結果

問題 No.1302 Random Tree Score
ユーザー 👑 rin204
提出日時 2023-06-01 01:09:43
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 394 ms / 3,000 ms
コード長 35,226 bytes
コンパイル時間 5,417 ms
コンパイル使用メモリ 276,368 KB
実行使用メモリ 15,512 KB
最終ジャッジ日時 2024-12-28 14:22:03
合計ジャッジ時間 8,976 ms
ジャッジサーバーID
(参考情報)
judge2 / judge1
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 14
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

// start A.cpp
// #pragma GCC target("avx2")
// #pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
template <class T>
using pq = priority_queue<T>;
template <class T>
using qp = priority_queue<T, vector<T>, greater<T>>;
#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__)));
#ifndef RIN__LOCAL
#define endl "\n"
#endif
#define spa ' '
#define len(A) A.size()
#define all(A) begin(A), end(A)
#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__)
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;
}
#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 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);
const ll MOD1 = 1000000007;
const ll MOD9 = 998244353;
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);
}
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(forward<Tail>(tail)...);
}
template <typename T>
void print(vector<T> &A) {
int n = A.size();
for (int i = 0; i < n; i++) {
cout << A[i];
if (i != n - 1) cout << ' ';
}
cout << endl;
}
template <typename T>
void print(vector<vector<T>> &A) {
for (auto &row : A) print(row);
}
template <typename T, typename S>
void print(pair<T, S> &A) {
cout << A.first << spa << A.second << endl;
}
template <typename T, typename S>
void print(vector<pair<T, S>> &A) {
for (auto &row : A) print(row);
}
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 priend(T A) {
priend(A, spa);
}
template <class... T>
void inp(T &... a) {
(cin >> ... >> a);
}
template <typename T>
void inp(vector<T> &A) {
for (auto &a : A) cin >> a;
}
template <typename T>
void inp(vector<vector<T>> &A) {
for (auto &row : A) inp(row);
}
template <typename T, typename S>
void inp(pair<T, S> &A) {
inp(A.first, A.second);
}
template <typename T, typename S>
void inp(vector<pair<T, S>> &A) {
for (auto &row : A) inp(row.first, row.second);
}
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;
}
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>
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>
vector<vector<pair<int, T>>> read_wtree(int n, int indexed = 1) {
return read_wedges<T>(n, n - 1, false, indexed);
}
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;
}
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;
}
// start other/Modint.hpp
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;
swap(a, b);
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 ostream &operator<<(ostream &os, const Modint &p) {
return os << p.x;
}
friend istream &operator>>(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;
swap(a, b);
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 ostream &operator<<(ostream &os, const Arbitrary_Modint &p) {
return os << p.x;
}
friend istream &operator>>(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;
// end other/Modint.hpp
// restart A.cpp
using mint = modint9;
// start math/Combination.hpp
template <typename T>
struct Combination {
int N;
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 >= 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 >= 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 +1, m -1, k
