#1005511 (C++23) No.109 N! mod M

• 問題: No.109 N! mod M
• ユーザー: eQe
• 提出日時: 2024-08-28 19:28:18
• 言語: C++23 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 71 ms / 5,000 ms
• コード長: 10,939 bytes
• コンパイル時間: 5,907 ms
• コンパイル使用メモリ: 328,640 KB
• 実行使用メモリ: 6,944 KB
• 最終ジャッジ日時: 2024-08-28 19:28:59
• 合計ジャッジ時間: 6,988 ms
• ジャッジサーバーID （参考情報）: judge5 / judge4

ファイルパターン	結果
other	AC * 9

ソースコード

#include<bits/stdc++.h>
#include<atcoder/all>
namespace my{
using namespace atcoder;
using ml=modint;
auto&operator<<(std::ostream&o,const ml&x){return o<<x.val();}
auto&operator>>(std::istream&i,ml&x){long long t;i>>t;x=t;return i;}
void main();
void solve();
}
int main(){my::main();}
namespace my{
#define eb emplace_back
#define all(a) (a).begin(),(a).end()
#define done(...) rr pp(__VA_ARGS__)
#define RD(T,...) T __VA_ARGS__;li(__VA_ARGS__)
#define LL(...) RD(ll,__VA_ARGS__)
#define JO(a,b) a##b
#define jo(a,b) JO(a,b)
#define FE(v,e,...) for(au&&__VA_OPT__([)e __VA_OPT__(,__VA_ARGS__]):v)
#define FO(n) for(ll jo(i,__LINE__)=n;jo(i,__LINE__)-->0;)
#define FOR(i,...) for(au[i,i##O,i##E]=range(0,__VA_ARGS__);i<i##O;i+=i##E)
#define fe(v,...) FE(v,__VA_ARGS__)
#define fo(i,...) FO##__VA_OPT__(R)(i __VA_OPT__(,__VA_ARGS__))
#define of(i,...) for(au[i,i##O,i##E]=range(1,__VA_ARGS__);i>=i##O;i-=i##E)
#define I template
#define J class
#define au auto
#define rr return
using namespace std;
I<J A,J B>constexpr bool same=is_same_v<A,B>;
using is=istream;using os=ostream;using dd=long double;using str=string;
using ll=long long;using ull=unsigned long long;using lll=__int128_t;using ulll=__uint128_t;
os&operator<<(os&o,const ulll&x){rr(x<10?o:o<<x/10)<<ll(x%10);}
os&operator<<(os&o,const lll&x){rr o<<str(x<0,'-')<<ulll(x>0?x:-x);}
constexpr dd ee=1e-12;
constexpr ll oo=3e18;
constexpr ll dx[]{-1,0,1,0,-1,1,1,-1},dy[]{0,-1,0,1,-1,-1,1,1};
constexpr char sp=32,nl=10;
au Yes(bool y){rr y?"Yes":"No";}
au No(){rr Yes(0);}
au range(bool s,ll a,ll b=oo,ll c=1){if(b==oo)b=a,(s?b:a)=0;rr tuple{a-s,b,c};}
ll rand(ll l=oo,ll r=oo){static ull a=495;a^=a<<7,a^=a>>9;rr r!=oo?a%(r-l)+l:l!=oo?a%l:a;}
bool eve(ll x){rr~x&1;}
I<J T>T sq(T a){rr a*a;}
I<J T>T zz(T x){rr x<0?-x:x;}
I<J T>ll len(const T&a){rr a.size();}
I<J...A>au min(const A&...a){rr min(initializer_list<common_type_t<A...>>{a...});}

