#999353 (C++17) No.2829 GCD Divination

提出ソース
結果

問題	No.2829 GCD Divination
ユーザー	hamamu
提出日時	2024-08-02 22:33:36
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	170 ms / 2,000 ms
コード長	40,830 bytes
コンパイル時間	6,314 ms
コンパイル使用メモリ	316,808 KB
実行使用メモリ	87,864 KB
最終ジャッジ日時	2024-08-02 22:33:46
合計ジャッジ時間	10,152 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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テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	1 ms 6,812 KB
testcase_01	AC	2 ms 6,944 KB
testcase_02	AC	167 ms 87,864 KB
testcase_03	AC	2 ms 6,944 KB
testcase_04	AC	167 ms 87,764 KB
testcase_05	AC	150 ms 76,584 KB
testcase_06	AC	124 ms 64,148 KB
testcase_07	AC	107 ms 57,932 KB
testcase_08	AC	69 ms 39,836 KB
testcase_09	AC	56 ms 33,948 KB
testcase_10	AC	82 ms 50,120 KB
testcase_11	AC	5 ms 6,940 KB
testcase_12	AC	22 ms 18,696 KB
testcase_13	AC	146 ms 78,512 KB
testcase_14	AC	92 ms 54,080 KB
testcase_15	AC	66 ms 39,720 KB
testcase_16	AC	28 ms 20,448 KB
testcase_17	AC	15 ms 12,708 KB
testcase_18	AC	10 ms 10,296 KB
testcase_19	AC	18 ms 15,400 KB
testcase_20	AC	2 ms 6,944 KB
testcase_21	AC	49 ms 34,060 KB
testcase_22	AC	66 ms 40,532 KB
testcase_23	AC	75 ms 46,980 KB
testcase_24	AC	132 ms 69,700 KB
testcase_25	AC	170 ms 85,536 KB
testcase_26	AC	56 ms 37,488 KB
testcase_27	AC	116 ms 64,308 KB
testcase_28	AC	19 ms 15,904 KB
testcase_29	AC	62 ms 40,552 KB
testcase_30	AC	158 ms 81,872 KB
testcase_31	AC	15 ms 12,844 KB
testcase_32	AC	88 ms 49,124 KB
testcase_33	AC	55 ms 36,284 KB
testcase_34	AC	117 ms 63,664 KB
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ソースコード

raw source code
#if !defined(MYLOCAL)//提出時用テンプレート

#pragma GCC optimize("Ofast")
#if defined(NDEBUG)
#undef NDEBUG
#endif
#include "bits/stdc++.h"
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif
using namespace std;
using ll=long long;
using dd=long double;
using pll=pair<ll,ll>;
using tll=tuple<ll,ll,ll>;
using qll=tuple<ll,ll,ll,ll>;
using ll2=array<ll,2>;
using ll3=array<ll,3>;
using ll4=array<ll,4>;
using namespace chrono;
constexpr ll INF = 1201001001001001001;
struct Fast{ Fast(){ cin.tie(0); ios::sync_with_stdio(false); cout<<fixed<<setprecision(numeric_limits<double>::max_digits10); } } fast;
#define EXPAND( x ) x//VS用おまじない
#define overload3(_1,_2,_3,name,...) name
#define overload4(_1,_2,_3,_4,name,...) name
#define overload5(_1,_2,_3,_4,_5,name,...) name
#define rep1(N)          for (ll dmyi = 0; dmyi < (N); dmyi++)
#define rep2(i, N)       for (ll i = 0; i < (N); i++)
#define rep3(i, S, E)    for (ll i = (S); i <= (E); i++)
#define rep4(i, S, E, t) for (ll i = (S); i <= (E); i+=(t))
#define rep(...) EXPAND(overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__))
#define dep3(i, E, S)    for (ll i = (E); i >= (S); i--)
#define dep4(i, E, S, t) for (ll i = (E); i >= (S); i-=(t))
#define dep(...) EXPAND(overload4(__VA_ARGS__, dep4, dep3,_,_)(__VA_ARGS__))
#define ALL1(v)     (v).begin(),     (v).end()
#define ALL2(v,E)   (v).begin(),     (v).begin()+((E)+1)
#define ALL3(v,S,E) (v).begin()+(S), (v).begin()+((E)+1)
#define all(...) EXPAND(overload3(__VA_ARGS__, ALL3, ALL2, ALL1)(__VA_ARGS__))
#define RALL1(v)     (v).rbegin(),     (v).rend()
#define RALL2(v,E)   (v).rbegin(),     (v).rbegin()+((E)+1)
#define RALL3(v,S,E) (v).rbegin()+(S), (v).rbegin()+((E)+1)
#define rall(...) EXPAND(overload3(__VA_ARGS__, RALL3, RALL2, RALL1)(__VA_ARGS__))
template<class T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; }return false; }
template<class T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; }return false; }
template<class T> inline auto maxe(T &&v,ll S,ll E){ return *max_element(all(v,S,E)); }
template<class T> inline auto maxe(T &&v){ return *max_element(all(v)); }
template<class T> inline auto mine(T &&v,ll S,ll E){ return *min_element(all(v,S,E)); }
template<class T> inline auto mine(T &&v){ return *min_element(all(v)); }
template<class T,class U=typename remove_reference<T>::type::value_type>
inline U sum(T &&v,ll S,ll E) {return accumulate(all(v,S,E),U());}
template<class T> inline auto sum(T &&v) {return sum(v,0,v.end()-v.begin()-1);}
template<class T> inline ll sz(T &&v){ return (ll)v.size(); }
inline ll Ceil(ll a,ll b){ return (a<0) ? -(-a/b) : (a+b-1)/b; } //負もOK
inline ll Floor(ll a,ll b){ return -Ceil(-a,b); } //負もOK
template<class T> inline T Pow(T a,ll n){ T r=1; for(; n>0; n>>=1,a*=a){ if(n&1)r*=a; } return r; }
inline ll Pow(int a,ll n){ return Pow((ll)a,n); }
ll limitmul(ll a,ll b,ll u){ return b==0||a<=u/b ? a*b : u; }//min(a*b,u) a,b,u≧0

