結果
| 問題 | No.3478 XOR-Folding Primes |
| コンテスト | |
| ユーザー |
👑  hamamu
|
| 提出日時 | 2026-03-20 22:34:31 |
| 言語 | C++23 (gcc 15.2.0 + boost 1.89.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 29,536 bytes |
| 記録 | |
| コンパイル時間 | 4,838 ms |
| コンパイル使用メモリ | 381,860 KB |
| 実行使用メモリ | 199,284 KB |
| 最終ジャッジ日時 | 2026-03-20 22:34:58 |
| 合計ジャッジ時間 | 14,851 ms |
|
ジャッジサーバーID （参考情報） |
judge2_0 / judge3_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 6 TLE * 2 |
ソースコード
#ifndef MYLOCAL
//# pragma GCC target("avx2")//yukiではNG
# pragma GCC optimize("O3")
# pragma GCC optimize("unroll-loops")
#endif
#if defined(NDEBUG)
#undef NDEBUG
#endif
#include "bits/stdc++.h"
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 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__))
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> [[nodiscard]] inline T limithi(T a,T b){ return min(a,b); }
template<class T> [[nodiscard]] inline T limitlo(T a,T b){ return max(a,b); }
template<class T> inline bool chlimithi(T &a,T b){ return chmin(a,b); }
template<class T> inline bool chlimitlo(T &a,T b){ return chmax(a,b); }
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(); }
//cin
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...>>(); }
//cout
template<class T,class S> inline ostream &operator<<(ostream &os,const pair<T,S> &a){ return os << a.first << ' ' << a.second; }
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); }
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; }
inline struct{
system_clock::time_point st = system_clock::now();
ll operator()()const{return duration_cast<microseconds>(system_clock::now()-st).count()/1000;}
} timeget;
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 };
};
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)){}
Vector(int n,cT& x):vT(n,x){}// ┬ 型推論のためラッパー
Vector(long long n,cT& x):vT(n,x){}
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); }
Vector &operator+=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]+=b[i]; return *this; }
Vector &operator-=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]-=b[i]; return *this; }
Vector &operator*=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]*=b[i]; return *this; }
Vector &operator/=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]/=b[i]; return *this; }
Vector &operator%=(cvT &b){ assert(size()==b.size()); for(Int i=0;i<size();++i) (*this)[i]%=b[i]; return *this; }
Vector &operator+=(const Vector<T> &b){ return *this+=(cvT&)b; }
Vector &operator-=(const Vector<T> &b){ return *this-=(cvT&)b; }
Vector &operator*=(const Vector<T> &b){ return *this*=(cvT&)b; }
Vector &operator/=(const Vector<T> &b){ return *this/=(cvT&)b; }
Vector &operator%=(const Vector<T> &b){ return *this%=(cvT&)b; }
Vector operator+(cvT &b){ return Vector(*this)+=b; }
Vector operator-(cvT &b){ return Vector(*this)-=b; }
Vector operator*(cvT &b){ return Vector(*this)*=b; }
Vector operator/(cvT &b){ return Vector(*this)/=b; }
Vector operator%(cvT &b){ return Vector(*this)%=b; }
Vector operator+(const Vector<T> &b){ return Vector(*this)+=b; }
Vector operator-(const Vector<T> &b){ return Vector(*this)-=b; }
Vector operator*(const Vector<T> &b){ return Vector(*this)*=b; }
Vector operator/(const Vector<T> &b){ return Vector(*this)/=b; }
Vector operator%(const Vector<T> &b){ return Vector(*this)%=b; }
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--(int){ return *this-=1; }
Vector &operator++(int){ return *this+=1; }
Vector operator-()const{ return Vector(*this)*=-1; }
template<class S> friend Vector operator-(S x,const Vector &a){ return -a+=x; }
T& at(Int i){ assert(i>=0); if(n()<=i)vT::resize(i+1); return vT::operator[](i); }
Vector slice(Int l,Int r,Int d=1)const{
Vector ret;
