結果

問題 No.136 Yet Another GCD Problem
コンテスト
ユーザー eQe
提出日時 2025-03-24 03:23:07
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 5,000 ms
コード長 8,963 bytes
コンパイル時間 7,023 ms
コンパイル使用メモリ 334,720 KB
実行使用メモリ 7,324 KB
最終ジャッジ日時 2025-03-24 03:23:16
合計ジャッジ時間 7,496 ms
ジャッジサーバーID
（参考情報） 		judge1 / 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 * 39
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>
#include<atcoder/all>
using namespace std;
namespace my{
#define eb emplace_back
#define LL(...) ll __VA_ARGS__;lin(__VA_ARGS__)
#define FO(n) for(ll ij=n;ij-->0;)
#define FOR(i,...) for(auto[i,i##stop,i##step]=range(0,__VA_ARGS__);i<i##stop;i+=i##step)
#define fo(i,...) FO##__VA_OPT__(R)(i __VA_OPT__(,__VA_ARGS__))
#define fe(a,e,...) for(auto&&__VA_OPT__([)e __VA_OPT__(,__VA_ARGS__]):a)
#define schrodinger(p,c) (p?c:remove_cvref_t<decltype(c)>{})
#define base_operator(op,type) auto operator op(const type&v)const{auto copy=*this;return copy op##=v;}
#define single_testcase void solve();}int main(){my::io();my::solve();}namespace my{
void io(){cerr<<endl;cin.tie(nullptr)->sync_with_stdio(0);cout<<fixed<<setprecision(15);}
using ll=long long;
using ull=unsigned long long;
using ulll=__uint128_t;
using lll=__int128_t;
istream&operator>>(istream&i,ulll&x){ull t;i>>t;x=t;return i;}
ostream&operator<<(ostream&o,const ulll&x){return(x<10?o:o<<x/10)<<ll(x%10);}
istream&operator>>(istream&i,lll&x){ll t;i>>t;x=t;return i;}
ostream&operator<<(ostream&o,const lll&x){return o<<(x<0?"-":"")<<ulll(x>0?x:-x);}
constexpr auto range(ll s,ll b){ll a=0;if(s)swap(a,b);return array{a-s,b,1-s*2};}
constexpr auto range(ll s,ll a,ll b,ll c=1){return array{a-s,b,(1-s*2)*c};}
const string newline{char(10)};
const string space{char(32)};
constexpr auto abs(auto x){return x<0?-x:x;}
constexpr auto pow(lll x,ll n){assert(n>=0);lll r=1;while(n)n&1?r*=x:r,x*=x,n>>=1;return r;}
template<class T,class U>common_type_t<T,U>gcd(T a,U b){return b?gcd(b,a%b):abs(a);}
auto gcd(auto...a){common_type_t<decltype(a)...>r=0;((r=gcd(r,a)),...);return r;}
auto mod(auto a,auto b){return(a%=b)<0?a+b:a;}

template<class A,class B>struct pair{
  A a;B b;
  pair()=default;
  pair(A a,B b):a(a),b(b){}
  pair(const std::pair<A,B>&p):a(p.first),b(p.second){}
  auto operator<=>(const pair&)const=default;
  pair operator+(const pair&p)const{return{a+p.a,b+p.b};}
  friend istream&operator>>(istream&i,pair&p){return i>>p.a>>p.b;}
  friend ostream&operator<<(ostream&o,const pair&p){return o<<p.a<<space<<p.b;}
};

template<class...A>using pack_back_t=tuple_element_t<sizeof...(A)-1,tuple<A...>>;

template<class V>concept vectorial=is_base_of_v<vector<typename remove_cvref_t<V>::value_type>,remove_cvref_t<V>>;
template<class V>constexpr int rank(){if constexpr(vectorial<V>)return rank<typename V::value_type>()+1;else return 0;}
template<class T>struct core_t_helper{using core_t=T;};
template<vectorial V>struct core_t_helper<V>{using core_t=typename core_t_helper<typename V::value_type>::core_t;};
template<class T>using core_t=core_t_helper<T>::core_t;
template<class V>istream&operator>>(istream&i,vector<V>&v){fe(v,e)i>>e;return i;}
template<class V>ostream&operator<<(ostream&o,const vector<V>&v){ll n=v.size();fo(i,n)o<<v[i]<<schrodinger(i<n-1,vectorial<V>?newline:space);return o;}

template<class V>struct vec;
template<int rank,class T>struct hvec_helper{using type=vec<typename hvec_helper<rank-1,T>::type>;};
template<class T>struct hvec_helper<0,T>{using type=T;};
template<int rank,class T>using hvec=typename hvec_helper<rank,T>::type;

template<class V>struct vec:vector<V>{
  static constexpr int R=rank<vec<V>>();
  using C=core_t<V>;
  using vector<V>::vector;
  vec(const vector<V>&v){vector<V>::operator=(v);}
  vec(const auto&...a)requires(sizeof...(a)>=3){resizes(a...);}
  void resizes(const auto&...a){*this=make(a...);}
  static auto make(ll n,const auto&...a){if constexpr(sizeof...(a)==1)return vec<C>(n,array{a...}[0]);else return vec<decltype(make(a...))>(n,make(a...));}