//pair用テンプレート
template<class T,class S> inline pair<T,S>& operator+=(pair<T,S> &a,const pair<T,S> &b){ a.first+=b.first; a.second+=b.second; return a; }
template<class T,class S> inline pair<T,S>& operator-=(pair<T,S> &a,const pair<T,S> &b){ a.first-=b.first; a.second-=b.second; return a; }
template<class T,class S> inline pair<T,S>& operator*=(pair<T,S> &a,const pair<T,S> &b){ a.first*=b.first; a.second*=b.second; return a; }
template<class T,class S> inline pair<T,S>& operator/=(pair<T,S> &a,const pair<T,S> &b){ a.first/=b.first; a.second/=b.second; return a; }
template<class T,class S> inline pair<T,S>& operator%=(pair<T,S> &a,const pair<T,S> &b){ a.first%=b.first; a.second%=b.second; return a; }
template<class T,class S,class R> inline pair<T,S>& operator+=(pair<T,S> &a,R b){ a.first+=b; a.second+=b; return a; }
template<class T,class S,class R> inline pair<T,S>& operator-=(pair<T,S> &a,R b){ a.first-=b; a.second-=b; return a; }
template<class T,class S,class R> inline pair<T,S>& operator*=(pair<T,S> &a,R b){ a.first*=b; a.second*=b; return a; }
template<class T,class S,class R> inline pair<T,S>& operator/=(pair<T,S> &a,R b){ a.first/=b; a.second/=b; return a; }
template<class T,class S,class R> inline pair<T,S>& operator%=(pair<T,S> &a,R b){ a.first%=b; a.second%=b; return a; }
template<class T,class S,class R> inline pair<T,S> operator+(const pair<T,S> &a,R b){ pair<T,S> c=a; return c+=b; }
template<class T,class S,class R> inline pair<T,S> operator-(const pair<T,S> &a,R b){ pair<T,S> c=a; return c-=b; }
template<class T,class S,class R> inline pair<T,S> operator*(const pair<T,S> &a,R b){ pair<T,S> c=a; return c*=b; }
template<class T,class S,class R> inline pair<T,S> operator/(const pair<T,S> &a,R b){ pair<T,S> c=a; return c/=b; }
template<class T,class S,class R> inline pair<T,S> operator%(const pair<T,S> &a,R b){ pair<T,S> c=a; return c%=b; }
template<class T,class S,class R> inline pair<T,S> operator-(R b,const pair<T,S> &a){ pair<T,S> c=-a; return c+=b; }
template<class T,class S> inline pair<T,S> operator-(const pair<T,S> &a,const pair<T,S> &b){ pair<T,S> c=a; return c-=b; }
template<class T,class S> inline pair<T,S> operator-(const pair<T,S> &a){ pair<T,S> c=a; return c*=(-1); }
template<class T,class S> inline ostream &operator<<(ostream &os,const pair<T,S> &a){ return os << a.first << ' ' << a.second; }

//tuple用テンプレート 出力用のみ
template<class T,class S,class R> inline ostream &operator<<(ostream &os,const tuple<T,S,R> &a){ return os << get<0>(a) << ' ' << get<1>(a) << ' ' << get<2>(a); }
template<class T,class S,class R,class Q> inline ostream &operator<<(ostream &os,const tuple<T,S,R,Q> &a){ return os << get<0>(a) << ' ' << get<1>(a) << ' ' << get<2>(a) << ' ' << get<3>(a); }

//vector用テンプレート
template<class T> inline ostream &operator<<(ostream &os,const vector<T> &a){ for (ll i=0; i<(ll)a.size(); i++) os<<(i>0?" ":"")<<a[i];  return os; }

//array用テンプレート
template<class T,size_t S> inline array<T,S>& operator+=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]+=b[i];  return a; }
template<class T,size_t S> inline array<T,S>& operator-=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]-=b[i];  return a; }
template<class T,size_t S> inline array<T,S>& operator*=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]*=b[i];  return a; }
template<class T,size_t S> inline array<T,S>& operator/=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]/=b[i];  return a; }
template<class T,size_t S> inline array<T,S>& operator%=(array<T,S> &a,const array<T,S> &b){ for (ll i=0; i<(ll)S; i++) a[i]%=b[i];  return a; }
template<class T,size_t S,class R> inline array<T,S>& operator+=(array<T,S> &a,R b){ for (T &e: a) e+=b;  return a; }
template<class T,size_t S,class R> inline array<T,S>& operator-=(array<T,S> &a,R b){ for (T &e: a) e-=b;  return a; }
template<class T,size_t S,class R> inline array<T,S>& operator*=(array<T,S> &a,R b){ for (T &e: a) e*=b;  return a; }
template<class T,size_t S,class R> inline array<T,S>& operator/=(array<T,S> &a,R b){ for (T &e: a) e/=b;  return a; }
template<class T,size_t S,class R> inline array<T,S>& operator%=(array<T,S> &a,R b){ for (T &e: a) e%=b;  return a; }
template<class T,size_t S,class R> inline array<T,S> operator+(const array<T,S> &a,R b){ array<T,S> c=a; return c+=b; }
template<class T,size_t S,class R> inline array<T,S> operator-(const array<T,S> &a,R b){ array<T,S> c=a; return c-=b; }
template<class T,size_t S,class R> inline array<T,S> operator*(const array<T,S> &a,R b){ array<T,S> c=a; return c*=b; }
template<class T,size_t S,class R> inline array<T,S> operator/(const array<T,S> &a,R b){ array<T,S> c=a; return c/=b; }
template<class T,size_t S,class R> inline array<T,S> operator%(const array<T,S> &a,R b){ array<T,S> c=a; return c%=b; }
template<class T,size_t S,class R> inline array<T,S> operator-(R b,const array<T,S> &a){ array<T,S> c=-a; return c+=b; }
template<class T,size_t S> inline array<T,S> operator-(const array<T,S> &a,const array<T,S> &b){ array<T,S> c=a; return c-=b; }
template<class T,size_t S> inline array<T,S> operator-(const array<T,S> &a){ array<T,S> c=a; return c*=(-1); }
template<class T,size_t S> inline ostream &operator<<(ostream &os,const array<T,S> &a){ for (ll i=0; i<(ll)S; i++) os<<(i>0?" ":"")<<a[i];  return os; }

struct cinutil{
  template<class T> static void cin1core(T &a){ cin>>a; }
  template<class T,class S> static void cin1core(pair<T,S> &a){
    cin1core(a.first), cin1core(a.second);
  }
  template<class... Args> static void cin1core(tuple<Args...> &a){
    cinTplRec<tuple<Args...>,sizeof...(Args)-1>()(a);
  }
  template<class T,size_t N>
  static void cin1core(array<T,N> &a){for(int i=0;i<(int)N;++i) cin>>a[i];}
private:
  template<class Tpl,int i> struct cinTplRec{
    void operator()(Tpl &a){ cinTplRec<Tpl,i-1>()(a); cin1core(get<i>(a)); }
  };
  template<class Tpl> struct cinTplRec<Tpl,0>{
    void operator()(Tpl &a){ cin1core(get<0>(a)); }
  };
};
template<class T> T cin1(){ T a; cinutil::cin1core(a); return a; }
template<class... Args> tuple<Args...> cins(){ return cin1<tuple<Args...>>(); }


