#585366 (C++17) No.1302 Random Tree Score

• 問題: No.1302 Random Tree Score
• ユーザー: tatyam
• 提出日時: 2020-11-27 21:54:47
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 168 ms / 3,000 ms
• コード長: 18,836 bytes
• コンパイル時間: 3,644 ms
• コンパイル使用メモリ: 232,780 KB
• 最終ジャッジ日時: 2025-01-16 07:05:34
• ジャッジサーバーID （参考情報）: judge5 / judge5

ファイルパターン	結果
sample	AC * 3
other	AC * 14

コンパイルメッセージ

main.cpp: In function ‘void scan(int&)’:
main.cpp:85:25: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
   85 | void scan(int& a){ scanf("%d", &a); }
      |                    ~~~~~^~~~~~~~~~
main.cpp: In function ‘void scan(unsigned int&)’:
main.cpp:86:30: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
   86 | void scan(unsigned& a){ scanf("%u", &a); }
      |                         ~~~~~^~~~~~~~~~
main.cpp: In function ‘void scan(long int&)’:
main.cpp:87:26: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
   87 | void scan(long& a){ scanf("%ld", &a); }
      |                     ~~~~~^~~~~~~~~~~
main.cpp: In function ‘void scan(long long int&)’:
main.cpp:88:31: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
   88 | void scan(long long& a){ scanf("%lld", &a); }
      |                          ~~~~~^~~~~~~~~~~~
main.cpp: In function ‘void scan(long long unsigned int&)’:
main.cpp:89:40: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
   89 | void scan(unsigned long long& a){ scanf("%llu", &a); }
      |                                   ~~~~~^~~~~~~~~~~~
main.cpp: In function ‘void scan(float&)’:
main.cpp:91:27: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
   91 | void scan(float& a){ scanf("%f", &a); }
      |                      ~~~~~^~~~~~~~~~
main.cpp: In function ‘void scan(double&)’:
main.cpp:92:28: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result