I<J A,J B=A>struct cp{
  A a={};B b={};
  cp(){}
  cp(A a,B b):a(a),b(b){}
  cp(pair<A,B>p):a(p.first),b(p.second){}
  bool operator==(const cp&c)const{rr a==c.a&&b==c.b;}
  auto operator<=>(const cp&c)const{rr a!=c.a?a<=>c.a:b<=>c.b;}
  friend is&operator>>(is&i,cp&c){rr i>>c.a>>c.b;}
  friend os&operator<<(os&o,const cp&c){rr o<<c.a<<sp<<c.b;}
};using cl=cp<ll>;
I<J A,J B=A,J C=A>struct tr{
  A a={};B b={};C c={};
  tr(){}
  tr(A a,B b,C c):a(a),b(b),c(c){}
  bool operator==(const tr&t)const{rr a==t.a&&b==t.b&&c==t.c;}
  auto operator<=>(const tr&t)const{rr a!=t.a?a<=>t.a:b!=t.b?b<=>t.b:c<=>t.c;}
  friend is&operator>>(is&i,tr&t){rr i>>t.a>>t.b>>t.c;}
  friend os&operator<<(os&o,const tr&t){rr o<<t.a<<sp<<t.b<<sp<<t.c;}
};using tl=tr<ll>;

I<J T>T&sort(T&a){sort(all(a));rr a;}
I<J T>decltype(au)first(T&a){rr*begin(a);}
I<J T>decltype(au)last(T&a){rr*rbegin(a);}
I<J T>au pop_front(T&a){assert(len(a));au r=first(a);a.pop_front();rr r;}
I<J T>au pop_back(T&a){assert(len(a));au r=last(a);a.pop_back();rr r;}

I<J T,size_t n>using array=std::array<T,n>;
I<J T,size_t n>os&operator<<(os&o,const array<T,n>&a){fo(i,n)o<<a[i]<<str(i!=n-1,sp);rr o;}
I<J T,J U=T>using map=std::map<T,U>;
I<J T,J U>os&operator<<(os&o,const map<T,U>&m){fe(m,e)o<<e.first<<sp<<e.second<<nl;rr o;}
I<J T,J U=T>using umap=unordered_map<T,U>;
I<J T,J U>os&operator<<(os&o,const umap<T,U>&m){fe(m,e)o<<e.first<<sp<<e.second<<nl;rr o;}
I<size_t n>using bset=bitset<n>;
I<size_t n>os&operator<<(os&o,const bset<n>&b){fo(i,n)o<<b[i];rr o;}

I<J...A>os&operator<<(os&o,const tuple<A...>&t){apply([&](const au&...a){ll i=sizeof...(a);(((o<<a<<str(--i>0,sp))),...);},t);rr o;}

I<J T,J F>struct priority_queue:std::priority_queue<T,vector<T>,F>{
  priority_queue(const initializer_list<T>&a={}){fe(a,e)this->emplace(e);}
  priority_queue(const vector<T>&a){fe(a,e)this->emplace(e);}
  T front(){rr this->top();}
  T pop_front(){T r=this->top();this->pop();rr r;}
  friend os&operator<<(os&o,priority_queue q){while(len(q))o<<q.pop_front()<<str(len(q)>0,sp);rr o;}
};
I<J T>using max_priority_queue=priority_queue<T,less<>>;
I<J T>using min_priority_queue=priority_queue<T,greater<>>;

I<J V>struct ve;
I<J V>constexpr bool isv=0;
I<J V>constexpr bool isv<ve<V>> =1;
I<J V>constexpr bool isv<vector<V>> =1;
I<J V>au rawv(V){if constexpr(isv<V>)rr rawv(V(1)[0]);else rr V();}

I<J V>struct ve:vector<V>{
  using vector<V>::vector;
  using T=decltype(rawv(V()));
  I<J U>ve(const vector<U>&v={}){static_assert(isv<V> ==isv<U>);fe(v,e)this->eb(e);}

  ve&operator+=(const ve&u){au&v=*this;fo(i,len(v))v[i]+=u[i];rr v;}ve operator+(const ve&u)const{rr ve(*this)+=u;}
  ve&operator-=(const ve&u){au&v=*this;fo(i,len(v))v[i]-=u[i];rr v;}ve operator-(const ve&u)const{rr ve(*this)-=u;}
  ve&operator^=(const ve&u){fe(u,e)this->eb(e);rr*this;}ve operator^(const ve&u)const{rr ve(*this)^=u;}
  ve&operator+=(const T&x){au&v=*this;fe(v,e)e+=x;rr v;}ve operator+(const T&x)const{rr ve(*this)+=x;}
  ve&operator-=(const T&x){au&v=*this;fe(v,e)e-=x;rr v;}ve operator-(const T&x)const{rr ve(*this)-=x;}
  ve&operator*=(const T&x){au&v=*this;fe(v,e)e*=x;rr v;}ve operator*(const T&x)const{rr ve(*this)*=x;}
  ve&operator++(){rr*this+=1;}
  ve&operator--(){rr*this-=1;}
  ve operator-()const{rr ve(*this)*=-1;}
  I<size_t n>au&operator+=(const bset<n>&a){fo(i,n)(*this)[i]+=a[i];rr*this;}
  I<size_t n>au&operator-=(const bset<n>&a){fo(i,n)(*this)[i]-=a[i];rr*this;}

