#921376 (C++17) No.2513 Power Eraser

• 問題: No.2513 Power Eraser
• ユーザー: chineristAC
• 提出日時: 2023-10-20 23:03:51
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 2,670 ms / 6,000 ms
• コード長: 14,566 bytes
• コンパイル時間: 4,050 ms
• コンパイル使用メモリ: 269,336 KB
• 最終ジャッジ日時: 2025-02-17 10:43:03
• ジャッジサーバーID （参考情報）: judge2 / judge3

ファイルパターン	結果
sample	AC * 3
other	AC * 39

ソースコード

//https://yukicoder.me/submissions/650286

#include <bits/stdc++.h>
#include <unistd.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif
using ll = long long;
using ld = long double;
using ull = long long;
#define REP3(i, m, n) for (int i = (m); (i) < int(n); ++ (i))
#define ALL(x) begin(x), end(x)
#define all(s) (s).begin(),(s).end()
#define rep2(i, m, n) for (int i = (m); i < (n); ++i)
#define rep(i, n) rep2(i, 0, n)
#define drep2(i, m, n) for (int i = (m)-1; i >= (n); --i)
#define drep(i, n) drep2(i, n, 0)
#define rever(vec) reverse(vec.begin(), vec.end())
#define sor(vec) sort(vec.begin(), vec.end())
#define fi first
#define se second
//#define P pair<ll,ll>
#define REP(i, n) for (int i = 0; i < (n); ++i)
#define in scanner.read_int()
const ll mod = 998244353;
//const ll mod = 1000000007;
const ll inf = 2000000000000000000ll;
static const long double pi = 3.141592653589793;
template<class T>void vcin(vector<ll> &n){for(int i=0;i<int(n.size());i++) cin>>n[i];}
template<class T>void vcout(vector<T> &n){for(int i=0;i<int(n.size());i++){cout<<n[i]<<" ";}cout<<endl;}
void YesNo(bool a){if(a){cout<<"Yes"<<endl;}else{cout<<"No"<<endl;}}
void YESNO(bool a){if(a){cout<<"YES"<<endl;}else{cout<<"NO"<<endl;}}
template<class T,class U> void chmax(T& t,const U& u){if(t<u) t=u;}
template<class T,class U> void chmin(T& t,const U& u){if(t>u) t=u;}
template<class T> void ifmin(T t,T u){if(t>u){cout<<-1<<endl;}else{cout<<t<<endl;}}
template<class T> void ifmax(T t,T u){if(t>u){cout<<-1<<endl;}else{cout<<t<<endl;}}
template<typename T,typename ...Args>auto make_vector(T x,int arg,Args ...args){if constexpr(sizeof...(args)==0)return vector<T>(arg,x);else return vector(arg,make_vector<T>(x,args...));}
ll modPow(ll a, ll n, ll mod) { ll ret = 1; ll p = a % mod; while (n) { if (n & 1) ret = ret * p % mod; p = p * p % mod; n >>= 1; } return ret; }

void gbjsmzmfuuvdf(){
  ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
  cout<< fixed << setprecision(20);
}
class Scanner {
    vector<char> buffer;
    ssize_t n_written;
    ssize_t n_read;

public:
    Scanner(): buffer(1024*1024) { do_read(); }

    int64_t read_int() {
        int64_t ret = 0, sgn = 1;
        int ch = current_char();
        while (isspace(ch)) { ch = next_char(); }
        if (ch == '-') { sgn = -1; ch = next_char(); }
        for (; isdigit(ch); ch = next_char())
            ret = (ret * 10) + (ch - '0');
        return sgn * ret;
    }

private:
    void do_read() {
        ssize_t r = read(0, &buffer[0], buffer.size());
        if (r < 0) {
            throw runtime_error(strerror(errno));
        }
        n_written = r;
        n_read = 0;
    }

    inline int next_char() {
        ++n_read;
        if (n_read == n_written) { do_read(); }
        return current_char();
    }

