結果

問題 No.2062 Sum of Subset mod 999630629
ユーザー eQe
提出日時 2025-08-24 15:06:24
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 768 ms / 5,000 ms
コード長 7,591 bytes
コンパイル時間 5,730 ms
コンパイル使用メモリ 334,656 KB
実行使用メモリ 32,104 KB
最終ジャッジ日時 2025-08-24 15:06:37
合計ジャッジ時間 12,642 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 29
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 # 

#include<bits/stdc++.h>
#if __has_include(<atcoder/all>)
#include<atcoder/modint>
#include<atcoder/lazysegtree>
#include<atcoder/convolution>
#endif
using namespace std;
#define eb emplace_back
#define done(...) return pp(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;lin(__VA_ARGS__)
#define RDVL(T,n,...) vec<T>__VA_ARGS__;fe(refs(__VA_ARGS__),e)e.get().resizes(n);lin(__VA_ARGS__)
#define VL(n,...) RDVL(ll,n,__VA_ARGS__)
#define fo(i,...) for(auto[i,i##stop,i##step]=for_range<ll>(0,__VA_ARGS__);i<i##stop;i+=i##step)
#define fe(a,e,...) for(auto&&__VA_OPT__([)e __VA_OPT__(,__VA_ARGS__]):a)
#define binary_operator(op,type) auto operator op(const type&rhs)const{auto copy=*this;return copy op##=rhs;}
#define defpp template<ostream&o=cout>void pp(const auto&...a){[[maybe_unused]]const char*c="";((o<<c<<a,c=" "),...);o<<'\n';}void epp(const auto&...a){pp<cerr>(a...);}
#define entry defpp void main();void main2();}int main(){my::io();my::main();}namespace my{
#define use_ml998244353 using ml=atcoder::modint998244353;
namespace my{
auto&operator<<(ostream&o,const atcoder::modint998244353&x){return o<<(int)x.val();}
void io(){cin.tie(nullptr)->sync_with_stdio(0);cout<<fixed<<setprecision(15);}
using ll=int;
template<class T>concept modulary=requires(T t){t.mod();};
constexpr auto refs(auto&...a){return array{ref(a)...};}
template<class T>constexpr auto for_range(T s,T b){T a=0;if(s)swap(a,b);return array{a-s,b,1-s*2};}
template<class T>constexpr auto for_range(T s,T a,T b,T c=1){return array{a-s,b,(1-s*2)*c};}
void lin(auto&...a){(cin>>...>>a);}
constexpr ll powm1(ll n){return 1-2*(n&1);}
auto min(auto...a){return min(initializer_list<common_type_t<decltype(a)...>>{a...});}
template<class A,class B=A>struct pair{
  A a;B b;
  pair()=default;
  pair(A aa,B bb):a(aa),b(bb){}
  auto operator<=>(const pair&)const=default;
};
template<class...A>using pack_back_t=tuple_element_t<sizeof...(A)-1,tuple<A...>>;
}
namespace my{
template<class V>concept vectorial=is_base_of_v<vector<typename remove_cvref_t<V>::value_type>,remove_cvref_t<V>>;
template<class V>istream&operator>>(istream&i,vector<V>&v){fe(v,e)i>>e;return i;}
template<class V>constexpr int depth=0;
template<vectorial V>constexpr int depth<V> =depth<typename V::value_type>+1;
template<class T>struct core_t_helper{using type=T;};
template<class T>using core_t=core_t_helper<T>::type;
template<class V>struct vec;
template<int D,class T>struct hvec_helper{using type=vec<typename hvec_helper<D-1,T>::type>;};
template<class T>struct hvec_helper<0,T>{using type=T;};
template<int D,class T>using hvec=hvec_helper<D,T>::type;
template<class V>struct vec:vector<V>{
  static constexpr int D=depth<vec<V>>;
  using C=core_t<V>;
  using vector<V>::vector;
  vec(const vector<V>&v):vector<V>(v){}
  void resizes(const auto&...a){if constexpr(sizeof...(a)==D)*this=make(a...,C{});else{ }}
  static auto make(ll n,const auto&...a){
    if constexpr(sizeof...(a)==1)return vec<C>(n,array{a...}[0]);
    else { }
  }
  ll size()const{return vector<V>::size();}
  auto&emplace_back(auto&&...a){vector<V>::emplace_back(std::forward<decltype(a)>(a)...);return*this;}
  auto fold(const auto&f)const{
    pair<C,bool>r{};
    fe(*this,e){
      if constexpr(!vectorial<V>){
        if(r.b)f(r.a,e);
        else r={e,1};
      }else { }