ソースコード

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using ull = unsigned long long;
using uint = unsigned;
using pcc = pair<char, char>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<ld, ld>;
using tuplis = array<ll, 3>;
template<class T> using pq = priority_queue<T, vector<T>, greater<T>>;
const ll LINF=0x1fffffffffffffff;
const ll MINF=0x7fffffffffff;
const int INF=0x3fffffff;
const int MOD=1000000007;
const int MODD=998244353;
const ld DINF=numeric_limits<ld>::infinity();
const ld EPS=1e-9;
const ld PI=3.1415926535897932;
const ll dx[] = {0, 1, 0, -1, 1, -1, 1, -1};
const ll dy[] = {1, 0, -1, 0, 1, 1, -1, -1};
#define overload4(_1,_2,_3,_4,name,...) name
#define overload3(_1,_2,_3,name,...) name
#define rep1(n) for(ll i=0;i<n;++i)
#define rep2(i,n) for(ll i=0;i<n;++i)
#define rep3(i,a,b) for(ll i=a;i<b;++i)
#define rep4(i,a,b,c) for(ll i=a;i<b;i+=c)
#define rep(...) overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__)
#define rrep1(n) for(ll i=n;i--;)
#define rrep2(i,n) for(ll i=n;i--;)
#define rrep3(i,a,b) for(ll i=b;i-->(a);)
#define rrep4(i,a,b,c) for(ll i=(a)+((b)-(a)-1)/(c)*(c);i>=(a);i-=c)
#define rrep(...) overload4(__VA_ARGS__,rrep4,rrep3,rrep2,rrep1)(__VA_ARGS__)
#define each1(i,a) for(auto&&i:a)
#define each2(x,y,a) for(auto&&[x,y]:a)
#define each3(x,y,z,a) for(auto&&[x,y,z]:a)
#define each(...) overload4(__VA_ARGS__,each3,each2,each1)(__VA_ARGS__)
#define all1(i) begin(i),end(i)
#define all2(i,a) begin(i),begin(i)+a
#define all3(i,a,b) begin(i)+a,begin(i)+b
#define all(...) overload3(__VA_ARGS__,all3,all2,all1)(__VA_ARGS__)
#define rall1(i) (i).rbegin(),(i).rend()
#define rall2(i,k) (i).rbegin(),(i).rbegin()+k
#define rall3(i,a,b) (i).rbegin()+a,(i).rbegin()+b
#define rall(...) overload3(__VA_ARGS__,rall3,rall2,rall1)(__VA_ARGS__)
#define sum(...) accumulate(all(__VA_ARGS__),0LL)
#define dsum(...) accumulate(all(__VA_ARGS__),0.0L)
#define Msum(...) accumulate(all(__VA_ARGS__),0_M)
#define elif else if
#define unless(a) if(!(a))
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;in(__VA_ARGS__)
#define Sort(a) sort(all(a))
#define Rev(a) reverse(all(a))
#define Uniq(a) sort(all(a));a.erase(unique(all(a)),end(a))
#define vec(type,name,...) vector<type>name(__VA_ARGS__)
#define VEC(type,name,size) vector<type>name(size);in(name)
#define vv(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__))
#define VV(type,name,h,w) vector<vector<type>>name(h,vector<type>(w));in(name)
#define vvv(type,name,h,w,...) vector<vector<vector<type>>>name(h,vector<vector<type>>(w,vector<type>(__VA_ARGS__)))
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)); }
inline ll popcnt(ull a){ return __builtin_popcountll(a); }
ll gcd(ll a, ll b){ while(b){ ll c = b; b = a % b; a = c; } return a; }
ll lcm(ll a, ll b){ if(!a || !b) return 0; return a * b / gcd(a, b); }
ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; }
ll modpow(ll a, ll b, ll p){ ll ans = 1; while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; }
template<class T> bool chmin(T& a, const T& b){ if(a > b){ a = b; return 1; } return 0; }
template<class T> bool chmax(T& a, const T& b){ if(a < b){ a = b; return 1; } return 0; }
template<class T, class U> bool chmin(T& a, const U& b){ if(a > T(b)){ a = b; return 1; } return 0; }
template<class T, class U> bool chmax(T& a, const U& b){ if(a < T(b)){ a = b; return 1; } return 0; }
vector<ll> iota(ll n, ll begin = 0){ vector<ll> a(n); iota(a.begin(), a.end(), begin); return a; }
vector<pll> factor(ull x){ vector<pll> ans; for(ull i = 2; i * i <= x; i++) if(x % i == 0){ ans.push_back({i, 1}); while((x /= i) % i == 0) ans.back().second++; } if(x != 1) ans.push_back({x, 1}); return ans; }
map<ll,ll> factor_map(ull x){ map<ll,ll> ans; for(ull i = 2; i * i <= x; i++) if(x % i == 0){ ans[i] = 1; while((x /= i) % i == 0) ans[i]++; } if(x != 1) ans[x] = 1; return ans; }
vector<ll> divisor(ull x){ vector<ll> ans; for(ull i = 1; i * i <= x; i++) if(x % i == 0) ans.push_back(i); rrep(ans.size() - (ans.back() * ans.back() == x)) ans.push_back(x / ans[i]); return ans; }
template<class T> unordered_map<T, ll> press(vector<T> a){ Uniq(a); unordered_map<T, ll> ans; rep(a.size()) ans[a[i]] = i; return ans; }