    inline int current_char() {
        return (n_read == n_written) ? EOF : buffer[n_read];
    }
};
enum Mode {
	FAST = 1,
	NAIVE = -1,
};
template <class T, Mode mode = FAST>
struct FormalPowerSeries : std::vector<T> {
	using std::vector<T>::vector;
	using std::vector<T>::size;
	using std::vector<T>::resize;
	using F = FormalPowerSeries;
  F &operator+=(const F &g){
    for(int i=0;i<int(min((*this).size(),g.size()));i++){
      (*this)[i]+=g[i];
    }
    return *this;
  }
  F &operator+=(const T &t){
    assert(int((*this).size()));
    (*this)[0]+=t;
    return *this;
  }
  F &operator-=(const F &g) {
    for(int i=0;i<int(min((*this).size(),g.size()));i++){
      (*this)[i]-=g[i];
    }
    return *this;
  }
  F &operator-=(const T &t){
    assert(int((*this).size()));
    (*this)[0]-=t;
    return *this;
  }
  F &operator*=(const T &g) {
    for(int i=0;i<int((*this).size());i++){
      (*this)[i]*=g;
    }
    return *this;
  }
  F &operator/=(const T &g) {
    T div=g.inv();
    for(int i=0;i<int((*this).size());i++){
      (*this)[i]*=div;
    }
    return *this;
  }
  F &operator<<=(const int d) {
    int n=(*this).size();
    (*this).insert((*this).begin(),d,0);
    (*this).resize(n);
    return *this;
  }
  F &operator>>=(const int d) {
    int n=(*this).size();
    (*this).erase((*this).begin(),(*this).begin()+min(n, d));
    (*this).resize(n);
    return *this;
  }
  F &operator=(const std::vector<T> &v) {
    int n = (*this).size();
    for(int i = 0; i < n; ++i) (*this)[i] = v[i];
    return *this;
  }
  F operator-() const {
    F ret = *this;
    return ret * -1;
  }
  F &operator*=(const F &g) {
    if(mode==FAST) {
      int n=(*this).size();
      auto tmp=atcoder::convolution(*this,g);
      int f=tmp.size();
      (*this).resize(f);
      *this=tmp;
      return *this;
    }
    else{
      int n = (*this).size(), m = g.size();
      for(int i = n - 1; i >= 0; --i) {
        (*this)[i] *= g[0];
        for(int j = 1; j < std::min(i + 1, m); j++)
          (*this)[i] += (*this)[i - j] * g[j];
      }
      return *this;
    }
  }
  F &operator/=(const F &g) {
  if(mode == FAST){
  int n = (*this).size();
  (*this) = atcoder::convolution(*this, g.inv());
  return *this;
  }
  else{
  assert(g[0] != T(0));
  T ig0 = g[0].inv();
  int n = (*this).size(), m = g.size();
  for(int i = 0; i < n; ++i) {
  for(int j = 1; j < std::min(i + 1, m); ++j)
  (*this)[i] -= (*this)[i - j] * g[j];
  (*this)[i] *= ig0;
  }
  return *this;
  }
  }
  