template<long long MOD> struct mll_{
  using Int = long long;
  using ll = long long;
  ll val_=0;
  /*---- utility ----*/
  mll_ &norm(){ return normR().normS(); }//正規化
  mll_ &normR(){ val_%=MOD; return *this; }//剰余正規化のみ
  mll_ &normS(){ if (val_<0) val_+=MOD; return *this; }//正負正規化のみ
  mll_ &normP(){ if (val_>=MOD) val_-=MOD; return *this; }//加算時正規化
  mll_ &invsg(){ val_=-val_; return normS(); }//正負反転
  ll modinv(int a){//a^-1 mod MOD
    int ypre=0,y=1,apre=MOD;
    while (a>1){
      int t=apre/a;
      apre-=a*t,swap(a,apre);
      ypre-=y*t,swap(y,ypre);
    }
    return y<0 ? y+MOD: y;
  }
  /*---- I/F ----*/
  mll_(){}
  mll_(ll v): val_(v){ norm(); }
  mll_(ll v,bool b): val_(v){} //正規化無のコンストラクタ
  Int val()const{ return (Int)val_; }
  bool isnone() const { return val_==-1; } //true:値なし
  mll_ &none() { val_=-1; return *this; } //値なしにする
  mll_ &inv(){ val_=modinv((int)val_); return *this; }
  mll_ &operator+=(mll_ b){ val_+=b.val_; return normP(); }
  mll_ &operator-=(mll_ b){ val_-=b.val_; return normS(); }
  mll_ &operator*=(mll_ b){ val_*=b.val_; return normR(); }
  mll_ &operator/=(mll_ b){ return *this*=b.inv(); }
  mll_ &operator+=(ll b){ return *this+=mll_(b); }
  mll_ &operator-=(ll b){ return *this-=mll_(b); }
  mll_ &operator*=(ll b){ return *this*=mll_(b); }
  mll_ &operator/=(ll b){ return *this/=mll_(b); }
  mll_ operator-()const{ return mll_(*this).invsg(); }
  mll_ operator+(mll_ b)const{ return mll_(*this)+=b; }
  mll_ operator-(mll_ b)const{ return mll_(*this)-=b; }
  mll_ operator*(mll_ b)const{ return mll_(*this)*=b; }
  mll_ operator/(mll_ b)const{ return mll_(*this)/=b; }
  mll_ operator+(ll b)const{ return mll_(*this)+=b; }
  mll_ operator-(ll b)const{ return mll_(*this)-=b; }
  mll_ operator*(ll b)const{ return mll_(*this)*=b; }
  mll_ operator/(ll b)const{ return mll_(*this)/=b; }
  friend mll_ operator+(ll a,mll_ b){ return b+a; }
  friend mll_ operator-(ll a,mll_ b){ return -b+a; }
  friend mll_ operator*(ll a,mll_ b){ return b*a; }
  friend mll_ operator/(ll a,mll_ b){ return mll_(a)/b; }
  bool operator==(mll_ b)const{ return val_==b.val_; }
  bool operator!=(mll_ b)const{ return val_!=b.val_; }
  bool operator==(ll b)const{ return *this==mll_(b); }
  bool operator!=(ll b)const{ return *this!=mll_(b); }
  friend bool operator==(ll a,mll_ b){ return mll_(a)==b; }
  friend bool operator!=(ll a,mll_ b){ return mll_(a)!=b; }
  friend ostream &operator<<(ostream &os,mll_  a){ return os << a.val_; }
  friend istream &operator>>(istream &is,mll_ &a){ return is >> a.val_; }
  mll_ pow(ll k)const{
    mll_ ret(1,false),a(*this);
    for (; k>0; k>>=1,a*=a) if (k&1)ret*=a;
    return ret;
  }
  static constexpr int mod() { return MOD; }
  //enum{ modll=MOD };
};


struct bll{ //第0～62bitまで対応
  ll s;
  bll(ll s_=0): s(s_){}
  struct ref {
    bll &b; const ll msk;
    ref(bll &b_,ll pos):b(b_),msk(1LL<<pos){}
    operator ll() const { return (b.s&msk)!=0; }
    ref &operator=(bool x){ if(x) b.s|=msk; else b.s&=~msk; return *this; }
  };
  ref operator[](ll pos){ return ref(*this,pos); }
  ll operator[](ll pos) const { return (s>>pos)&1; }
  bll &operator=(ll b){ s=b; return *this; }
  bll operator++(int){ bll b(*this); s++; return b; }
  bll operator--(int){ bll b(*this); s--; return b; }
  operator ll() const noexcept { return s; }
  bll &on(ll l,ll r){ s|= rangemask(l,r); return *this; }
  bll &off(ll l,ll r){ s&=~rangemask(l,r); return *this; }
  bll &flip(ll l,ll r){ s^= rangemask(l,r); return *this; }
  bll &on(ll i){ s|= (1LL<<i); return *this; }
  bll &off(ll i){ s&=~(1LL<<i); return *this; }
  bll &flip(ll i){ s^= (1LL<<i); return *this; }
  static ll rangemask(ll l,ll r){ return (1LL<<(r+1))-(1LL<<l); }
  ll msbit()const{
    for(ll o=63,x=-1;;){
      ll m=(o+x)/2;
      if(s < (1LL<<m)) o=m; else x=m;
      if(o-x==1) return x;
    }
  }
  ll lsbit()const{ return bll(lsb()).msbit(); }
  ll msb()const{ ll pos=msbit(); return (pos<0) ? 0LL : 1LL<<pos; }
  ll lsb()const{ return s&-s; }
  ll count()const{ return bitset<64>(s).count(); }
  vector<ll> idxes()const{
    vector<ll> v;
    for(ll i=0,t=s; t; t>>=1,i++) if(t&1)v.push_back(i);
    return v;
  }
};


template<class T> struct SET: set<T>{
  using P=set<T>;
  typename P::iterator it=P::end();
  template<class...Args> SET(Args...args): P(args...){}
  SET(initializer_list<T> a): P(a.begin(),a.end()){}
  ll size() const { return (ll)P::size(); }
  bool insert(const T &x){ bool r; tie(it,r)=P::insert(x); return r; }
  template <class It> void insert(It st,It en){ P::insert(st,en); }
  void insert(initializer_list<T> a){ P::insert(a.begin(),a.end()); }
  template<class...A> bool emplace(A&&...a){ bool r; tie(it,r)=P::emplace(a...); return r; }
  void eraseit(){ it=P::erase(it); }
  void find(const T &x){ it=P::find(x); }
  bool contains(const T &x){ return P::count(x)==1; }
  void lower_bound(const T &x){ it=P::lower_bound(x); }
  void upper_bound(const T &x){ it=P::upper_bound(x); }
  bool isend() { return it==P::end(); }
  T getit() { return *it; }
  T next() { return *(++it); }
  T prev() { return *(--it); }
  bool nextok() { return !isend() && it!=--P::end(); }
  bool prevok() { return it!=P::begin(); }
  T front() { return *(it=P::begin()); }
  T back()  { return *(it=--P::end()); }
  void pop_front(){ front(); eraseit(); }
  void pop_back(){ back(); eraseit(); }
  void push_front(const T &x){ it=P::insert(P::begin(),x); }
  void push_back (const T &x){ it=P::insert(P::end(),x); }
  void push_out(SET &b){ b.push_front(back()); pop_back(); }
  void pull_in(SET &b){ push_back(b.front()); b.pop_front(); }
};