  vec&operator^=(const vec&u){this->insert(this->end(),u.begin(),u.end());return*this;}
  vec&operator+=(const vec&u){vec&v=*this;assert(v.size()==u.size());fo(i,v.size())v[i]+=u[i];return v;}
  vec&operator-=(const vec&u){vec&v=*this;assert(v.size()==u.size());fo(i,v.size())v[i]-=u[i];return v;}
  base_operator(^,vec)
  base_operator(+,vec)
  base_operator(-,vec)

  vec&operator++(){fe(*this,e)++e;return*this;}
  vec&operator--(){fe(*this,e)--e;return*this;}

  ll size()const{return vector<V>::size();}

  template<class F=less<>>auto sort(F f={})const{vec v=*this;ranges::sort(v,f);return v;}

  auto transform(const auto&f)const{
    hvec<R,decltype(f(C()))>res(size());
    if constexpr(vectorial<V>)fo(i,size())res[i]=(*this)[i].transform(f);
    else std::transform(this->begin(),this->end(),res.begin(),f);
    return res;
  }

  auto rle()const{vec<pair<V,ll>>r;fe(*this,e)r.size()&&e==r.back().a?++r.back().b:r.eb(e,1).b;return r;}
  auto rce()const{return sort().rle();}

  auto as()const{return transform([](const auto&e){return e.a;});}
};
template<class...A>requires(sizeof...(A)>=2)vec(const A&...a)->vec<hvec<sizeof...(A)-2,pack_back_t<A...>>>;
vec(ll)->vec<ll>;

auto pack_vec(const auto&...a){return vec<common_type_t<decltype(a)...>>{a...};}

void lin(auto&...a){(cin>>...>>a);}
void pp(const auto&...a){ll n=sizeof...(a);((cout<<a<<schrodinger(--n>0,space)),...);cout<<newline;}

template<class F=less<>>auto&sort(auto&a,F f={}){ranges::sort(a,f);return a;}

ll rand(){static ll x=495;x^=x<<7;x^=x>>9;return x;}
ll rand(ll l,ll r=0){if(l>r)swap(l,r);return rand()%(r-l)+l;}

struct montgomery64{
  using modular=montgomery64;
  using i64=__int64_t;
  using u64=__uint64_t;
  using u128=__uint128_t;

  static inline u64 N;
  static inline u64 N_inv;
  static inline u64 R2;

  static int set_mod(u64 N){
    if(modular::N==N)return 0;
    assert(N<(1ULL<<63));
    assert(N&1);
    modular::N=N;
    R2=-u128(N)%N;
    N_inv=N;
    fo(5)N_inv*=2-N*N_inv;
    assert(N*N_inv==1);
    return 0;
  }
  static inline int init=set_mod(998244353);

  static u64 mod(){return N;}

  u64 a;
  montgomery64(const i64&a=0):a(reduce((u128)(a%(i64)N+N)*R2)){}

  static u64 reduce(const u128&T){
    u128 r=(T+u128(u64(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(u128(a)*b.a);return*this;}
  auto&operator/=(const modular&b){*this*=b.inv();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 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;}
  auto operator-()const{return modular{}-modular{*this};}

  modular pow(u128 n)const{
    modular r{1},x{*this};
    while(n){
      if(n&1)r*=x;
      x*=x;
      n>>=1;
    }
    return r;
  }

  modular inv()const{u64 a=val(),b=N,u=1,v=0;assert(gcd(a,b)==1);while(b)swap(u-=a/b*v,v),swap(a-=a/b*b,b);return u;}
  u64 val()const{return reduce(a);}

  friend istream&operator>>(istream&i,montgomery64&b){ll t;i>>t;b=t;return i;}
  friend ostream&operator<<(ostream&o,const montgomery64&b){return o<<b.val();}
};

template<class T>T one(T n){return n>0;}

void sort(auto&...a){auto v=pack_vec(a...).sort();ll i=0;((a=v[i++]),...);}

bool miller_rabin(ll n,vec<ll>as){
  ll d=n-1;
  while(~d&1)d>>=1;

  using modular=montgomery64;
  auto pre_mod=modular::mod();
  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 modular::set_mod(pre_mod),0;
  }
  return modular::set_mod(pre_mod),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;
  auto pre_mod=modular::mod();
  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 modular::set_mod(pre_mod),g;
  }
}

auto factorize(ll n){
  assert(n>0);
  auto f=[](auto&f,ll m){
    if(m==1)return vec<ll>{};
    ll d=pollard_rho(m);
    return d==m?vec<ll>{d}:f(f,d)^f(f,m/d);
  };
  return f(f,n).rce();
}

auto divisors(const vec<pair<ll,ll>>&prime_exponent){
  vec<ll>r{1};
  for(auto[p,e]:prime_exponent){
    ll sz=size(r);
    for(ll t=p;e;--e,t*=p)fo(i,sz)r.eb(r[i]*t);
  }
  return sort(r);
}

vec<ll>divisors(ll n){return divisors(factorize(n));}

single_testcase
void solve(){
  LL(K,N);
  pp(divisors(K).end()[-2]);
}}
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