#1104999 (C++23) No.1879 How many matchings?

• 問題: No.1879 How many matchings?
• ユーザー: eQe
• 提出日時: 2025-07-15 23:16:56
• 言語: C++23 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 3 ms / 2,000 ms
• コード長: 11,731 bytes
• コンパイル時間: 5,058 ms
• コンパイル使用メモリ: 325,912 KB
• 実行使用メモリ: 7,716 KB
• 最終ジャッジ日時: 2025-07-15 23:17:02
• 合計ジャッジ時間: 5,886 ms
• ジャッジサーバーID （参考情報）: judge1 / judge3

ファイルパターン	結果
other	AC * 15

ソースコード

#include<bits/stdc++.h>
#if __has_include(<atcoder/all>)
#include<atcoder/modint>
#endif
using namespace std;
#define eb emplace_back
#define LL(...) ll __VA_ARGS__;lin(__VA_ARGS__)
#define fo(i,...) for(auto[i,i##stop,i##step]=for_range(0,__VA_ARGS__);i<i##stop;i+=i##step)
#define of(i,...) for(auto[i,i##stop,i##step]=for_range(1,__VA_ARGS__);i>=i##stop;i+=i##step)
#define fe(a,e,...) for(auto&&__VA_OPT__([)e __VA_OPT__(,__VA_ARGS__]):a)
#define base_operator(op,type) auto operator op(const type&rhs)const{auto copy=*this;return copy op##=rhs;}
#define defpp void pp(const auto&...a){const char*c="";((cout<<c<<a,c=" "),...);cout<<'\n';}
#define entry defpp void main();void main2();}int main(){my::io();my::main();}namespace my{
#define use_ml1000000007 using ml=atcoder::modint1000000007;
namespace my{
auto&operator<<(ostream&o,const atcoder::modint1000000007&x){return o<<(int)x.val();}
void io(){cin.tie(nullptr)->sync_with_stdio(0);cout<<fixed<<setprecision(15);}
using ll=long long;
using lll=__int128_t;
template<class T>concept modulary=requires(T t){t.mod();};
constexpr auto for_range(ll s,ll b){ll a=0;if(s)swap(a,b);return array{a-s,b,1-s*2};}
constexpr auto for_range(ll s,ll a,ll b,ll c=1){return array{a-s,b,(1-s*2)*c};}
void lin(auto&...a){(cin>>...>>a);}
constexpr auto even(auto x){return~x&1;}
constexpr auto abs(auto x){return x<0?-x:x;}
auto min(auto...a){return min(initializer_list<common_type_t<decltype(a)...>>{a...});}
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>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 vector<V>::vector;
  vec(const vector<V>&v):vector<V>(v){}
  ll size()const{return vector<V>::size();}
  auto&emplace_back(auto&&...a){vector<V>::emplace_back(std::forward<decltype(a)>(a)...);return*this;}
  auto pop_back(){auto r=this->back();vector<V>::pop_back();return r;}
};
template<class...A>requires(sizeof...(A)>=2)vec(const A&...a)->vec<hvec<sizeof...(A)-2,pack_back_t<A...>>>;
}
namespace my{
template<class T>auto inv_enumerate(ll n){
  vec<T>v(n+1);
  v[0]=0;
  if(n>=1)v[1]=1;
  fo(i,2,n+1)v[i]=-v[T::mod()%i]*(T::mod()/i);
  return v;
}
}
namespace my{
template<class T>T fac(ll n){static vec<T>v{1};if(ll m=v.size();m<=n){v.resize(n+1);fo(i,m,n+1)v[i]=v[i-1]*i;}return v[n];}
template<class T>T fac_inv(ll n){static vec<T>v{1};if(ll m=v.size();m<=n){v.resize(n+1);v[n]=fac<T>(n).inv();of(i,n,m)v[i]=v[i+1]*(i+1);}return v[n];}
template<class T>T comb(ll n,ll k){
  if(n<0||k<0||n<k)return 0;
  if constexpr(modulary<T>)return fac<T>(n)*fac_inv<T>(k)*fac_inv<T>(n-k);
  else { }
}
}
namespace my{
namespace fft{
using real=double;
struct complex{
  real x,y;
  complex()=default;
  complex(real x,real y):x(x),y(y){}
  inline complex operator+(const complex &c)const{return complex(x+c.x,y+c.y);}
  inline complex operator-(const complex &c)const{return complex(x-c.x,y-c.y);}
  inline complex operator*(const complex &c)const{return complex(x*c.x-y*c.y,x*c.y+y*c.x);}
  inline complex conj()const{return complex(x,-y);}
};
const real PI=acosl(-1);
ll base=1;
vector<complex>rts={{0,0},{1,0}};
vector<int>fft_rev={0,1};
void ensure_base(int nbase){
  if(nbase<=base)return;
  fft_rev.resize(1<<nbase);
  rts.resize(1<<nbase);
  fo(i,1<<nbase)fft_rev[i]=(fft_rev[i>>1]>>1)+((i&1)<<(nbase-1));
  while(base<nbase){
    real angle=PI*2.0/(1<<(base+1));
    fo(i,1<<(base-1),1<<base){
      rts[i<<1]=rts[i];
      real angle_i=angle*(2*i+1-(1<<base));
      rts[(i<<1)+1]=complex(std::cos(angle_i),std::sin(angle_i));
    }
    ++base;
  }
}
void fast_fourier_transform(vector<complex>&a,int n){
  assert((n&(n-1))==0);
  int zeros=__builtin_ctz(n);
  ensure_base(zeros);
  int shift=base-zeros;
  fo(i,n)if(i<(fft_rev[i]>>shift))swap(a[i],a[fft_rev[i]>>shift]);