  F &operator%=(const F &g) { return *this-=*this/g*g; }
  F operator*(const T &g) const { return F(*this)*=g;}
  F operator-(const T &g) const { return F(*this)-=g;}
  F operator*(const F &g) const { return F(*this)*=g;}
  F operator-(const F &g) const { return F(*this)-=g;}
  F operator+(const F &g) const { return F(*this)+=g;}
  F operator/(const F &g) const { return F(*this)/=g;}
  F operator%(const F &g) const { return F(*this)%=g;}
  F operator<<(const int d) const { return F(*this)<<=d;}
  F operator>>(const int d) const { return F(*this)>>=d;}  
  void onemul(const int d,const T c){
    int n=(*this).size();
    for(int i=n-d-1;i>=0;i--){
      (*this)[i+d]+=(*this)[i]*c;
    }
  }
  void onediv(const int d,const T c){
    int n=(*this).size();
    for(int i=0;i<n-d;i++){
      (*this)[i+d]-=(*this)[i]*c;
    }
  }
  T eval(const T &t) const {
  int n = (*this).size();
  T res = 0, tmp = 1;
  for(int i = 0; i < n; ++i){
  res += (*this)[i] * tmp, tmp *= t;
  }
  return res;
  }
  F inv(int deg = -1) const {
  int n = (*this).size();
  assert(mode == FAST and n and (*this)[0] != 0);
  if(deg == -1) deg = n;
  assert(deg > 0);
  F res{(*this)[0].inv()};
  while(int(res.size()) < deg) {
  int m = res.size();
  F f((*this).begin(), (*this).begin() + std::min(n, m * 2)), r(res);
  f.resize(m * 2), atcoder::internal::butterfly(f);
  r.resize(m * 2), atcoder::internal::butterfly(r);
  for(int i = 0; i < m * 2; ++i) f[i] *= r[i];
  atcoder::internal::butterfly_inv(f);
  f.erase(f.begin(), f.begin() + m);
  f.resize(m * 2), atcoder::internal::butterfly(f);
  for(int i = 0; i < m * 2; ++i) f[i] *= r[i];
  atcoder::internal::butterfly_inv(f);
  T iz = T(m * 2).inv();
  iz *= -iz;
  for(int i = 0; i < m; ++i) f[i] *= iz;
  res.insert(res.end(), f.begin(), f.begin() + m);
  }
  res.resize(deg);
  return res;
  }
  F &diff_inplace() {
  int n = (*this).size();
  for(int i = 1; i < n; ++i) (*this)[i - 1] = (*this)[i] * i;
  (*this)[n - 1] = 0;
  return *this;
  }
  F diff() const { F(*this).diff_inplace();}
  F &integral_inplace() {
  int n = (*this).size(), mod = T::mod();
  std::vector<T> inv(n);
  {
  inv[1] = 1;
  for(int i = 2; i < n; ++i)
  inv[i] = T(mod) - inv[mod % i] * (mod / i);
  }
  for(int i = n - 2; i >= 0; --i) (*this)[i + 1] = (*this)[i] * inv[i + 1];
  (*this)[0] = 0;
  return *this;
  }
  F integral() const { return F(*this).integral_inplace(); }
  F &log_inplace() {
  int n = (*this).size();
  assert(n and (*this)[0] == 1);
  F f_inv = (*this).inv();
  (*this).diff_inplace();
  (*this) *= f_inv;
  (*this).resize(n);
  (*this).integral_inplace();
  return *this;
  }
  F log() const { return F(*this).log_inplace(); }
  F &deriv_inplace() {
  int n = (*this).size();
  assert(n);
  for(int i = 2; i < n; ++i) (*this)[i] *= i;
 (*this).erase((*this).begin());
 (*this).push_back(0);
 return *this;
 }
 F deriv() const { return F(*this).deriv_inplace(); }
 F &exp_inplace() {
 int n = (*this).size();
 assert(n and (*this)[0] == 0);
 F g{1};
 (*this)[0] = 1;
 F h_drv((*this).deriv());
 for(int m = 1; m < n; m *= 2) {	
 F f((*this).begin(), (*this).begin() + m);
 f.resize(2 * m), atcoder::internal::butterfly(f);
 auto mult_f = [&](F &p) {
 p.resize(2 * m);
 atcoder::internal::butterfly(p);
 for(int i = 0; i < 2 * m; ++i) p[i] *= f[i];
 atcoder::internal::butterfly_inv(p);
 p /= 2 * m;
 };
 if(m > 1) {
 F g_(g);
 g_.resize(2 * m), atcoder::internal::butterfly(g_);
 for(int i = 0; i < 2 * m; ++i) g_[i] *= g_[i] * f[i];
 atcoder::internal::butterfly_inv(g_);
 T iz = T(-2 * m).inv();
 g_ *= iz;
 g.insert(g.end(), g_.begin() + m / 2, g_.begin() + m);
 }
 F t((*this).begin(), (*this).begin() + m);
 t.deriv_inplace();
 {
 F r{h_drv.begin(), h_drv.begin() + m - 1};
 mult_f(r);
 for(int i = 0; i < m; ++i) t[i] -= r[i] + r[m + i];
 }
 t.insert(t.begin(), t.back());
 t.pop_back();
 t *= g;
 F v((*this).begin() + m, (*this).begin() + std::min(n, 2 * m));
 v.resize(m);
 t.insert(t.begin(), m - 1, 0);
 t.push_back(0);
 t.integral_inplace();
 for(int i = 0; i < m; ++i) v[i] -= t[m + i];
 mult_f(v);
 for(int i = 0; i < std::min(n - m, m); ++i)
 (*this)[m + i] = v[i];
 }
 return *this;
 }
 F exp() const { return F(*this).exp_inplace(); }
 F &pow_inplace(long long k) {
 int n = (*this).size(), l = 0;
 assert(k >= 0);
 if(!k){
 for(int i = 0; i < n; ++i) (*this)[i] = !i;
 return *this;
 }
 while(l < n and (*this)[l] == 0) ++l;
 if(l > (n - 1) / k or l == n) return *this = F(n);
 T c = (*this)[l];
 (*this).erase((*this).begin(), (*this).begin() + l);
 (*this) /= c;
 (*this).log_inplace();
 (*this).resize(n - l * k);
 (*this) *= k;
 (*this).exp_inplace();
 (*this) *= c.pow(k);
 (*this).insert((*this).begin(), l * k, 0);
 return *this;
 }
 F pow(const long long k) const { return F(*this).pow_inplace(); }
 void spacemul(vector<pair<int, T>> g) {
    int n = (*this).size();
    auto [d, c] = g.front();
    if (d == 0) g.erase(g.begin());
    else c = 0;
    for(int i=n-1;i>=0;i--){
      (*this)[i] *= c;
      for (auto &[j, b] : g) {
        if (j > i) break;
        (*this)[i] += (*this)[i-j] * b;
      }
    }
  }
  void spacediv(vector<pair<int, T>> g) {
    int n = (*this).size();
    auto [d, c] = g.front();
    assert(d == 0 && c != T(0));
    T ic = c.inv();
    g.erase(g.begin());
    for(int i=0;i<n;i++){
      for (auto &[j, b] : g) {
        if (j > i) break;
        (*this)[i] -= (*this)[i-j] * b;
      }
      (*this)[i] *= ic;
    }
  }
};
using fps = FormalPowerSeries<atcoder::modint998244353, FAST>;
using mint = modint998244353;
constexpr ll MAX = 300000;
ll fac[MAX],finv[MAX],inv[MAX];
void COMinit(){
  fac[0]=fac[1]=1;
  finv[0]=finv[1]=1;
  inv[1]=1;
  for(int i=2;i<MAX;i++){
    fac[i]=fac[i-1]*i%mod;
    inv[i]=mod-inv[mod%i]*(mod/i)%mod;
    finv[i]=finv[i-1]*inv[i]%mod;
  }
}
ll COM(ll n,ll k){
  if(n<k) return 0;
  if(n<0||k<0) return 0;
  return fac[n]*(finv[k]*finv[n-k]%mod)%mod;
}
ll HOM(ll n,ll k){
  if(n+k-1>=n-1&&n-1>=0){
  return COM(n+k-1,n-1);
  }
  else{
    return 0;
  }
}
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>& l, const vector<T>& r) {
  l.resize(max(l.size(), r.size()));
  for (int i = 0; i < (int)r.size(); ++i) l[i] += r[i];
  return l;
}
template <class T> vector<T> operator+(vector<T> l, const vector<T>& r) {
  return l += r;
}
template <class T> vector<T>& operator-=(vector<T>& l, const vector<T>& r) {
  l.resize(max(l.size(), r.size()));
  for (int i = 0; i < (int)r.size(); ++i) l[i] -= r[i];
  return l;
}
template <class T> vector<T> operator-(vector<T> l, const vector<T>& r) {
  return l -= r;
}
template <class T> vector<T> operator*(const vector<T>& l, const vector<T>& r) {
  return convolution(l,r);
}
template <class T> vector<T>& operator*=(vector<T>& l, const vector<T>& r) {
  return l = l * r;
}
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> l, vector<T> r) {
  if (l.size() < r.size()) return {};
  reverse(begin(l), end(l)), reverse(begin(r), end(r));
  int n = l.size() - r.size() + 1;
  l.resize(n), r.resize(n);
  l *= inverse(r);
  return {rend(l) - n, rend(l)};
}
template <class T> vector<T>& operator/=(vector<T>& l, const vector<T>& r) {
  return l = l / r;
}
template <class T> vector<T> operator%(vector<T> l, const vector<T>& r) {
  if (l.size() < r.size()) return l;
  l -= l / r * r;
  return {begin(l), begin(l) + (r.size() - 1)};
}
template <class T> vector<T>& operator%=(vector<T>& l, const vector<T>& r) {
  return l = l % r;
}

