T y = Mint(1);
for (int ed = 1; ed <= n; ed++) {
int l = int(c.size()), m = int(b.size());
T x = 0;
for (int i = 0; i < l; i++) {
x += c[i] * s[ed - l + i];
}
b.push_back(0);
m++;
if (!x) {
continue;
}
T freq = x / y;
if (l < m) {
auto tmp = c;
c.insert(begin(c), m - l, Mint(0));
for (int i = 0; i < m; i++) {
c[m - 1 - i] -= freq * b[m - 1 - i];
}
b = tmp;
y = x;
} else {
for (int i = 0; i < m; i++) {
c[l - 1 - i] -= freq * b[m - 1 - i];
}
}
}
return c;
}
// HUPC 2020 day3 K, ABC225H
// calculate vec[0] * vec[1] * ...
// deg(result) must be bounded
template <class T>
Poly<T> prod(const V<Poly<T>>& vec) {
auto comp = [](const auto& a, const auto& b) -> bool {
return a.size() > b.size();
};
priority_queue<Poly<T>, V<Poly<T>>, decltype(comp)> que(comp);
que.push(Poly<T>{1});
for (auto& pl : vec) que.push(pl);
while (que.size() > 1) {
auto va = que.top();
que.pop();
auto vb = que.top();
que.pop();
que.push(va * vb);
}
return que.top();
}
// ABC215 G
// expand f(x + c)
// require factorial
template <class T>
Poly<T> taylor_shift(const Poly<T>& f, ll c) {
using P = Poly<T>;
int n = f.size();
T powc = 1;
P p(n), q(n);
rep(i, n) {
p[i] = f[i] * fact[i];
q[n - 1 - i] = powc * ifact[i];
powc *= c;
}
p = p * q;
rep(i, n) q[i] = p[n - 1 + i] * ifact[i];
return q;
}
template <class D>
struct MultiEval {
using P = MultiEval*;
P lc, rc;
V<D> xs;
int sz;
Poly<D> dpol;
const int B = 100;
MultiEval(const V<D>& _xs, int l, int r) : sz(r - l) {
if (r - l <= B) {
xs = {_xs.begin() + l, _xs.begin() + r};
dpol = {{1}};
for (auto x : xs) {
dpol *= {-x, 1};
}
return;
}
lc = new MultiEval(_xs, l, (l + r) / 2);
rc = new MultiEval(_xs, (l + r) / 2, r);
dpol = lc->dpol * rc->dpol;
}
MultiEval(const V<D>& xs) : MultiEval(xs, 0, xs.size()) {}
void eval(const Poly<D>& poly, V<D>& res) {
auto p = poly % dpol;
if (sz <= B) {
for (auto x : xs) {
res.pb(p.eval(x));
}
return;
}
lc->eval(p, res);
rc->eval(p, res);
}
V<D> eval(const Poly<D>& poly) {
V<D> res;
eval(poly, res);
return res;
}
};
void slv() {
int M, N;
cin >> M >> N;
V<int> A(N);
cin >> A;
A -= 1;
V<int> C(M);
for (int x : A) C[x]++;
using P = Poly<Mint>;
V<P> vp;
rep(i, M) {
rep(j, C[i]) { vp.eb(P{-j, 1}); }
}
auto f = prod(vp);
V<Mint> xs(N + 1);
iota(ALL(xs), 0);
MultiEval me(xs);
auto ff = me.eval(f);
debug(ff);
V<Mint> v1(N + 1), v2(N + 1);
rep(i, N + 1) {
v1[i] = ff[i] * ifact[i];
v2[i] = ifact[i] * (i % 2 ? -1 : 1);
}
auto v3 = ntt.mul(v1, v2);
Mint ans;
rep(i, N + 1) ans += v3[i] * fact[i];
show(ans);
}
int main() {
int cases = 1;
// cin >> cases;
rep(i, cases) slv();
return 0;
}