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);
}
};
// end math/Combination.hpp
// restart A.cpp
// start polynomial/FormalPowerSeries.hpp
// start convolution/NTT.hpp
template <typename mint>
struct NumberTheoreticTransform {
static 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(vector<mint> &A) {
init();
int n = 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(vector<mint> &A, bool f = true) {
init();
int n = 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 vector<mint> multiply(vector<mint> A, vector<mint> B) {
int need = A.size() + B.size() - 1;
if (min(A.size(), B.size()) < 60) {
vector<mint> C(need, 0);
for (int i = 0; i < A.size(); i++)
for (int 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>
vector<mint> NumberTheoreticTransform<mint>::roots = vector<mint>();
template <typename mint>
vector<mint> NumberTheoreticTransform<mint>::iroots = vector<mint>();
template <typename mint>
vector<mint> NumberTheoreticTransform<mint>::rate3 = vector<mint>();
template <typename mint>
vector<mint> NumberTheoreticTransform<mint>::irate3 = vector<mint>();
template <typename mint>
int NumberTheoreticTransform<mint>::max_base = 0;
// end convolution/NTT.hpp
// restart polynomial/FormalPowerSeries.hpp
// start math/cipolla.hpp
// start math/modpow.hpp
template <typename T>
T modpow(T a, long long b, T MOD) {
T ret = 1;
while (b > 0) {
if (b & 1) {
ret *= a;
ret %= MOD;
}
a *= a;
a %= MOD;
b >>= 1;
}
return ret;
}
// end math/modpow.hpp
// restart math/cipolla.hpp
long long cipolla(long long a, long long MOD) {
if (MOD == 2)
return a;
else if (a == 0)
return 0;
else if (modpow(a, (MOD - 1) / 2, MOD) != 1)
return -1;
long long b = 1;
while (modpow((b * b + MOD - a) % MOD, (MOD - 1) / 2, MOD) == 1) {
b++;
}
long long base = (b * b + MOD - a) % MOD;
auto multi = [&](long long a0, long long b0, long long a1, long long b1) -> pair<long long, long long> { return {(a0 * a1 + (b0 * b1 % MOD)
        * base) % MOD, (a0 * b1 + b0 * a1) % MOD}; };
auto pow_ = [&](auto self, long long a, long long b, long long n) -> pair<long long, long long> {
if (n == 0) return {1, 0};
auto tmp = multi(a, b, a, b);
auto ret = self(self, tmp.first, tmp.second, n / 2);
if (n & 1) {
ret = multi(ret.first, ret.second, a, b);
}
return ret;
};
return pow_(pow_, b, 1LL, (MOD + 1) / 2).first;
}
// end math/cipolla.hpp
// restart polynomial/FormalPowerSeries.hpp
template <typename mint>
struct FormalPowerSeries : vector<mint> {
using vector<mint>::vector;
using FPS = FormalPowerSeries;
static vector<mint> inv_x;
void shrink() {
while (this->size() && this->back() == mint(0)) {
this->pop_back();
}
}
FPS &operator+=(const FPS &A) {
if (A.size() > this->size()) this->resize(A.size());
for (int i = 0; i < A.size(); i++) (*this)[i] += A[i];
return *this;
}
FPS &operator+=(const mint &x) {
if (this->empty()) this->resize(1);
(*this)[0] += x;
return *this;
}
FPS &operator-=(const FPS &A) {
if (A.size() > this->size()) this->resize(A.size());
for (int i = 0; i < A.size(); i++) (*this)[i] -= A[i];
return *this;
}
FPS &operator-=(const mint &x) {
if (this->empty()) this->resize(1);
(*this)[0] -= x;
return *this;
}
FPS &operator*=(const FPS &A) {
if (this->empty() || A.empty()) {
this->clear();
return *this;
}
auto res = NumberTheoreticTransform<mint>::multiply(*this, A);
return *this = {begin(res), end(res)};
}
FPS &operator*=(const mint &x) {
for (int i = 0; i < this->size(); i++) (*this)[i] *= x;
return *this;
}