template<class T> struct cumulativesum{
  using Int = long long;
  using ll = long long;
  ll n=0;  vector<T> c;
  cumulativesum():c(1){}
  template<class S> cumulativesum(S &&v): n((ll)v.size()),c(n+1) { Ini(v); }
  template<class S> void init(S &&v){ n=(ll)v.size(); c.resize(n+1); Ini(v); }
  void add(T x) { n++; c.push_back(c.back()+x); }
  T operator()(Int l,Int r){ return c[max(min(n,r+1),0LL)]-c[min(max(0LL,l),n)]; }
  pair<Int,T> group(T i){
    ll g=upper_bound(c.begin(),c.end(),i)-c.begin()-1;
    T r = g>=0 ? i-c[g] : i;
    return {g,r};
  }
  T mx(){//区間和max
    T mn=T(),samx=0;
    for(ll i=1;i<=n;++i){
      chmax(samx,c[i]-mn);
      chmin(mn,c[i]);
    }
    return samx;
  }
  template<class S> void Ini(S &&v) { for(ll i=0;i<n;++i) c[i+1]=c[i]+v[i]; }
};
template<class S> cumulativesum(S) -> cumulativesum<typename remove_reference<S>::type::value_type>;


template<class T> vector<T> powers(T m,ll n){
  vector<T> ret(n+1,1);
  for(ll i=1;i<=n;++i) ret[i]=ret[i-1]*m;
  return ret;
}


template <class T> auto runlength(T &&v){
  vector<pair<typename remove_reference<T>::type::value_type,ll>> ret;
  for(auto&&e:v){
    if(ret.empty() or ret.back().first!=e) ret.emplace_back(e,1);
    else ret.back().second++;
  }
  return ret;
}


template<class T> struct combination{
  vector<T> f,g; ll mxN=0;
  combination(){}
  combination(ll maxN): f(maxN+1,1),g(maxN+1),mxN(maxN) {
    for (ll i=1;i<=mxN;++i) { f[i]=f[i-1]*i; }
    g[mxN]=1/f[mxN];
    for (ll i=mxN;i>=1;--i) { g[i-1]=g[i]*i; }
  }
  T P(ll n,ll r){ return (n<0 || r<0 || n<r) ? T(0) : f[n]*g[n-r]; } //nPr
  T H(ll n,ll r){ return operator()(n+r-1,n-1); }//nHr
  T inv(ll n) { return f[n-1] * g[n]; } //1/n
  T fact(ll n) { return f[n]; } //n!
  T finv(ll n) { return g[n]; } //1/n!
  T operator()(ll n,ll r){
    if (r<0) return 0;
    if (n<0) return operator()(-n+r-1,r) * ((r&1)?-1:1); //-nＣr = (-1)^r * n+r-1Ｃr
    if (n<r) return 0;
    if (n<=mxN) return f[n]*g[n-r]*g[r]; //通常
    //n巨大、rかn-r小
    if (n-r<r) r=n-r;
    T bunsi=1,bunbo=1;
    for (ll i=0;i<r;++i) bunsi*=n-i;
    for (ll i=0;i<r;++i) bunbo*=i+1;
    return bunsi/bunbo;
  }
  template<class SP>
  vector<T> CnLnR(long long nL,long long nR,long long r,SP sp){
    if (nR-nL+1<=0) return vector<T>();
    if (r<0) return vector<T>(nR-nL+1,0);
    vector<T> v=sp(nL-r+1,nR-r+1,r);
    for (T& e: v) e*=finv(r);
    return v;
  }
  template<class SP>
  vector<T> HrLrR(long long n,long long rL,long long rR,SP sp){//r<0不可
    return CnLnR(n-1+rL,n-1+rR,n-1,sp);
  }
};


template<class T> struct wrapVector1d{
  using S=typename T::value_type;
  using Int = long long;
  const T *v;
  S Ini;
  wrapVector1d(const T &v_,S ini_=S()):v(&v_),Ini(ini_){}
  S operator[](Int i)const{ return (i<0 || (Int)v->size()<=i) ? Ini : (*v)[i]; }
};
template<class T> struct wrapVector2d{
  using S=typename T::value_type;
  using Int = long long;
  const vector<T> *v;
  S Ini;
  T dmy;
  wrapVector2d(const vector<T> &v_,S ini_=S()):v(&v_),Ini(ini_){}
  wrapVector1d<T> operator[](ll i)const{
    return (i<0 || (Int)v->size()<=i) ?
      wrapVector1d(dmy,Ini) : wrapVector1d((*v)[i],Ini);
  }
};


namespace dumpstring{//dummy
struct args{
  using Int = long long;
  args(){}
  args &wd(Int wd__){ return *this; }
  template<size_t DIM> args &rngs(array<array<Int,DIM>,2> rngs){ return *this; }
  args &tr(vector<Int> tr__){ return *this; }
  args &tr(){ return *this; }
  args &labels(vector<string> labels__){ return *this; }
  args &xrev(){ return *this; }
  args &yrev(){ return *this; }
  args &zrev(){ return *this; }
  args &wrev(){ return *this; }
};
template<class NdT>
void dumpNd(const string &h,const NdT &fd,const args &p=args(),ostream &os=cerr){}
};
using dumpstring::args; using dumpstring::dumpNd;

#endif//テンプレートend

struct{
  system_clock::time_point st = system_clock::now();
  ll operator()()const{return duration_cast<microseconds>(system_clock::now()-st).count()/1000;}
} timeget;
//////////////////////////////////////////