  au lower_bound(const V&x)const{rr std::lower_bound(all(*this),x);}
  au upper_bound(const V&x)const{rr std::upper_bound(all(*this),x);}

  I<J F>au scan(F f)const{cp<T,bool>r;fe(*this,e)if constexpr(!isv<V>)r.b?f(r.a,e),r:r={e,1};else if(au s=e.scan(f);s.b)r.b?f(r.a,s.a),r:r=s;rr r;}
  T min()const{rr scan([](T&a,const T&b){a>b?a=b:0;;}).a;}
  ve zeta()const{ve v=*this;if constexpr(isv<V>)fe(v,e)e=e.zeta();fo(i,len(v)-1)v[i+1]+=v[i];rr v;}

  void af(const V&x={}){this->emplace(this->begin(),x);}

  friend is&operator>>(is&i,ve&v){fe(v,e)i>>e;rr i;}
  friend os&operator<<(os&o,const ve&v){fe(v,e)o<<e<<str(&e!=&v.back(),isv<V>?nl:sp);rr o;}
};
I<J T=ll,size_t n,size_t i=0>au vec(const ll(&s)[n],T x={}){if constexpr(n==i+1)rr ve<T>(s[i],x);else{au X=vec<T,n,i+1>(s,x);rr ve<decltype(X)>(s[i],X);}}
I<ll n,J...A>void set_size(const ll(&l)[n],A&...a){((a=vec(l,rawv(a))),...);}
I<J T>using v2=ve<ve<T>>;using u1=ve<ll>;using u2=v2<ll>;
using graph=v2<cl>;

void io(){cin.tie(0)->sync_with_stdio(0);cout<<fixed<<setprecision(15);cerr<<nl;}
I<J...A>void li(A&...a){(cin>>...>>a);}
I<char c=sp,J...A>void pp(const A&...a){ll i=sizeof...(a);((cout<<a<<str(--i>0,c)),...);cout<<nl;}

ll floor_sqrt(ll x){ll r=sqrt(zz(x-ee));while(r+1<=x/(r+1))++r;rr r;}
I<J T,J U=T>au rle(const ve<T>&a){ve<cp<T,U>>r;fe(a,e)len(r)&&e==r.back().a?++r.back().b:r.eb(e,1).b;rr r;}
I<J T,J U=T>au rce(ve<T>a){rr rle<T,U>(sort(a));}
ll inv(ll x,ll m){ll a=(x%m+m)%m,b=m,u=1,v=0;while(b)u-=a/b*v,swap(u,v),a-=a/b*b,swap(a,b);rr(u%m+m)%m;}
I<J F>struct rec:F{rec(F&&f):F(std::forward<F>(f)){}I<J...A>decltype(au)operator()(A&&...a)const{rr F::operator()(*this,std::forward<A>(a)...);}};

ve<ll>prime_enumerate(ll n){
  ve<bool>sieve(n/3+1,1);
  for(ll p=5,d=4,i=1,rn=floor_sqrt(n);p<=rn;p+=d=6-d,i++){
    if(!sieve[i])continue;
    for(ll q=sq(p)/3,r=d*p/3+(d*p%3==2),s=p*2;q<len(sieve);q+=r=s-r)sieve[q]=0;
  }
  ve<ll>r{2,3};
  for(ll p=5,d=4,i=1;p<=n;p+=d=6-d,i++)if(sieve[i])r.eb(p);
  while(len(r)&&r.back()>n)r.pop_back();
  return r;
}

struct montgomery64{
  using ml=montgomery64;
  using i64=ll;
  using u64=ull;
  using u128=__uint128_t;

  static inline u64 m=998244353;
  static inline u64 miv;
  static inline u64 n2;