FPS operator+(const FPS &A) const {
return FPS(*this) += A;
}
FPS operator+(const mint &x) const {
return FPS(*this) += x;
}
FPS operator-(const FPS &A) const {
return FPS(*this) -= A;
}
FPS operator-(const mint &x) const {
return FPS(*this) -= x;
}
FPS operator*(const FPS &A) const {
return FPS(*this) *= A;
}
FPS operator*(const mint &x) const {
return FPS(*this) *= x;
}
FPS operator-() const {
FPS ret(this->size);
for (int i = 0; i < this->size(); i++) ret[i] = -(*this)[i];
return ret;
}
FPS inv(int deg = -1) {
assert((*this)[0] != mint(0));
if (deg == -1) deg = this->size();
FPS g = {mint(1) / (*this)[0]};
int l = 1;
while (l < deg) {
FPS tmp = g * 2;
l <<= 1;
FPS tmp2;
g *= g;
if (this->size() >= l)
tmp2 = FPS({this->begin(), this->begin() + l}) * g;
else
tmp2 = (*this) * g;
g = tmp - tmp2;
g.resize(l);
}
g.resize(deg);
return g;
}
void iinv(int deg = -1) {
*this = inv(deg);
}
FPS differential() {
FPS ret(this->size() - 1);
for (int i = 0; i < this->size() - 1; i++) ret[i] = (*this)[i + 1] * (i + 1);
return ret;
}
void idifferential() {
*this = this->differential();
}
void extend_inv(int n) {
int bn = inv_x.size();
if (n >= bn) {
inv_x.resize(n + 1, 0);
if (bn == 0) {
inv_x[0] = 0;
inv_x[1] = 1;
bn = 2;
}
ll mod = mint::get_mod();
for (int i = bn; i <= n; i++) {
inv_x[i] = mod - inv_x[mod % i].x * (mod / i) % mod;
}
}
}
FPS integral() {
extend_inv(this->size());
FPS ret(this->size() + 1);
for (int i = 0; i < this->size(); i++) ret[i + 1] = (*this)[i] * inv_x[i + 1];
return ret;
}
void iintegral() {
*this = this->integral();
}
FPS log(int deg = -1) {
assert((*this)[0] == mint(1));
if (deg == -1) deg = this->size();
FPS B = (this->differential()) * (this->inv());
B.resize(deg - 1);
return B.integral();
}
void ilog(int deg = -1) {
*this = this->log(deg);
}
FPS exp(int deg = -1) {
assert((*this)[0] == mint(0));
if (deg == -1) deg = this->size();
FPS g = {1};
int l = 1;
while (l < deg * 2) {
l *= 2;
FPS tmp = {1};
tmp -= g.log(l);
if (this->size() >= l)
tmp += FPS({this->begin(), this->begin() + l});
else
tmp += (*this);
g *= tmp;
g.resize(l);
}
g.resize(deg);
return g;
}
void iexp(int deg = -1) {
*this = this->exp(deg);
}
FPS pow(long long k, int deg = -1) {
if (deg == -1) deg = this->size();
if (k == 0) {
FPS ret(deg, 0);
ret[0] = 1;
return ret;
}
int p = -1;
for (int i = 0; i < deg; i++) {
if ((*this)[i] != 0) {
p = i;
break;
}
}
if (p == -1 || p > deg / k) {
FPS ret(deg, 0);
return ret;
}
mint inv = mint(1) / (*this)[p];
FPS A = FPS({(*this).begin() + p, (*this).end()});
A *= inv;
A.ilog(deg);
A *= k % mint::get_mod();
A.iexp(deg);
FPS B(p * k, 0);
B.insert(B.end(), A.begin(), A.begin() + (deg - p * k));
B *= (*this)[p].pow(k);
return B;
}
void ipow(long long k, int deg = -1) {
*this = this->pow(k, deg);
}
FPS sqrt(int deg = -1) {
if (deg == -1) deg = this->size();
if (this->size() == 0) {
FPS ret(deg, 0);
return ret;
}
if ((*this)[0] == mint(0)) {
for (int i = 1; i < this->size(); i++) {
if ((*this)[i] != 0) {
if (i & 1) {
FPS ret;
return ret;
}
if (deg <= i / 2) break;
FPS ret = FPS({this->begin() + i, this->end()}).sqrt(deg - i / 2);
if (ret.size() == 0) return ret;
FPS ret2(i / 2, 0);
ret2.insert(ret2.end(), ret.begin(), ret.end());
swap(ret, ret2);
if (ret.size() < deg) ret.resize(deg);
return ret;
}
}
FPS ret(deg, 0);
return ret;
}
ll sq = cipolla((*this)[0].x, mint::get_mod());
if (sq == -1) {
FPS ret;
return ret;
}
mint inv2 = mint(1) / 2;
FPS g = {sq};
int l = 1;
while (l < deg) {
l *= 2;