template<class T> struct Vector: vector<T>{
  using Int = long long;
  using vT=vector<T>;
  using cvT=const vector<T>;
  using cT=const T;
  using vT::vT; //親クラスのコンストラクタの隠蔽を回避
  using vT::begin,vT::end,vT::insert,vT::erase;
  auto it(Int i){ return begin()+i; }
  auto it(Int i)const{ return begin()+i; }
  Vector(cvT& b):vT(b){}
  Vector(vT&& b):vT(move(b)){}
  template<class S> Vector(const Vector<S>& b):vT(b.begin(),b.end()){}
  template<class S> Vector(const vector<S>& b):vT(b.begin(),b.end()){}
  Vector(Int n,T s,T d){ iota(n,s,d); }
  Vector(Int n,function<T(Int)> g):vT(n){ for (Int i=0;i<n;++i) (*this)[i]=g(i); }
  template<class S> Vector &operator+=(S x){ for (T &e: *this) e+=x;  return *this; }
  template<class S> Vector &operator-=(S x){ for (T &e: *this) e-=x;  return *this; }
  template<class S> Vector &operator*=(S x){ for (T &e: *this) e*=x;  return *this; }
  template<class S> Vector &operator/=(S x){ for (T &e: *this) e/=x;  return *this; }
  template<class S> Vector &operator%=(S x){ for (T &e: *this) e%=x;  return *this; }
  template<class S> Vector operator+(S x)const{ return Vector(*this)+=x; }
  template<class S> Vector operator-(S x)const{ return Vector(*this)-=x; }
  template<class S> Vector operator*(S x)const{ return Vector(*this)*=x; }
  template<class S> Vector operator/(S x)const{ return Vector(*this)/=x; }
  template<class S> Vector operator%(S x)const{ return Vector(*this)%=x; }
  Vector operator-()const{ return Vector(*this)*=-1; }
  template<class S> friend Vector operator-(S x,const Vector &a){ return -a+=x; }
  Int size()const{ return (Int)vT::size(); }
  Vector &push_back(cT& x){ vT::push_back(x); return *this; }
  Vector &pop_back(){ vT::pop_back(); return *this; }
  Vector &push_front(cT& x){ insert(begin(),x); return *this; }
  Vector &pop_front(){ erase(0); return *this; }
  T pull_back(){ T x=move(vT::back()); vT::pop_back(); return x; }
  T pull_front(){ T x=move(vT::front()); erase(0); return x; }
  Vector &insert(Int i,cT& x){ insert(it(i),x); return *this; }
  Vector &insert(Int i,cvT& b){ insert(it(i),b.begin(),b.end()); return *this; }
  Vector &erase(Int i){ erase(it(i)); return *this; }
  Vector &erase(Int l,Int r){ erase(it(l),it(r+1)); return *this; }
  Vector &concat(cvT &b){ insert(end(),b.begin(),b.end()); return *this; }
  Vector &concat(cvT &b,Int n){ for (int i=0;i<n;++i) concat(b); return *this; }
  Vector &repeat(Int n){ concat(vT(*this),n-1); return *this; }
  Vector &reverse(){ std::reverse(begin(),end()); return *this; }
  Vector &sort(){ std::sort(begin(),end()); return *this; }
  Vector &rsort(){ std::sort(vT::rbegin(),vT::rend()); return *this; }
  template<class Pr> Vector &sort(Pr pr){ std::sort(begin(),end(),pr); return *this; }
  Vector &uniq(){ erase(unique(begin(),end()),end()); return *this; }
  Vector &sortq(){ return sort().uniq(); }
  Vector &fill(Int l,Int r,cT& x){ std::fill(it(l),it(r+1),x); return *this; }
  template<class S=Int> Vector &iota(Int n,T s=0,S d=1){
    vT::resize(n);
    if (n==0) return *this;
    (*this)[0]=s;
    for (int i=1;i<n;++i) (*this)[i]=(*this)[i-1]+d;
    return *this;
  }
  Int count(cT& x)const{ return Int(std::count(begin(),end(),x)); }
  Int count(Int l,Int r,cT& x)const{ return Int(std::count(it(l),it(r+1),x)); }
  template<class Pr> Int countif(Pr pr)const{ return Int(count_if(begin(),end(),pr)); }
  template<class Pr> Int countif(Int l,Int r,Pr pr)const{ return Int(count_if(it(l),it(r+1),pr)); }
  Int find(cT& x)const{ return Int(std::find(begin(),end(),x)-begin()); }
  Int find(Int l,Int r,cT& x)const{ return Int(std::find(it(l),it(r+1),x)-begin()); }
  template<class Pr> Int findif(Pr pr)const{ return Int(find_if(begin(),end(),pr)-begin()); }
  template<class Pr> Int findif(Int l,Int r,Pr pr)const{ return Int(find_if(it(l),it(r+1),pr)-begin()); }
  Vector<Int> findall(cT& x)const{ return findall(0,size()-1,x); }
  Vector<Int> findall(Int l,Int r,cT& x)const{ return findallif(l,r,[&](cT& y){return y==x;}); }
  template<class Pr> Vector<Int> findallif(Pr pr)const{ return findallif(0,size()-1,pr); }
  template<class Pr> Vector<Int> findallif(Int l,Int r,Pr pr)const{
    Vector<Int> ret;
    for (Int i=l;i<=r;++i) if (pr((*this)[i])) ret.push_back(i);
    return ret;
  }
  Int  flooridx(cT& x)const{ return Int(upper_bound(begin(),end(),x)-begin()-1); }
  Int   ceilidx(cT& x)const{ return Int(lower_bound(begin(),end(),x)-begin()); }
  Int  leftnmof(cT& x)const{ return flooridx(x)+1; }
  Int rightnmof(cT& x)const{ return size()-ceilidx(x); }
  bool contains(cT& x)const{ Int i=flooridx(x); return i>=0 && (*this)[i]==x; }
  template<class Pr> Int  flooridx(cT& x,Pr pr)const{ return Int(upper_bound(begin(),end(),x,pr)-begin()-1); }
  template<class Pr> Int   ceilidx(cT& x,Pr pr)const{ return Int(lower_bound(begin(),end(),x,pr)-begin()); }
  template<class Pr> Int  leftnmof(cT& x,Pr pr)const{ return flooridx(x,pr)+1; }
  template<class Pr> Int rightnmof(cT& x,Pr pr)const{ return size()-ceilidx(x,pr); }
  template<class Pr> bool contains(cT& x,Pr pr)const{ Int i=flooridx(x,pr); return i>=0 && (*this)[i]==x; }
};
/*
vll a={9,8,7},b={1,2,3};
vpll p={{5,3},{7,8},{0,2},};
- -------- 操作系 --------
a+=x a-=x a*=x a/=x a%=x a+x a-x a*x a/x a%x -a x-a  //∀i a[i]にxを演算
a.push_front(x);
a.push_back(x);
a.pop_front();
a.pop_back();
a.insert(i,x); //a[i]にx挿入
a.insert(i,b); //a[i]にvll b挿入
a.erase(i);    //a[i]削除
a.erase(l,r);  //区間[l,r]削除
a.concat(b);   //aにbを結合
a.concat(b,n); //aにbをn回結合
a.repeat(n);   //aをn回繰り返す
a.reverse(); //反転
a.sort();    //ソート
a.rsort();   //逆順ソート
p.sort([&](pll x,pll y){return x.second<y.second;});//比較関数指定ソート
a.uniq();      //連続同値を1つにする
a.sortq();     //ソートしてユニーク
a.fill(l,r,x); //[l,r]にx代入
a.iota(n,s,d); //aを等差数列にする 長さn,初項s,公差d
vll a(n,s,d);  //コンストラクタ版iota
- -------- 検索系 --------
auto pr=[&](auto &x){ return x>0; };  //検索条件
ll m=a.count(x);     //xの個数
ll m=a.count(l,r,x); //xの個数in[l,r]
ll m=a.countif(pr);     //条件満たす個数
ll m=a.countif(l,r,pr); //条件満たす個数in[l,r]
ll i=a.find(x);         //xの最左位置i         ない時N(配列長)
ll i=a.find(l,r,x);     //xの最左位置i in[l,r] ない時r+1
ll i=a.findif(pr);      //条件満たす最左位置i         ない時N(配列長)
ll i=a.findif(l,r,pr);  //条件満たす最左位置i in[l,r] ない時r+1
vll is=a.findall(x);        //xの位置i列挙
vll is=a.findall(l,r,x);    //xの位置i列挙in[l,r]
vll is=a.findallif(pr);     //条件満たす位置i列挙
vll is=a.findallif(l,r,pr); //条件満たす位置i列挙in[l,r]
- -------- 昇順sort済み配列用 --------
ll i=a.flooridx(x);   //x以下の最近傍位置i ない時-1
ll i=a.ceilidx(x);    //x以上の最近傍位置i ない時N(配列長)
ll m=a.leftnmof(x);   //x以下の個数
ll m=a.rightnmof(x);  //x以上の個数
bool b=a.contains(x); //xを含む
- -------- 比較関数prでsort済みの配列用 --------
auto pr=[&](auto &x,auto &y){ return x>y; }; //降順ソート時
ll i=a.flooridx(x,pr);   //x以左の最近傍位置i ない時-1
ll i=a.ceilidx(x,pr);    //x以右の最近傍位置i ない時N(配列長)
ll m=a.leftnmof(x,pr);   //x以左の個数
ll m=a.rightnmof(x,pr);  //x以右の個数
bool b=a.contains(x,pr); //xを含む