    }
    return r;
  }
  auto sum()const{return fold([](auto&a,const auto&b){a+=b;}).a;}
  auto max()const{return fold([](auto&a,auto b){if(a<b)a=b;}).a;}
  auto min()const{return fold([](auto&a,auto b){if(b<a)a=b;}).a;}
  vec zeta()const{vec v=*this;if constexpr(vectorial<V>){ }fo(i,v.size()-1)v[i+1]+=v[i];return v;}
  auto count_enumerate(C M=-1)const{
    assert(min()>=0);
    if(M==-1)M=max();
    vec<C>res(M+1);
    auto f=[&]<class U>(auto&f,const vec<U>&v){
      fe(v,e){
        if constexpr(vectorial<U>){ }
        else if(e<=M)res[e]++;
      }
    };
    f(f,*this);
    return res;
  }
};
template<class...A>requires(sizeof...(A)>=2)vec(const A&...a)->vec<hvec<sizeof...(A)-2,pack_back_t<A...>>>;
}
namespace my{
template<class T>auto inv_enumerate(ll n){
  vec<T>v(n+1);
  v[0]=0;
  if(n>=1)v[1]=1;
  fo(i,2,n+1)v[i]=-v[T::mod()%i]*(T::mod()/i);
  return v;
}
}
namespace my{
template<class T>T inv(ll n){static vec<T>v{0,1};if(ll m=v.size();m<=n){v.resize(n+1);fo(i,m,n+1)v[i]=-v[T::mod()%i]*(T::mod()/i);}return v[n];}
}
namespace my{
template<class T>struct formal_power_series:vec<T>{
  using vec<T>::vec;
  using fps=formal_power_series;
  static constexpr ll SPARSE_THRESHOLD=20;
  static fps mul(const fps&a,const fps&b){
    if constexpr(!modulary<T>){ }
    else if constexpr(is_same_v<T,atcoder::modint998244353>)return atcoder::convolution(a,b);
    else { }
  }
  fps pre(ll deg)const{fps r(this->begin(),this->begin()+min(this->size(),deg));r.resize(deg);return r;}
  fps&operator-=(const fps&g){if(g.size()>this->size())this->resize(g.size());fo(i,g.size())(*this)[i]-=g[i];return*this;}
  fps&operator*=(const fps&g){return*this=(this->size()&&g.size()?mul(*this,g):fps{});}
  binary_operator(-,fps)
  binary_operator(*,fps)
  fps operator-()const{auto r=*this;fe(r,x)x=-x;return r;}
  fps&operator+=(const T&c){if(!this->size())this->resize(1);(*this)[0]+=c;return*this;}
  fps&operator*=(const T&c){fo(i,this->size())(*this)[i]*=c;return*this;}
  binary_operator(+,T)
  binary_operator(*,T)
  fps differential()const{
    assert(this->size());
    fps r(this->size()-1);
    fo(i,r.size())r[i]=(*this)[i+1]*T{i+1};
    return r;
  }
  fps integral()const{
    fps r(this->size()+1);
    auto iv=inv_enumerate<T>(r.size());
    fo(i,r.size()-1)r[i+1]=(*this)[i]*iv[i+1];
    return r;
  }
  fps inv_sparse(ll deg=-1)const{
    assert((*this)[0]!=T{});
    ll n=this->size();
    if(deg==-1)deg=n;
    vec<pair<ll,T>>p;
    fo(i,1,n)if((*this)[i]!=T{})p.eb(i,(*this)[i]);
    fps r(deg);
    r[0]=T{1}/(*this)[0];
    fo(i,1,deg){
      T t{};
      fe(p,k,fk){
        if(i-k<0)break;
        t-=fk*r[i-k];
      }
      r[i]=r[0]*t;
    }
    return r;
  }
  fps exp_sparse(ll deg=-1)const{
    assert((*this)[0]==T{});
    ll n=this->size();
    if(deg==-1)deg=n;

    vec<pair<ll,T>>p;
    fo(i,1,n)if((*this)[i]!=T{})p.eb(i-1,T{i}*(*this)[i]);
    auto iv=inv_enumerate<T>(deg);
    fps r(deg);
    r[0]=1;
    fo(i,1,deg){
      T t{};
      fe(p,k,fk){
        if(i-k-1<0)break;
        t+=fk*r[i-k-1];
      }
      r[i]=t*iv[i];
    }
    return r;
  }
  ll nonzero_terms_count()const{ll r=0;fe(*this,e)r+=(e!=T{});return r;}
  fps inv(ll deg=-1)const{
    assert((*this)[0]!=T{});
    if(deg==-1)deg=this->size();
    if(nonzero_terms_count()<SPARSE_THRESHOLD)return inv_sparse(deg);
    fps r{T{1}/(*this)[0]};
    for(ll i=1;i<deg;i<<=1)r=(r*2-this->pre(i<<1)*(r*r)).pre(i<<1);
    return r.pre(deg);
  }
  fps log(ll deg=-1)const{
    assert((*this)[0]==T{1});
    if(deg==-1)deg=this->size();
    return(differential()*inv(deg)).integral().pre(deg);
  }
  fps exp(ll deg=-1)const{
    assert((*this)[0]==T{});
    if(deg==-1)deg=this->size();
    if(nonzero_terms_count()<SPARSE_THRESHOLD)return exp_sparse(deg);
    fps r{1};
    for(ll i=1;i<deg;i<<=1)r=(r*(this->pre(i<<1)+T{1}-r.log(i<<1))).pre(i<<1);
    return r.pre(deg);
  }
};
template<class T>using fps=formal_power_series<T>;
}
namespace my{entry
void main(){
  LL(N);
  VL(N,a);
  ll P=999630629;
  ll S=a.sum();
  ll M=S-P+1;

  use_ml998244353
  if(M<=1)done(ml(2).pow(N-1)*S);

  auto c=a.count_enumerate(M);

  fps<ml>f(M);
  fo(j,1,M){
    fo(n,1,(M-1)/j+1){
      f[j*n]+=c[j]*powm1(n)*inv<ml>(n);
    }
  }
  f=(-f).exp();
  f=f.zeta();
  pp(ml(2).pow(N-1)*S-P*f[M-1]);
}}
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