結果

問題 No.2318 Phys Bone Maker
コンテスト
ユーザー eQe
提出日時 2025-09-07 04:51:37
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,496 ms / 3,000 ms
コード長 6,757 bytes
コンパイル時間 4,667 ms
コンパイル使用メモリ 314,904 KB
実行使用メモリ 6,656 KB
最終ジャッジ日時 2025-09-07 04:51:53
合計ジャッジ時間 16,310 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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 * 45
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>
#endif
using namespace std;
#define eb emplace_back
#define LL(...) ll __VA_ARGS__;lin(__VA_ARGS__)
#define FO(n) for(ll IJK=n;IJK-->0;)
#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 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=long long;
using i64=int64_t;
using ui64=uint64_t;
using ui128=__uint128_t;
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};}
void lin(auto&...a){(cin>>...>>a);}
constexpr auto pow(auto x,ll n,auto e){assert(n>=0);decltype(x)r=e;for(;n;x*=x,n>>=1)if(n&1)r*=x;return r;}
constexpr auto pow(auto x,ll n){return pow(x,n,1);}
i64 rand(){static i64 x=495;x^=x<<7;x^=x>>9;return x;}
i64 rand(i64 l,i64 r=0){if(l>r)swap(l,r);return rand()%(r-l)+l;}
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 F=less<>>auto&sort(auto&a,F f={}){ranges::sort(a,f);return a;}
template<class...A>using pack_back_t=tuple_element_t<sizeof...(A)-1,tuple<A...>>;
}
namespace my{
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>{
  using vector<V>::vector;
  ll size()const{return vector<V>::size();}
  auto&emplace_back(auto&&...a){vector<V>::emplace_back(std::forward<decltype(a)>(a)...);return*this;}
  auto pop_back(){auto r=this->back();vector<V>::pop_back();return r;}
  template<class F=less<>>auto sort(F f={})const{vec v=*this;ranges::sort(v,f);return v;}
  auto rle()const{vec<pair<V,ll>>r;fe(*this,e)if(r.size()&&e==r.back().a)++r.back().b;else r.eb(e,1);return r;}
  auto rce()const{return sort().rle();}
};
template<class...A>requires(sizeof...(A)>=2)vec(const A&...a)->vec<hvec<sizeof...(A)-2,pack_back_t<A...>>>;
}
namespace my{
template<int tag>struct montgomery64{
  using modular=montgomery64;
  static inline ui64 N=998244353;
  static inline ui64 N_inv=996491785301655553ull;
  static inline ui64 R2=299560064;
  static int set_mod(ui64 N){
    if(modular::N==N)return 0;
    assert(N<(1ull<<63));
    assert(N&1);
    modular::N=N;
    R2=-ui128(N)%N;
    N_inv=N;
    FO(5)N_inv*=2-N*N_inv;
    assert(N*N_inv==1);
    return 0;
  }
  ui64 a;
  montgomery64(const i64&a=0):a(reduce((ui128)(a%(i64)N+N)*R2)){}
  static ui64 reduce(const ui128&T){ui128 r=(T+ui128(ui64(T)*-N_inv)*N)>>64;return r>=N?r-N:r;}
  auto&operator+=(const modular&b){if((a+=b.a)>=N)a-=N;return*this;}
  auto&operator-=(const modular&b){if(i64(a-=b.a)<0)a+=N;return*this;}
  auto&operator*=(const modular&b){a=reduce(ui128(a)*b.a);return*this;}
  friend auto operator+(const modular&a,const modular&b){return modular{a}+=b;}
  friend auto operator-(const modular&a,const modular&b){return modular{a}-=b;}
  friend auto operator*(const modular&a,const modular&b){return modular{a}*=b;}
  friend bool operator==(const modular&a,const modular&b){return a.a==b.a;}
  modular pow(ui128 n)const{return my::pow(*this,n);}
  ui64 val()const{return reduce(a);}
};
}
namespace my{
bool miller_rabin(ll n,vec<ll>as){
  ll d=n-1;
  while(~d&1)d>>=1;

  using modular=montgomery64<__COUNTER__>;
  modular::set_mod(n);