  static void set_mod(u64 m){
    assert(m<(1ULL<<63));
    assert(m&1);
    ml::m=m;
    n2=-u128(m)%m;
    miv=m;
    fo(5)miv*=2-m*miv;
    assert(m*miv==1);
  }

  static u64 mod(){
    return m;
  }

  u64 a;
  montgomery64(const i64&a=0):a(reduce((u128)(a%(i64)m+m)*n2)){}

  static u64 reduce(const u128&a){
    u128 r=(a+u128(u64(a)*-miv)*m)>>64;
    return r>=m?r-m:r;
  }

  ml&operator+=(const ml&b){if((a+=b.a)>=m)a-=m;return*this;}
  ml&operator-=(const ml&b){if(i64(a-=b.a)<0)a+=m;return*this;}
  ml&operator*=(const ml&b){a=reduce(u128(a)*b.a);return*this;}
  ml&operator/=(const ml&b){*this*=b.inv();return*this;}

  ml operator+(const ml&b)const{return ml(*this)+=b;}
  ml operator-(const ml&b)const{return ml(*this)-=b;}
  ml operator*(const ml&b)const{return ml(*this)*=b;}
  ml operator/(const ml&b)const{return ml(*this)/=b;}
  bool operator==(const ml&b)const{return a==b.a;}
  bool operator!=(const ml&b)const{return a!=b.a;}
  ml operator-()const{return ml()-ml(*this);}

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

  ml inv()const{

    u64 a=this->a,b=m,u=1,v=0;
    while(b)u-=a/b*v,swap(u,v),a-=a/b*b,swap(a,b);
    return u;
  }

  u64 val()const{
    return reduce(a);
  }

  friend is&operator>>(is&i,ml&b){
    ll t;i>>t;b=t;
    return i;
  }

  friend os&operator<<(os&o,const ml&b){
    return o<<b.val();
  }
};

template<class mont>bool miller_rabin(ll n,ve<ll>as){
  ll t=0,d=n-1;
  while(eve(d))d>>=1;

  if(mont::mod()!=n)mont::set_mod(n);
  mont one=1,minus_one=n-1;
  fe(as,a){
    if(a%n==0)continue;
    ll t=d;
    mont y=mont(a).pow(t);
    while(t!=n-1&&y!=one&&y!=minus_one)y*=y,t<<=1;
    if(y!=minus_one&&eve(t))return 0;
  }
  return 1;
}

bool is_prime(ll n){
  if(eve(n))return n==2;
  if(n<=1)return 0;
  if(n<4759123141LL)return miller_rabin<montgomery64>(n,{2,7,61});
  return miller_rabin<montgomery64>(n,{2,325,9375,28178,450775,9780504,1795265022});
}

template<class mont>ll pollard_rho(ll n){
  if(eve(n))return 2;
  if(is_prime(n))return n;
  if(mont::mod()!=n)mont::set_mod(n);
  mont R,one=1;
  auto f=[&](mont x){return x*x+R;};
  while(1){
    mont 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;
  }
}

ve<ll>inner_factorize(ll n){
  if(n<=1)return{};
  ll d=pollard_rho<montgomery64>(n);
  if(d==n)return{d};
  return inner_factorize(d)^inner_factorize(n/d);
}

ve<cl>factorize(ll n){
  return rce(inner_factorize(n));
}

ve<ll>prime_table(ll n){
  ve<bool>r(n+1);
  fe(prime_enumerate(n),p)r[p]=1;
  rr r;
}

void main(){io();ll T=1;li(T);fo(T)solve();}
void solve(){
  LL(N,M);
  if(N>=M)done(0);

  ml::set_mod(M);
  if(M<=2e5){
    ml t=1;
    fo(i,1,N+1)t*=i;
    done(t);
  }

  if(is_prime(M)){
    ml::set_mod(M);
    ml t=1;
    fo(i,N+1,M)t*=i;
    done(-t.inv());
  }else{
    au fa=factorize(M);
    if(len(fa)>1){
      done(0);
    }else{
      //Mは素数の累乗

      if(N>=fa[0].a*fa[0].b){
        done(0);
      }else{
        ml t=1;
        fo(i,1,N+1)t*=i;
        done(t);
      }
    }
  }
}}