template<class T> map<T, ll> press_map(vector<T> a){ Uniq(a); map<T, ll> ans; rep(a.size()) ans[a[i]] = i; return ans; }
int scan(){ return getchar(); }
void scan(int& a){ scanf("%d", &a); }
void scan(unsigned& a){ scanf("%u", &a); }
void scan(long& a){ scanf("%ld", &a); }
void scan(long long& a){ scanf("%lld", &a); }
void scan(unsigned long long& a){ scanf("%llu", &a); }
void scan(char& a){ do{ a = getchar(); }while(a == ' ' || a == '\n'); }
void scan(float& a){ scanf("%f", &a); }
void scan(double& a){ scanf("%lf", &a); }
void scan(long double& a){ scanf("%Lf", &a); }
void scan(vector<bool>& a){ for(unsigned i = 0; i < a.size(); i++){ int b; scan(b); a[i] = b; } }
void scan(char a[]){ scanf("%s", a); }
void scan(string& a){ cin >> a; }
template<class T> void scan(vector<T>&);
template<class T, size_t size> void scan(array<T, size>&);
template<class T, class L> void scan(pair<T, L>&);
template<class T, size_t size> void scan(T(&)[size]);
template<class T> void scan(vector<T>& a){ for(auto&& i : a) scan(i); }
template<class T> void scan(deque<T>& a){ for(auto&& i : a) scan(i); }
template<class T, size_t size> void scan(array<T, size>& a){ for(auto&& i : a) scan(i); }
template<class T, class L> void scan(pair<T, L>& p){ scan(p.first); scan(p.second); }
template<class T, size_t size> void scan(T (&a)[size]){ for(auto&& i : a) scan(i); }
template<class T> void scan(T& a){ cin >> a; }
void in(){}
template <class Head, class... Tail> void in(Head& head, Tail&... tail){ scan(head); in(tail...); }
void print(){ putchar(' '); }
void print(bool a){ printf("%d", a); }
void print(int a){ printf("%d", a); }
void print(unsigned a){ printf("%u", a); }
void print(long a){ printf("%ld", a); }
void print(long long a){ printf("%lld", a); }
void print(unsigned long long a){ printf("%llu", a); }
void print(char a){ printf("%c", a); }
void print(char a[]){ printf("%s", a); }
void print(const char a[]){ printf("%s", a); }
void print(float a){ printf("%.15f", a); }
void print(double a){ printf("%.15f", a); }
void print(long double a){ printf("%.15Lf", a); }
void print(const string& a){ for(auto&& i : a) print(i); }
template<class T> void print(const complex<T>& a){ if(a.real() >= 0) print('+'); print(a.real()); if(a.imag() >= 0) print('+'); print(a.imag()); print('i'); }
template<class T> void print(const vector<T>&);
template<class T, size_t size> void print(const array<T, size>&);
template<class T, class L> void print(const pair<T, L>& p);
template<class T, size_t size> void print(const T (&)[size]);
template<class T> void print(const vector<T>& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } }
template<class T> void print(const deque<T>& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } }
template<class T, size_t size> void print(const array<T, size>& a){ print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } }
template<class T, class L> void print(const pair<T, L>& p){ print(p.first); putchar(' '); print(p.second); }
template<class T, size_t size> void print(const T (&a)[size]){ print(a[0]); for(auto i = a; ++i != end(a); ){ putchar(' '); print(*i); } }
template<class T> void print(const T& a){ cout << a; }
int out(){ putchar('\n'); return 0; }
template<class T> int out(const T& t){ print(t); putchar('\n'); return 0; }
template<class Head, class... Tail> int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; }
#ifdef DEBUG
inline ll __lg(ull x){ return 63 - __builtin_clzll(x); }
#define debug(...) { print(#__VA_ARGS__); print(":"); out(__VA_ARGS__); }
#else
#define debug(...) void(0)
#endif
int first(bool i = true){ return out(i?"first":"second"); }
int First(bool i = true){ return out(i?"First":"Second"); }
int yes(bool i = true){ return out(i?"yes":"no"); }
int Yes(bool i = true){ return out(i?"Yes":"No"); }
int No(){ return out("No"); }
int YES(bool i = true){ return out(i?"YES":"NO"); }
int NO(){ return out("NO"); }
int Yay(bool i = true){ return out(i?"Yay!":":("); }
int possible(bool i = true){ return out(i?"possible":"impossible"); }
int Possible(bool i = true){ return out(i?"Possible":"Impossible"); }
int POSSIBLE(bool i = true){ return out(i?"POSSIBLE":"IMPOSSIBLE"); }
void Case(ll i){ printf("Case #%lld: ", i); }