a.concat(b,n).pop_back().rsort().uniq();  //連続適用できる
*/

#if 0
#define MODLL (1000000007LL)
#else
#define MODLL (998244353LL)
#endif
using mll = mll_<MODLL>;
//using mll = fraction;

//　１
//０┼２
//　３              左     上     右    下
vector<pll> dxys={{0,-1},{-1,0},{0,1},{1,0},};

vector<ll> str2num(string &s,char base){
  vector<ll>  v(s.size());
  for (ll i=0;i<(ll)s.size();++i) v[i]=s[i]-(ll)base;
  return v;
}


namespace SolvingSpace{

template<class T> using vector = Vector<T>;
using    vll=vector<   ll>; using    vmll=vector<   mll>; using    vdd=vector<   dd>;
using   vvll=vector<  vll>; using   vvmll=vector<  vmll>; using   vvdd=vector<  vdd>;
using  vvvll=vector< vvll>; using  vvvmll=vector< vvmll>; using  vvvdd=vector< vvdd>;
using vvvvll=vector<vvvll>; using vvvvmll=vector<vvvmll>; using vvvvdd=vector<vvvdd>;
using   vpll=vector<  pll>; using    vtll=vector<   tll>; using   vqll=vector<  qll>;
using  vvpll=vector< vpll>; using   vvtll=vector<  vtll>; using  vvqll=vector< vqll>;
using   vll2=vector<  ll2>; using    vll3=vector<   ll3>; using   vll4=vector<  ll4>;
using  vvll2=vector< vll2>; using   vvll3=vector<  vll3>; using  vvll4=vector< vll4>;
using vvvll2=vector<vvll2>; using  vvvll3=vector< vvll3>; using vvvll4=vector<vvll4>;
using vss=vector<string>;
template<class T> vector<T> cinv(ll nm){ return vector<T>(nm,[](ll i){ (void)i; return cin1<T>(); }); }
template<class T> vector<vector<T>> cinvv(ll H,ll W){ return vector<vector<T>>(H,[&](ll i){ (void)i; return cinv<T>(W); }); }

//////////////



template<class STATE> struct map4id{
  using Int = long long;
  map<STATE,Int> mp_toid;
  vector<STATE> fromid;
  auto toID(){
    return [&](const STATE &vx){
      auto it=mp_toid.lower_bound(vx);
      if(it!=mp_toid.end() && it->first==vx) return it->second;
      Int no=(Int)mp_toid.size();
      mp_toid.insert(it,{vx,no});
      fromid.push_back(vx);
      return no;
    };
  }
  auto fromID(){
    return [&](Int id){ return fromid[id]; };
  }
  template<class VAL> void dump(const vector<VAL> &v){
    for(auto&&[key,id]:mp_toid){
      cout << v[id] << " : " << key << '\n';
    }
  }
};