for(Int i=l;(d>0&&i<=r)||(d<0&&r<=i);i+=d) ret.push_back((*this)[i]);
return ret;
}
Int size()const{ return (Int)vT::size(); }
Int n()const{ return size(); }
Vector &push_back(cT& x,Int n=1){ for(Int i=0;i<n;++i){ vT::push_back(x); } return *this; }
Vector &pop_back(Int n=1){ for(Int i=0;i<n;++i){ vT::pop_back(); } return *this; }
Vector &push_front(cT& x,Int n=1){ this->insert(0,x,n); return *this; }
Vector &pop_front(Int n=1){ erase(0,n-1); 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,Int n=1){ insert(it(i),n,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 &erase(const Vector<Int> &idxs){
for (Int I=0; I<idxs.n(); ++I){
Int l=idxs[I]+1, r = (I<idxs.n()-1) ? idxs[I+1] : this->n();
copy(it(l),it(r),it(l-I-1));//[l,r)を前にI+1個ずらす
}
vT::resize(this->n()-idxs.n());
return *this;
}
Vector &eraseall(cT& x){ return eraseall(0,size()-1,x); }
Vector &eraseall(Int l,Int r,cT& x){ erase(remove(it(l),it(r+1),x),it(r+1)); return *this; }
template<class Pr> Vector &eraseif(Pr pr){ return eraseif(0,size()-1,pr); }
template<class Pr> Vector &eraseif(Int l,Int r,Pr pr){ erase(remove_if(it(l),it(r+1),pr),it(r+1)); return *this; }
Vector &concat(cvT &b,Int n=1){
cvT B = (&b==this) ? *this : vT{};
for(int i=0;i<n;++i) this->insert(size(),(&b==this)?B:b);
return *this;
}
Vector repeat(Int n){ return Vector{}.concat(*this,n); }
Vector &reverse(Int l=0,Int r=-1){ r+=r<0?size():0; std::reverse(it(l),it(r+1)); return *this; }
Vector &rotate(Int m){ return rotate(0,size()-1,m); }
Vector &rotate(Int l,Int r,Int m){ std::rotate(it(l),it(m),it(r+1)); return *this; }
Vector &sort(Int l=0,Int r=-1){ r+=r<0?size():0; std::sort(it(l),it(r+1)); return *this; }
Vector &rsort(Int l=0,Int r=-1){ return sort(l,r).reverse(l,r); }
template<class Pr> Vector &sort(Pr pr){ return sort(0,size()-1,pr); }
template<class Pr> Vector &sort(Int l,Int r,Pr pr){ std::sort(it(l),it(r+1),pr); return *this; }
template<int key> Vector &sortbykey(Int l=0,Int r=-1){
r+=r<0?size():0;
sort(l,r,[](cT &x,cT &y){return get<key>(x)<get<key>(y);});
return *this;
}
Vector &uniq(){ erase(unique(begin(),end()),end()); return *this; }
Vector &sortq(){ return sort().uniq(); }
Vector &fill(cT& x){ return fill(0,size()-1,x); }
Vector &fill(Int l,Int r,cT& x){ std::fill(it(l),it(r+1),x); return *this; }
Vector ©(Int i,cvT &b,Int n=1){//A[i]スタートでbをn回分コピー
for (int t=0; t<n; ++t) for (int j=0; j<(int)b.size(); ++j){
if (i>=size()) return *this;
if (i>=0) (*this)[i]=b[j];
i++;
}
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 count(0,size()-1,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 countif(0,size()-1,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 find(0,size()-1,x); }
Int find(Int l,Int r,cT& x)const{ return Int(std::find(it(l),it(r+1),x)-begin()); }
Int rfind(cT& x)const{ return rfind(0,size()-1,x); }
Int rfind(Int l,Int r,cT& x)const{
for (int i=r;i>=l;--i) if ((*this)[i]==x) return i;
return l-1;
}
template<class Pr> Int findif(Pr pr)const{ return findif(0,size()-1,pr); }
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; }
template<class S> using VV = Vector<Vector<S>>; template<class S> using sVV = vector<vector<S>>;
template<class S> using VVV = Vector<VV<S>>; template<class S> using sVVV = vector<sVV<S>>;
template<class S> using VVVV = Vector<VVV<S>>; template<class S> using sVVVV = vector<sVVV<S>>;
template<class S> using VVVVV = Vector<VVVV<S>>; template<class S> using sVVVVV = vector<sVVVV<S>>;
auto tostd()const{ return tov(*this); }
template <class S> static vector<S> tov(const Vector<S>&v){ return v; }
template <class S> static sVV<S> tov(const VV<S> &v){ sVV<S> ret; for(auto&& e:v) ret.push_back(e); return ret; }
template <class S> static sVVV<S> tov(const VVV<S> &v){ sVVV<S> ret; for(auto&& e:v) ret.push_back(e.tostd()); return ret; }