template <class T> vector<T> operator-(vector<T> a) {
  for (auto&& e : a) e = -e;
  return a;
}
template <class T> vector<T>& operator+=(vector<T>& a, const vector<T>& b) {
  a.resize(max(a.size(), b.size()));
  for (int i = 0; i < (int)b.size(); ++i) a[i] += b[i];
  return a;
}
template <class T> vector<T> operator+(vector<T> a, const vector<T>& b) {
  return a += b;
}
template <class T> vector<T>& operator-=(vector<T>& a, const vector<T>& b) {
  a.resize(max(a.size(), b.size()));
  for (int i = 0; i < (int)b.size(); ++i) a[i] -= b[i];
  return a;
}
template <class T> vector<T> operator-(vector<T> a, const vector<T>& b) {
  return a -= b;
}
template <class T> vector<T>& operator<<=(vector<T>& a, size_t n) {
  return a.insert(begin(a), n, 0), a;
}
template <class T> vector<T> operator<<(vector<T> a, size_t n) {
  return a <<= n;
}
template <class T> vector<T>& operator>>=(vector<T>& a, size_t n) {
  return a.erase(begin(a), begin(a) + min(a.size(), n)), a;
}
template <class T> vector<T> operator>>(vector<T> a, size_t n) {
  return a >>= n;
}
template <class T> vector<T> operator*(const vector<T>& a, const vector<T>& b) {
  if (a.empty() or b.empty()) return {};
  vector<T> res(a.size() + b.size() - 1);
  for (int i = 0; i < (int)a.size(); ++i)
    for (int j = 0; j < (int)b.size(); ++j) res[i + j] += a[i] * b[j];
  return res;
}
template <class T> vector<T>& operator*=(vector<T>& a, const vector<T>& b) {
  return a = a * b;
}
template <class T> vector<T> inverse(const vector<T>& a) {
  assert(not a.empty() and not (a[0] == 0));
  vector<T> b{1 / a[0]};
  while (b.size() < a.size()) {
    vector<T> x(begin(a), begin(a) + min(a.size(), 2 * b.size()));
    x *= b * b;
    b.resize(2 * b.size());
    for (auto i = b.size() / 2; i < min(x.size(), b.size()); ++i) b[i] = -x[i];
  }
  return {begin(b), begin(b) + a.size()};
}
template <class T> vector<T> operator/(vector<T> a, vector<T> b) {
  if (a.size() < b.size()) return {};
  reverse(begin(a), end(a)), reverse(begin(b), end(b));
  int n = a.size() - b.size() + 1;
  a.resize(n), b.resize(n);
  a *= inverse(b);
  return {rend(a) - n, rend(a)};
}
template <class T> vector<T>& operator/=(vector<T>& a, const vector<T>& b) {
  return a = a / b;
}
template <class T> vector<T> operator%(vector<T> a, const vector<T>& b) {
  if (a.size() < b.size()) return a;
  a -= a / b * b;
  return {begin(a), begin(a) + (b.size() - 1)};
}
template <class T> vector<T>& operator%=(vector<T>& a, const vector<T>& b) {
  return a = a % b;
}
template <class T> vector<T> derivative(const vector<T>& a) {
  vector<T> res(max((int)a.size() - 1, 0));
  for (int i = 0; i < (int)res.size(); ++i) res[i] = (i + 1) * a[i + 1];
  return res;
}
template <class T> vector<T> primitive(const vector<T>& a) {
  vector<T> res(a.size() + 1);
  for (int i = 1; i < (int)res.size(); ++i) res[i] = a[i - 1] / i;
  return res;
}
template <class T> vector<T> logarithm(const vector<T>& a) {
  assert(not a.empty() and a[0] == 1);
  auto res = primitive(derivative(a) * inverse(a));
  return {begin(res), begin(res) + a.size()};
}
template <class T> vector<T> exponent(const vector<T>& a) {
  assert(a.empty() or a[0] == 0);
  vector<T> b{1};
  while (b.size() < a.size()) {
    vector<T> x(begin(a), begin(a) + min(a.size(), 2 * b.size()));
    x[0] += 1;
    b.resize(2 * b.size());
    x -= logarithm(b);
    x *= {begin(b), begin(b) + b.size() / 2};
    for (auto i = b.size() / 2; i < min(x.size(), b.size()); ++i) b[i] = x[i];
  }
  return {begin(b), begin(b) + a.size()};
}