template<class STATE,class VAL,class Ope,class Tran,class ToID,class FromID>
struct memoDP{
  using Int = long long;
  using ll = long long;
  Ope ope; //貰うときの演算
  Tran tran;
  ToID toID;
  FromID fromID;
  VAL yet,ini,dmy; //yet:未計算印の値 ini:ope演算の初期値
  vector<VAL> dp_;
  bool autoResize = true;
  bool nextdp = false; //true:nextDP
  //-------- コンストラクタ --------
  memoDP(STATE,VAL,Ope ope_,Tran tran_,ToID toID_,FromID fromID_,VAL yet_,VAL ini_)
    : ope(ope_),tran(tran_),toID(toID_),fromID(fromID_),yet(yet_),ini(ini_),dmy(ini_){}
  //事前メモリ確保用コンストラクタ
  template<class RNG> memoDP(STATE,VAL,Ope ope_,Tran tran_,ToID toID_,
    FromID fromID_,VAL yet_,VAL ini_,const RNG &rng)
    : ope(ope_),tran(tran_),toID(toID_),fromID(fromID_),yet(yet_),ini(ini_),dmy(ini_),
    dp_(rng.isCycle() ? rng.csize()*rng.cycle() : rng.size(),yet),
    autoResize(false),nextdp(rng.isCycle()){}
  //-------- アクセス・計算実行 --------
  template<class... Args> VAL &operator()(Args&&... args){ return Dp({args...}); }
  template<class... Args> VAL calcIfAny(Args&&... args){ return calcIfAnySt({args...}); }
  template<class... Args> void calc(Args&&... args){ calcSt({args...}); }
  template<class RNG> void calcall(const RNG &rng){
    if(nextdp) calcallNextDp(rng);
    else        calcallNormal(rng);
  }
  using   vVAL = vector<  VAL>;  using   vvVAL = vector<  vVAL>;
  using vvvVAL = vector<vvVAL>;  using vvvvVAL = vector<vvvVAL>;
  vVAL    tov(array<Int,1> ls){ return tov(ls[0]); }
  vvVAL   tov(array<Int,2> ls){ return tov(ls[0],ls[1]); }
  vvvVAL  tov(array<Int,3> ls){ return tov(ls[0],ls[1],ls[2]); }
  vvvvVAL tov(array<Int,4> ls){ return tov(ls[0],ls[1],ls[2],ls[3]); }
  vVAL tov(Int xl){
    dp_.resize(xl,yet);  return vVAL(dp_);
  }
  vvVAL tov(Int xl,Int yl){
    dp_.resize(xl*yl,yet);
    vvVAL ret(xl,vVAL(yl));
    for(ll i=0;i<xl;++i) for(ll j=0;j<yl;++j) ret[i][j]=dp_[i*yl+j];
    return ret;
  }
  vvvVAL tov(Int xl,Int yl,Int zl){
    dp_.resize(xl*yl*zl,yet);
    vvvVAL ret(xl,vvVAL(yl,vVAL(zl)));
    for(ll i=0;i<xl;++i) for(ll j=0;j<yl;++j) for(ll k=0;k<zl;++k){
      ret[i][j][k]=dp_[i*yl*zl+j*zl+k];
    }
    return ret;
  }
  vvvvVAL tov(Int xl,Int yl,Int zl,Int wl){
    dp_.resize(xl*yl*zl*wl,yet);
    vvvvVAL ret(xl,vvvVAL(yl,vvVAL(zl,vVAL(wl))));
    for(ll i=0;i<xl;++i) for(ll j=0;j<yl;++j) for(ll k=0;k<zl;++k){
      for(ll l=0;l<wl;++l) ret[i][j][k][l]=dp_[i*yl*zl*wl+j*zl*wl+k*wl+l];
    }
    return ret;
  }
private:
  VAL &Dp(const STATE &vx){ //dp_がreallocされると参照が無効になることに注意
    ll id=toID(vx);
    if(autoResize && (ll)dp_.size()<=id) dp_.resize(id+1,yet);
    return id<0 ? (dmy=ini) : dp_[id];
  }
  VAL calcIfAnySt(const STATE &vx){
    VAL &Dpvx=Dp(vx);
    if(Dpvx!=yet) return Dpvx;
    Dpvx=ini;
    auto src_calc2srcVa=[&](const STATE &src,auto calc2srcVa){
      VAL srcVa=calcIfAnySt(src);
      VAL &DpvxL = autoResize ? Dp(vx) : Dpvx; //resizeすると参照が無効になるため
      VAL nVa=ope(DpvxL,calc2srcVa(srcVa));
      if(DpvxL!=nVa) DpvxL=nVa,preRenew(vx,src);
    };
    auto dpWrap=[this](auto &&... args)->VAL{ return calcIfAny(args...); };
    auto setVal=[&](VAL va){
      (autoResize ? Dp(vx) : Dpvx) = va; //resizeすると参照が無効になるため
    };
    tran(vx,src_calc2srcVa,dpWrap,setVal);
    return autoResize ? Dp(vx) : Dpvx; //resizeすると参照が無効になるため
  }
  void calcSt(const STATE &vx,bool force=false){ //force=true:計算済でも再計算
    VAL &Dpvx=Dp(vx);
    if(!force && Dpvx!=yet) return;
    Dpvx=ini;
    auto src_calc2srcVa=[&](const STATE &src,auto calc2srcVa){
      VAL srcVa=Dp(src);
      VAL nVa=ope(Dpvx,calc2srcVa(srcVa));
      if(Dpvx!=nVa) Dpvx=nVa,preRenew(vx,src);
    };
    auto dpWrap=[this](auto &&... args)->VAL{ return (*this)(args...); };
    auto setVal=[&](VAL va){ Dpvx=va; };
    tran(vx,src_calc2srcVa,dpWrap,setVal);
  }
  template<class RNG> void calcallNormal(const RNG &rng){
    STATE vx=rng.start();
    do calcSt(vx); while(rng.next(vx));
  }
  template<class RNG> void calcallNextDp(const RNG &rng){
    assert(rng.isCycle());
    for(ll xx=0;xx<rng.ls()[0];++xx){
      STATE vx=rng.start(xx);
      bool force = rng.cycle()<=xx;
      do calcSt(vx,force); while(rng.next(vx,1));
    }
  }
  //-------- ダンプ --------
public:
  #if 0
  template<int N>
  void dump(rangeNd<N> &rng,vector<string> labels={},const vector<ll> axes={0,1,2,3}){
    auto ls=rng.ls();
    if(nextdp) ls[0]=rng.cycle();
    dumpstring::dumpNd("",tov(ls),args().rngs(rng.rngs()).tr(axes).labels(labels));
  }
  #endif
  //-------- 最適パス --------
  #if 0
private:
  vector<ll> pre;
  ll preini=-1,predmy=-1;
  ll &Pre(const STATE &vx){
    ll id=toID(vx);
    if((ll)pre.size()<=id) pre.resize(id+1,preini);
    return id<0 ? (predmy=preini) : pre[id];
  }
  void preRenew(const STATE &vx,const STATE &src){ Pre(vx)=toID(src); }
public:
  template<class... Args> vector<STATE> pathget(Args&&... endargs){
    vector<ll> ids{toID({endargs...})};
    while(ids.back()<(ll)pre.size() && pre[ids.back()]!=preini) ids.push_back(pre[ids.back()]);
    reverse(ids.begin(),ids.end());
    vector<STATE> path;
    for(auto&& id: ids) path.push_back(fromID(id));
    return path;
  }
  #else
  void preRenew(const STATE &vx,const STATE &src){ (void)vx,(void)src; }
  #endif
};


