結果

問題 No.747 循環小数N桁目 Hard
ユーザー eQe
提出日時 2025-08-14 06:58:52
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 8 ms / 2,000 ms
コード長 8,102 bytes
コンパイル時間 4,317 ms
コンパイル使用メモリ 309,548 KB
実行使用メモリ 6,272 KB
最終ジャッジ日時 2025-08-14 06:59:03
合計ジャッジ時間 9,374 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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 * 4
other AC * 120
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>)
#endif
using namespace std;
#define eb emplace_back
#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{
namespace my{
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};}
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);}
auto encode_integer(char c){return c-'0';}
constexpr auto abs(auto x){return x<0?-x:x;}
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);}
bool amax(auto&a,const auto&b){return a<b?a=b,1:0;}
template<class T,class U>common_type_t<T,U>gcd(T a,U b){return b?gcd(b,a%b):abs(a);}
auto lcm(auto a,auto b){auto r=a/gcd(a,b);return!__builtin_mul_overflow(r,b,&r)?r:0;}
auto mod(auto a,auto b){return(a%=b)<0?a+b:a;}
auto inv_mod(auto x,auto m){assert(gcd(x,m)==1);decltype(x)a=mod(x,m),b=m,u=1,v=0;while(b)swap(u-=a/b*v,v),swap(a-=a/b*b,b);return mod(u,m);}
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...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 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>{
  using C=core_t<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 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;}
  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...>>>;
auto sin(){string s;lin(s);return s;}
template<class T=ll>auto sinen_integer(){vec<T>r;fe(sin(),e)r.eb(encode_integer(e));return r;}
}
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();
}
}
namespace my{
template<class T>T lcm(const vec<T>&a){T r=1;fe(a,e)r=lcm(r,e);return r;}
template<class T>pair<T,T>inv_gcd(T a,T b){
  a=mod(a,b);
  if(a==0)return{b,0};
  T s=b,t=a;
  T m0=0,m1=1;
  while(t){
    T u=s/t;
    s-=t*u;
    m0-=m1*u;
    swap(s,t);
    swap(m0,m1);
  }
  return{s,m0};
}
template<class T>auto canonicalize_congruence_system(const vec<T>&R,const vec<T>&M){
  unordered_map<T,pair<T,T>>max_exponent_congruence;
  fo(i,R.size())fe(factorize(M[i]),p,q)amax(max_exponent_congruence[p],pair{(T)q,R[i]});

  vec<T>r,m;
  fe(max_exponent_congruence,p,v){
    T pq=pow(p,v.a);
    r.eb(v.b%pq);
    m.eb(pq);
  }
  return tuple{r,m};
}
template<class T>T chinese_remainder_theorem_extended_euclidean(const vec<T>&R,const vec<T>&M){
  T r0=0,m0=1;
  fo(i,R.size()){
    T r1=mod(R[i],M[i]),m1=M[i];
    if(m0<m1)swap(r0,r1),swap(m0,m1);

    if(m0%m1==0){
      if(r0%m1!=r1)return-1;
      continue;
    }

    auto[g,im]=inv_gcd(m0,m1);
    if((r1-r0)%g)return-1;

    T u1=m1/g;
    T x=(r1-r0)/g%u1*im%u1;

    r0+=x*m0;
    m0*=u1;
    if(r0<0)r0+=m0;
  }
  return r0;
}
template<class T>T chinese_remainder_theorem_coprime_garner(const vec<T>&r,const vec<T>&m){
  ll K=r.size();
  vec<T>t(K),S(K+1),P(K+1,1);
  fo(i,K){
    t[i]=mod((r[i]-S[i])*inv_mod(P[i],m[i]),m[i]);
    fo(j,i+1,K+1){
      S[j]+=t[i]*P[j];
      P[j]*=m[i];
      if(j<K)S[j]%=m[j],P[j]%=m[j];
    }
  }
  return S[K];
}
template<class T>T chinese_remainder_theorem(const vec<T>&R,const vec<T>&M){
  if(lcm(M))return chinese_remainder_theorem_extended_euclidean(R,M);
  fo(i,R.size())fo(j,i+1,R.size())if((R[i]-R[j])%gcd(M[i],M[j]))return-1;
  auto[r,m]=canonicalize_congruence_system(R,M);
  return chinese_remainder_theorem_coprime_garner(r,m);
}
}
namespace my{entry
void main(){
  auto ns=sinen_integer();
  auto ks=sinen_integer();

  ll r2=ns.back()%2;
  ll r3=(ns.sum()%3==0?0:mod(pow(ns.sum()%3,ks.back()%2),3)); // ns.sum()%3!=0ならオイラーの定理
  vec<ll>ans{2,8,5,7,1,4};
  pp(ans[mod(chinese_remainder_theorem<ll>({r2,r3},{2,3})-1,6)]);
}}
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