template <class T, class Op = multiplies<T>>
constexpr T power(T a, long long n, Op op = Op(), T e = {1}) {
  assert(n >= 0);
  while (n) {
    if (n & 1) e = op(e, a);
    if (n >>= 1) a = op(a, a);
  }
  return e;
}

template <class T> void ntt(vector<T>& a, bool inverse) {
  int n = size(a);
  assert((n & (n - 1)) == 0);
  if (n < 2) return;
  assert((T::mod - 1) % n == 0);
  static vector<T> w{1}, iw{1};
  for (int m = size(w); m < n / 2; m *= 2) {
    static T root = 2;
    while (power(root, (T::mod - 1) / 2) == 1) root += 1;
    T dw = power(root, (T::mod - 1) / (4 * m)), idw = 1 / dw;
    w.resize(2 * m), iw.resize(2 * m);
    for (int i = 0; i < m; ++i) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * idw;
  }
  if (not inverse) {
    for (int m = n; m >>= 1; ) {
      for (int s = 0, k = 0; s < n; s += 2 * m, ++k) {
        for (int i = s, j = s + m; i < s + m; ++i, ++j) {
          T x = a[i], y = a[j] * w[k];
          a[i] = x + y, a[j] = x - y;
        }
      }
    }
  } else {
    for (int m = 1; m < n; m *= 2) {
      for (int s = 0, k = 0; s < n; s += 2 * m, ++k) {
        for (int i = s, j = s + m; i < s + m; ++i, ++j) {
          T x = a[i], y = a[j];
          a[i] = x + y, a[j] = (x - y) * iw[k];
        }
      }
    }
    auto inv = 1 / T(n);
    for (auto&& e : a) e *= inv;
  }
}

template <unsigned M> struct montgomery {
  using m = montgomery;
  static constexpr unsigned mod = M, neg_inv = [] {
    static_assert(mod < 1 << 30 and mod & 1);
    auto inv = mod;
    while (mod * inv != 1) inv *= 2 - mod * inv;
    return -inv;
  }(), sq = -(uint64_t)mod % mod;
  static unsigned reduce(uint64_t x) {
    return (x + (uint64_t)mod * ((unsigned)x * neg_inv)) >> 32;
  }
  unsigned v;
  montgomery() : v(0) {}
  montgomery(long long x) {
    if ((x %= mod) < 0) x += mod;
    v = reduce((uint64_t)x * sq);
  }
  int get() const {
    auto res = reduce(v);
    return res < mod ? res : res - mod;
  }
  m operator-() const { return m() -= *this; }
  m& operator+=(m b) {
    if ((int)(v += b.v - 2 * mod) < 0) v += 2 * mod;
    return *this;
  }
  m& operator-=(m b) {
    if ((int)(v -= b.v) < 0) v += 2 * mod;
    return *this;
  }
  m& operator*=(m b) {
    v = reduce((uint64_t)v * b.v);
    return *this;
  }
  m& operator/=(m b) { return *this *= power(b, mod - 2); }
  friend m operator+(m a, m b) { return a += b; }
  friend m operator-(m a, m b) { return a -= b; }
  friend m operator*(m a, m b) { return a *= b; }
  friend m operator/(m a, m b) { return a /= b; }
  friend bool operator==(m a, m b) { return a.v == b.v; }
};

using mint = montgomery<998244353>;

vector<mint> fact, inv_fact, minv;
void prepare(int n) {
  fact.resize(n + 1), inv_fact.resize(n + 1), minv.resize(n + 1);
  for (int i = 0; i <= n; ++i) fact[i] = i ? fact[i - 1] * i : 1;
  inv_fact[n] = power(fact[n], mint::mod - 2);
  for (int i = n; i--; ) inv_fact[i] = (i + 1) * inv_fact[i + 1];
  for (int i = 1; i <= n; ++i) minv[i] = inv_fact[i] * fact[i - 1];
}
mint binom(int n, int k) {
  if (k < 0 or k > n) return 0;
  return fact[n] * inv_fact[k] * inv_fact[n - k];
}
template <> mint& mint::operator/=(mint b) {
  return *this *= b.v < minv.size() ? minv[b.v] : power(b, mod - 2);
}