if (this->size() >= l)
g += FPS({this->begin(), this->begin() + l}) * g.inv(l);
else
g += (*this) * g.inv(l);
g *= inv2;
}
g.resize(deg);
return g;
}
void isqrt(int deg = -1) {
*this = this->sqrt(deg);
}
FPS taylorshift(mint a) {
auto A = (*this);
int deg = A.size();
extend_inv(deg);
mint fac = 1;
for (int i = 0; i < deg; i++) {
A[i] *= fac;
fac *= (i + 1);
}
reverse(A.begin(), A.end());
FPS g(deg, 0);
g[0] = 1;
for (int i = 1; i < deg; i++) g[i] = g[i - 1] * a * inv_x[i];
A *= g;
if (A.size() > deg) A.resize(deg);
reverse(A.begin(), A.end());
mint invfac = 1;
for (int i = 0; i < deg; i++) {
A[i] *= invfac;
invfac *= inv_x[i + 1];
}
return A;
}
void itaylorshift(mint a) {
int deg = this->size();
extend_inv(deg);
mint fac = 1;
for (int i = 0; i < deg; i++) {
(*this)[i] *= fac;
fac *= (i + 1);
}
reverse(this->begin(), this->end());
FPS g(deg, 0);
g[0] = 1;
for (int i = 1; i < deg; i++) g[i] = g[i - 1] * a * inv_x[i];
(*this) *= g;
if (this->size() > deg) this->resize(deg);
reverse(this->begin(), this->end());
mint invfac = 1;
for (int i = 0; i < deg; i++) {
(*this)[i] *= invfac;
invfac *= inv_x[i + 1];
}
}
pair<FPS, FPS> division_of_polynomial(FPS G) {
FPS F = *this;
if (F.size() < G.size()) {
return {{}, F};
}
reverse(F.begin(), F.end());
reverse(G.begin(), G.end());
int deg = F.size() - G.size() + 1;
auto Q = F * G.inv(deg);
if (Q.size() > deg) Q.resize(deg);
reverse(Q.begin(), Q.end());
reverse(F.begin(), F.end());
reverse(G.begin(), G.end());
auto R = F - G * Q;
R.shrink();
return {Q, R};
}
vector<mint> multipoint_evaluation(vector<mint> &X) {
int m = X.size();
int m2 = 1;
while (m2 <= m - 1) m2 *= 2;
vector<FPS> G(m2 << 1, FPS(1, 1));
for (int i = 0; i < m; i++) G[m2 + i] = {-X[i], 1};
for (int i = m2 - 1; i >= 0; i--) G[i] = G[i << 1] * G[(i << 1) | 1];
G[1] = this->division_of_polynomial(G[1]).second;
for (int i = 2; i < m2 + m; i++) G[i] = G[i >> 1].division_of_polynomial(G[i]).second;
vector<mint> Y(m);
for (int i = 0; i < m; i++) {
if (G[m2 + i].empty())
Y[i] = 0;
else
Y[i] = G[m2 + i][0];
}
return Y;
}
vector<long long> multipoint_evaluation(vector<long long> &X) {
int m = X.size();
int m2 = 1;
while (m2 <= m - 1) m2 *= 2;
vector<FPS> G(m2 << 1, FPS(1, 1));
for (int i = 0; i < m; i++) G[m2 + i] = {-X[i], 1};
for (int i = m2 - 1; i >= 0; i--) G[i] = G[i << 1] * G[(i << 1) | 1];
G[1] = this->division_of_polynomial(G[1]).second;
for (int i = 2; i < m2 + m; i++) G[i] = G[i >> 1].division_of_polynomial(G[i]).second;
vector<long long> Y(m);
for (int i = 0; i < m; i++) {
if (G[m2 + i].empty())
Y[i] = 0;
else
Y[i] = G[m2 + i][0].x;
}
return Y;
}
friend ostream &operator<<(ostream &os, const FPS &A) {
for (int i = 0; i < A.size(); i++) {
os << A[i];
if (i != A.size() - 1) os << ' ';
}
return os;
}
friend istream &operator>>(istream &is, FPS &A) {
for (int i = 0; i < A.size(); i++) {
is >> A[i];
}
return (is);
}
};
template <typename mint>
vector<mint> FormalPowerSeries<mint>::inv_x = vector<mint>();
// end polynomial/FormalPowerSeries.hpp
// restart A.cpp
using FPS = FormalPowerSeries<mint>;
void solve() {
LL(n);
FPS F(n);
Combination<mint> C(n + 10);
fori(i, n) {
F[i] = C.invfact[i] * (i + 1);
}
F = F.pow(n);
mint ans = F[n - 2] * C.fact[n - 2];
ans /= mint(n).pow(n - 2);
print(ans);
}
int main() {
cin.tie(0)->sync_with_stdio(0);
// cout << fixed << setprecision(12);
int t;
t = 1;
// cin >> t;
while (t--) solve();
return 0;
}
// end A.cpp
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0