template <class T>
vector<T> multipoint_evaluation(const vector<T>& poly, const vector<T>& x) {
  int n = x.size();
  vector<vector<T>> t(2 * n);
  for (int i = 0; i < n; ++i) t[n + i] = {-x[i], 1};
  for (int i = n; i-- > 1; ) t[i] = t[2 * i] * t[2 * i + 1];
  t[1] = poly % t[1];
  for (int i = 2; i < 2 * n; ++i) t[i] = t[i / 2] % t[i];
  vector<T> res(n);
  for (int i = 0; i < n; ++i) res[i] = t[n + i][0];
  return res;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);

  int N;
  cin>>N;
  vector<int> A(N);
  rep(i,N) cin>>A[i];

  auto calc = [&](auto self,int l,int r)->pair<mint,vector<mint>> {
    if (r==l+1){
      return {1,{-A[l],1}};
    }
    mint res_val = 1;
    vector<mint> res_poly = {1};

    int mid = (l+r)>>1;
    auto [l_val,l_p] = self(self,l,mid);
    auto [r_val,r_p] = self(self,mid,r);

    res_val = l_val * r_val;
    res_poly = l_p * r_p;

    vector<mint> left_a = {A.begin()+l,A.begin()+mid};
    vector<mint> right_a = {A.begin()+mid,A.begin()+r};

    rep(_,1){
      auto Y = multipoint_evaluation(l_p,right_a);
      for (auto y:Y){
        res_val *= y;
      }
    }
    return {res_val,res_poly};
  };

  auto [res_val,res_poly] = calc(calc,0,N);

  if (((ll)N*(N-1)/2ll) & 1){
    res_val = -res_val;
  }

  cout << res_val.val() << endl;

}