struct dual_vec {
  vector<mint> v;
  void resize(int sz) { v.resize(sz); }
};
dual_vec mfft(const vector<mint>& a, int sz) {
  dual_vec fa{a};
  fa.resize(sz), ntt(fa.v, false);
  return fa;
}
dual_vec operator*(dual_vec a, const dual_vec& b) {
  for (int i = 0; i < (int)a.v.size(); ++i) a.v[i] *= b.v[i];
  return a;
}
vector<mint> ifft(dual_vec fa, int n) {
  ntt(fa.v, true), fa.resize(n);
  return fa.v;
}

vector<mint> operator*(const vector<mint>& a, const vector<mint>& b) {
  if (a.empty() or b.empty()) return {};
  int n = a.size(), m = b.size(), sz = 1 << __lg(2 * (n + m - 1) - 1);
  if (min(n, m) < 30) {
    vector<mint> c(n + m - 1);
    for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j)
      c[i + j] += a[i] * b[j];
    return c;
  }
  if (a == b) {
    dual_vec fl = mfft(a, sz);
    return ifft(fl * fl, n + m - 1);
  }
  return ifft(mfft(a, sz) * mfft(b, sz), n + m - 1);
}
vector<mint> inverse(const vector<mint>& a) {
  assert(not a.empty() and not (a[0] == 0));
  vector<mint> b{1 / a[0]};
  for (int m = 1; m < (int)a.size(); m *= 2) {
    vector<mint> x(begin(a), begin(a) + min<int>(a.size(), 2 * m));
    dual_vec fb = mfft(b, 2 * m);
    x = ifft(mfft(x, 2 * m) * fb, 2 * m);
    fill(begin(x), begin(x) + m, 0);
    x = -ifft(mfft(x, 2 * m) * fb, 2 * m);
    b.insert(end(b), begin(x) + m, end(x));
  }
  return {begin(b), begin(b) + a.size()};
}
vector<mint> exponent(const vector<mint>& a) {
  assert(a.empty() or a[0] == 0);
  vector<mint> b{1, 1 < a.size() ? a[1] : 0}, c{1};
  dual_vec half_fc = mfft(c, 1), fc = mfft(c, 2);
  for (int m = 2; m < (int)a.size(); m *= 2) {
    dual_vec fb = mfft(b, 2 * m), half_fb = fb;
    half_fb.resize(m);
    half_fc = fc;
    vector<mint> z = ifft(half_fb * half_fc, m);
    fill(begin(z), begin(z) + m / 2, 0);
    z = -ifft(mfft(z, m) * half_fc, m);
    c.insert(end(c), begin(z) + m / 2, end(z));
    fc = mfft(c, 2 * m);
    vector<mint> x(begin(a), begin(a) + min<int>(a.size(), m));
    x = derivative(x), x.push_back(0);
    dual_vec fx = mfft(x, m);
    x = ifft(fx * half_fb, m);
    x -= derivative(b);
    x.resize(2 * m);
    for (int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = 0;
    x = ifft(mfft(x, 2 * m) * fc, 2 * m);
    x = primitive(x), x.pop_back();
    for (int i = m; i < min<int>(a.size(), 2 * m); ++i) x[i] += a[i];
    fill(begin(x), begin(x) + m, 0);
    x = ifft(mfft(x, 2 * m) * fb, 2 * m);
    b.insert(end(b), begin(x) + m, end(x));
  }
  return {begin(b), begin(b) + a.size()};
}

vector<mint> power(vector<mint> a, long long m) {
  int n = size(a), tz = 0;
  while (tz < n and a[tz] == 0) ++tz;
  if (n == 0 or (tz and m >= (n + tz - 1) / tz)) return vector<mint>(n);
  a >>= tz;
  auto a0 = a[0];
  a *= vector<mint>{1 / a0};
  a = exponent(logarithm(a) * vector<mint>{m});
  a *= vector<mint>{power(a0, m)};
  return a <<= tz * m;
}
int main(){
    LL(n);
    prepare(n);
    vector<mint>f(n-1);
    rep(n-1)f[i]=mint(i+1)*inv_fact[i];
    f=power(f,n);
    mint ans=f[n-2]*fact[n-2]/power<mint>(n,n-2);
    out(ans.get());
}