  modular one=1,minus_one=n-1;
  fe(as,a){
    if(a%n==0)continue;
    ll t=d;
    modular y=modular(a).pow(t);
    while(t!=n-1&&y!=one&&y!=minus_one)y*=y,t<<=1;
    if(y!=minus_one&&~t&1)return 0;
  }
  return 1;
}
bool is_prime(ll n){
  if(~n&1)return n==2;
  if(n<=1)return 0;
  if(n<4759123141LL)return miller_rabin(n,{2,7,61});
  return miller_rabin(n,{2,325,9375,28178,450775,9780504,1795265022});
}
ll pollard_rho(ll n){
  if(~n&1)return 2;
  if(is_prime(n))return n;

  using modular=montgomery64<__COUNTER__>;
  modular::set_mod(n);

  modular R,one=1;
  auto f=[&](const modular&x){return x*x+R;};
  while(1){
    modular x,y,ys,q=one;
    R=rand(2,n),y=rand(2,n);
    ll g=1;
    constexpr ll m=128;
    for(ll r=1;g==1;r<<=1){
      x=y;
      FO(r)y=f(y);
      for(ll k=0;g==1&&k<r;k+=m){
        ys=y;
        for(ll i=0;i<m&&i<r-k;++i)q*=x-(y=f(y));
        g=std::gcd(q.val(),n);
      }
    }
    if(g==n)do g=std::gcd((x-(ys=f(ys))).val(),n);while(g==1);
    if(g!=n)return g;
  }
}
auto factorize(ll n){
  assert(n>0);
  vec<ll>res;
  auto f=[&](auto&f,ll m){
    if(m==1)return;
    auto d=pollard_rho(m);
    if(d==m)res.eb(d);
    else f(f,d),f(f,m/d);
  };
  f(f,n);
  return res.rce();
}
auto divisors(const vec<pair<ll,ll>>&factor){
  vec<ll>res{1};
  for(auto[p,q]:factor){
    ll m=res.size();
    for(ll t=p;q--;t*=p)fo(i,m)res.eb(res[i]*t);
  }
  return sort(res);
}
template<class T>auto divisors_multiple_enumerate(ll D,ll N,const vec<pair<T,T>>&factor){
  vec<T>res;

  vec<T>rem;
  T c=D;
  fe(factor,p,e){
    T q=0;
    while(c%p==0){
      c/=p;
      q++;
    }
    rem.eb(e-q);
  }

  auto dfs=[&](auto&dfs,ll k,ll x){
    if(k==factor.size()){
      res.eb(x);
      return;
    }

    auto[p,_]=factor[k];
    fo(i,rem[k]+1){
      dfs(dfs,k+1,x);
      x*=p;
    }
  };
  dfs(dfs,0,D);
  return res;
}
}
namespace my {
template<class T>auto divisors_factorize_enumerate(ll N){
  auto factor=factorize(N);
  vec<T>v;

  unordered_map<T,vec<T>>res;
  auto dfs=[&](auto&dfs,ll k,ll x){
    if(k==factor.size()){
      res[x]=v;
      return;
    }

    auto[p,e]=factor[k];
    fo(i,e+1){
      v.eb(i);
      dfs(dfs,k+1,x);
      x*=p;
      v.pop_back();
    }
  };
  dfs(dfs,0,1);
  return pair{factor,map<T,vec<T>>(res.begin(),res.end())};
}
}
namespace my{entry
void main(){
  LL(N);
  auto[factor,div_exps]=divisors_factorize_enumerate<ll>(N);
  ll P=factor.size(); // 素因数の個数

  auto div=divisors(factor);

  use_ml998244353

  ml ans=0;
  unordered_map<ll,ml>dp;
  dp[1]=1;
  fe(div,a){
    fe(divisors_multiple_enumerate<ll>(a,N,factor),b){
      if(a==b)continue;

      ml t=1;
      fo(i,P){
        if(div_exps[a][i]==div_exps[b][i])t*=div_exps[a][i]+1;
        else t*=1;
      }
      dp[b]+=dp[a]*t;
    }
  }

  pp(dp[N]);
}}
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