#ifdef _MSC_VER
#include <intrin.h>
#endif
struct primefactorization{
  using ull = unsigned long long;
  ll fmax=0; //篩のmax
  vll mnpr; //最小素因数表
  vll primes; //素数リスト
  vpll pfact; //素因数分解結果 例:{<2,3>,<3,1>,<5,2>}→2^3×3^1×5^2
  vll divs; //約数列挙結果
  primefactorization(){} //篩無し
  primefactorization(ll fmx){ init(fmx); } //篩使用
  void init(ll fmx){ //エラトステネスの篩で最小素因数表+素数リストを作成
    fmax=fmx;
    mnpr.resize(fmx+1);
    primes.reserve(fmx/10+1);
    for(ll i=2; i<=fmax; i++){
      if(mnpr[i]) continue;
      primes.push_back(i);
      mnpr[i]=i;
      for(ll j=i*i; j<=fmax; j+=i) if(mnpr[j]==0) mnpr[j]=i;
    }
  }
  vll &primelist(){ return primes; }
  bool isprime(ll a){
    if(a<=fmax) return mnpr[a]==a;
    else return MillerRabin((ull)a);
  }
  vpll &operator()(ll a){//素因数分解
    return this->pfact=Factorization(a);
  }
  vll pfactlist(ll a){//素因数リスト(指数は返さない)
    (*this)(a);//素因数分解実行
    vll ret;
    for(auto&&[p,_]:this->pfact) ret.push_back(p);
    return ret;
  }
  /*!
  @brief   素因数分解結果pfactから約数列挙divsを得る
  @details e乗しても約数のもののみ raise=trueならe乗後を返す
  */
  static void divisorCore(const vpll &pfact,vll &divs,ll e=1,bool raise=false){
    divs.assign(1,1);
    for(auto [p,nm]: pfact){
      ll prenm=(ll)divs.size();
      for(int i=0;i<prenm*(nm/e);++i) divs.push_back(divs[i]*p);
    }
    if(raise){ //e乗
      for(auto&& y: divs){
        for(ll i=1,yorg=y;i<e;++i) y*=yorg;
      }
    }
  }
  vll &divisor(ll a,ll e=1,bool raise=false){//約数列挙 e乗して約数のもの
    (*this)(a);//素因数分解実行
    divisorCore(this->pfact,this->divs,e,raise);//約数列挙コア
    return divs;
  }
  vpll Factorization(ll a){
    if(a<(1LL<<31)) return FactorizationCore((int)a);
    else             return FactorizationCore(a);
  }
  template<class T> vpll FactorizationCore(T a){//素因数分解
    vpll ret;
    if(a<=1) return ret;
    if(a<=fmax){//篩の範囲→osa_k法
      for(; mnpr[a]!=a; a/=(T)mnpr[a]) Add(ret,mnpr[a]);
      Add(ret,a);
      return ret;
    }
    if(MillerRabin((ull)a)){//素数の時
      ret.emplace_back(a,1);
      return ret;
    }
    //それ以外→ロー法で再帰
    ll y=RhoAlgorithm((ull)a);
    vpll ret1=Factorization(y);
    vpll ret2=Factorization(a/y);
    ll i=0,j=0,len1=(ll)ret1.size(),len2=(ll)ret2.size();
    while(i<len1 || j<len2){
      if(j==len2 || (i<len1 && ret1[i]<ret2[j])) AddBlock(ret,ret1[i++]);
      else                                        AddBlock(ret,ret2[j++]);
    }
    return ret;
  }
  bool MillerRabin(ull n){//true:素数 定数は http://miller-rabin.appspot.com/ より
    auto modpow=[&](ull a,ull b,ull m){ //a^b (mod m)
      ull r=1;
      for(; b>0; b>>=1,a=ModMul(a,a,m)) if(b&1) r=ModMul(r,a,m);
      return r;
    };
    auto f=[&](ull a){//true:素数かもしれない、false:合成数確定
      a%=n;
      if(a==0) return true;
      ull t=n-1,s=0;
      while(t%2==0) t>>=1,s++;
      ull x=modpow(a,t,n);
      if(x==1 || x==n-1) return true;
      for(ull r=1; r<s; ++r){
        if((x=ModMul(x,x,n))==n-1) return true;
      }
      return false;
    };
    if(n<=1) return false;
    if(n==2) return true;
    if(n%2==0) return false;
    if(n<4759123141) return f(2)&&f(7)&&f(61);
    return f(2)&&f(325)&&f(9375)&&f(28178)&&f(450775)&&f(9780504)&&f(1795265022);
  }
  ll RhoAlgorithm(ull n){//約数の1つを返す 素数はNG(無限ループする)
    if((n&1)==0) return 2;
    for(ull c=1,x=1;;++c){
      auto f=[&](ull x){ return (ModMul(x,x,n)+c)%n; };
      ull y=x,g=1;
      while(g==1){
        x=f(x);
        y=f(f(y));
        g=gcd(abs(ll(x-y)),n);
      }
      if(g<n) return (ll)g;
    }
  }
  void AddBlock(vpll &v,pll &p){
    if(!v.empty() and v.back().first==p.first) v.back().second+=p.second;
    else v.push_back(p);
  }
  void Add(vpll &v,ll x){
    if(!v.empty() and v.back().first==x) v.back().second++;
    else v.emplace_back(x,1);
  }
  inline ull ModMul(ull a,ull b,ull m){ //a*b%m
    if(a < 1ULL<<32 && b < 1ULL<<32) return a*b%m;
    #ifdef _MSC_VER
    ull upper,lower,rem;
    lower=_umul128(a,b,&upper);
    _udiv128(upper,lower,m,&rem);
    return rem;
    #else
    return (ull)((unsigned __int128)(a)*b%m);
    #endif
  }
};
/*
- -------- 定義 -------- M:篩最大値
primefactorization pr;
primefactorization pr(M);
- -------- 素数判定 -------- 篩内なら使用、篩外ならミラーラビンで判定
bool b=pr.isprime(x);
- -------- 素数リスト --------  {2,3,5,7,11,…}
vll &primes=pr.primelist();
- -------- 素因数分解 --------
vpll &pfact=pr(x);
.      ↑例: x=1  → {}
.            x=2  → {<2,1>} //2^1の意味
.            x=600→ {<2,3>,<3,1>,<5,2>} //2^3×3^1×5^2 素因数昇順
- -------- 素因数分解(指数なし) -------- 例:x=600→{2,3,5} (600=2^3×3^1×5^2)
vll plist=pr.pfactlist(x);
- -------- 約数列挙 -------- 例:x=12→{1,2,4,3,6,12}＜未ソート＞
vll &div=pr.divisor(x);
vll &div=pr.divisor(x,e);      //e乗が約数のものを列挙
vll &div=pr.divisor(x,e,true); //約数でe乗数のものを列挙
*/


void cin2solve()
{
  auto N=cin1<ll>();

  primefactorization pr(N+10);

  auto kata=[&](ll y,ll p){
    ll ret=0;
    while(y%p==0) ret++,y/=p;
    return ret;
  };

  auto f=[&](vpll &pfact,ll y){
    dd ret=1.;
    for(auto&&[p,ct]:pfact){
      ll kt=kata(y,p);
      if(kt==ct) ret*=1./Pow(p,kt);
      else ret*=1./Pow(p,kt)-1./Pow(p,kt+1);
    }
    return ret;
  };

  using STATE=array<ll,1>; //i
  using VAL=dd;     VAL yet=(dd)-INF*7;
  auto operation=[&](VAL a,VAL b){return a+b;};  VAL ini=0;

  auto transition=[&](const STATE &vx,auto src_calc2srcVa,auto dp,auto setVal){
    auto[n]=vx;
    if(n==1){
      setVal(0.);
      return;
    }
    vll div=pr.divisor(n);
    vpll pfact=pr(n);
    div.sort();
    div.pop_back();//n除く

    //dp(現在位置)をdp(…)から計算
    VAL va=1.;
    for(auto&& y: div){
      va+=f(pfact,y)*dp(y);
    }
    va/=1.-f(pfact,n);

    //結果セット
    setVal(va);
  };

  map4id<STATE> mpid;

  memoDP dp(STATE(),VAL(),operation,transition,mpid.toID(),mpid.fromID(),yet,ini);

  VAL ans=dp.calcIfAny(N);
  cout << ans << '\n';

  return;
}

};//SolvingSpace

//////////////////////////////////////////

int main(){
  #if 1
  //SolvingSpace::labo();
  SolvingSpace::cin2solve();
  //SolvingSpace::generand();
  #else
  ll t;  cin >> t;
  rep(i,0,t-1){
    SolvingSpace::cin2solve();
    //SolvingSpace::generand();
  } 
  #endif
  cerr << timeget() <<"ms"<< '\n';
  return 0;
}
yukicoder

結果

テストケース

ソースコード