template <class S> static sVVVV<S> tov(const VVVV<S> &v){ sVVVV<S> ret; for(auto&& e:v) ret.push_back(e.tostd()); return ret; }
template <class S> static sVVVVV<S> tov(const VVVVV<S> &v){ sVVVVV<S> ret; for(auto&& e:v) ret.push_back(e.tostd()); return ret; }
};
#if 0
#define MODLL (1000000007LL)
#else
#define MODLL (998244353LL)
#endif
using mll = mll_<MODLL>;
//using mll = fraction;
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 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); }); }
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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);
}
};
#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
*/
template<class T> struct mat_: std::vector<std::vector<T>>{
using P=std::vector<std::vector<T>>;
mat_(){}
mat_(initializer_list<initializer_list<T>> a): P(a.begin(),a.end()){
assert(all_of(this->begin(),this->end(),[&](auto &x){return (ll)x.size()==w(); }));
}
mat_(ll h,ll w,T x=T()): P(h,std::vector<T>(w,x)){}
mat_(ll n): P(n,std::vector<T>(n)){}
mat_(ll n,const string &c): P(n,std::vector<T>(n)){ if (c=="E")E(); }
mat_(std::vector<T> &v,bool istranspose=false){
if (istranspose){
P::resize(1,std::vector<T>((ll)v.size()));
for (ll j=0; j<w(); ++j) (*this)[0][j]=v[j];
}
else{
P::resize((ll)v.size(),std::vector<T>(1));
for (ll i=0; i<h(); ++i) (*this)[i][0]=v[i];
}
}
ll h() const { return (ll)P::size(); }
ll w() const { return h()==0 ? 0 : (ll)(*this)[0].size(); }
mat_ &operator+=(const mat_ &b){ for (ll i=0; i<h(); ++i) for (ll j=0; j<w(); ++j) (*this)[i][j]+=b[i][j]; return *this; }
mat_ &operator-=(const mat_ &b){ for (ll i=0; i<h(); ++i) for (ll j=0; j<w(); ++j) (*this)[i][j]-=b[i][j]; return *this; }
mat_ &operator*=(T b) { for (ll i=0; i<h(); ++i) for (ll j=0; j<w(); ++j) (*this)[i][j]*=b; return *this; }
mat_ operator+(const mat_ &b) const { return mat_(*this)+=b; }
mat_ operator-(const mat_ &b) const { return mat_(*this)-=b; }
mat_ operator*(T b) const { return mat_(*this)*=b; }
friend mat_ operator*(T a,const mat_ &b) { return b*a; }
mat_ &operator*=(const mat_ &b){ return *this=*this*b; }
mat_ operator*(const mat_ &b) const {//行列*行列
mat_ ret(h(),b.w());
for (ll i=0; i<h(); ++i) for (ll j=0; j<b.w(); ++j) for (ll k=0; k<w(); ++k){
ret[i][j]+=(*this)[i][k]*b[k][j];
}
return ret;
}
std::vector<T> operator*(const std::vector<T> &v) const {//行列*ベクトル
std::vector<T> ret(h());
for (ll i=0; i<h(); ++i) for (ll j=0; j<w(); ++j) ret[i]+=(*this)[i][j]*v[j];
return ret;
}
mat_ pow(const ll n) const {
mat_ ret(h(),"E"),a(*this);
for (ll i=n; i>0; i>>=1,a*=a){ if (i&1) ret*=a; }
return ret;
}
mat_ t() const {
mat_ ret(w(),h());
for (ll i=0; i<w(); ++i) for (ll j=0; j<h(); ++j) ret[i][j]=(*this)[j][i];
return ret;
}
void E(){ for (ll i=0; i<min(h(),w()); ++i) (*this)[i][i]=1; }
};
using mat=mat_<mll>;
/*
mat m={{2,3,4},{1,0,5}};
. ↓2x2正方行列、all0
mat m(2);
. ↓2x2 単位行列
mat m(2,"E");
. ↓vectorを縦(n×1)のmat型に変換
mat m(v);
. ↓vectorを横(1×n)のmat型に変換
mat m(v,true);
. ↓定数倍
m*=mll(2);
mat mm=m.pow(i);
*/
void cin2solve()
{
auto [N,M]=cins<ll,ll>();
primefactorization pr(M);
if (N==1){
vll &primes=pr.primelist();
cout << sz(primes) << '\n'; return;
}
ll X=0;
{
vll &primes=pr.primelist();
rep(i,1,sz(primes)-1){
ll pp=primes[i-1];
ll np=primes[i];
if ((pp^2)==np) X+=2;
}
}
mat m={{0,X},{1,1}};
vmll an=m.pow(N-1)*vmll{1,1};
mll ans=an[0]+an[1]*X;
cout << ans << '\n';
return;
}
}//SolvingSpace
//////////////////////////////////////////
int main(){
#if defined(RANDOM_TEST)
//SolvingSpace::cin2solve();
SolvingSpace::generand();
#else
#if 0
//SolvingSpace::labo();'
SolvingSpace::cin2solve();
#else
ll t; cin >> t;
rep(i,0,t-1){
SolvingSpace::cin2solve();
}
#endif
#endif
cerr << timeget() <<"ms"<< '\n';
return 0;
}