  for(int k=1;k<n;k<<=1){
    for(int i=0;i<n;i+=2*k){
      for(int j=0;j<k;j++){
        complex z=a[i+j+k]*rts[j+k];
        a[i+j+k]=a[i+j]-z;
        a[i+j]=a[i+j]+z;
      }
    }
  }
}
}
template<class T>struct arbitrary_mod_convolution{
  using real=fft::real;
  using complex=fft::complex;
  arbitrary_mod_convolution(){}
  auto multiply(const vector<T>&a,const vector<T>&b,int need=-1){
    if(need==-1)need=a.size()+b.size()-1;
    int nbase=0;
    while((1<<nbase)<need)nbase++;
    fft::ensure_base(nbase);
    int sz=1<<nbase;
    vector<complex>fa(sz);
    fo(i,a.size())fa[i]=complex(a[i].val()&((1<<15)-1),a[i].val()>>15);

    fft::fast_fourier_transform(fa,sz);
    vector<complex>fb(sz);
    if(a==b){
      fb=fa;
    }else{
      fo(i,b.size())fb[i]=complex(b[i].val()&((1<<15)-1),b[i].val()>>15);
      fft::fast_fourier_transform(fb,sz);
    }
    real ratio=0.25/sz;
    complex r2(0,-1),r3(ratio,0),r4(0,-ratio),r5(0,1);
    for(int i=0;i<=(sz>>1);i++){
      int j=(sz-i)&(sz-1);
      complex a1=(fa[i]+fa[j].conj());
      complex a2=(fa[i]-fa[j].conj())*r2;
      complex b1=(fb[i]+fb[j].conj())*r3;
      complex b2=(fb[i]-fb[j].conj())*r4;
      if(i!=j){
        complex c1=(fa[j]+fa[i].conj());
        complex c2=(fa[j]-fa[i].conj())*r2;
        complex d1=(fb[j]+fb[i].conj())*r3;
        complex d2=(fb[j]-fb[i].conj())*r4;
        fa[i]=c1*d1+c2*d2*r5;
        fb[i]=c1*d2+c2*d1;
      }
      fa[j]=a1*b1+a2*b2*r5;
      fb[j]=a1*b2+a2*b1;
    }
    fft::fast_fourier_transform(fa,sz);
    fft::fast_fourier_transform(fb,sz);
    vector<T>ret(need);
    fo(i,need){
      int64_t aa=llround(fa[i].x);
      int64_t bb=llround(fb[i].x);
      int64_t cc=llround(fa[i].y);
      aa=T(aa).val(),bb=T(bb).val(),cc=T(cc).val();
      ret[i]=aa+(bb<<15)+(cc<<30);
    }
    return ret;
  }
};
template<class T>struct formal_power_series:vec<T>{
  using vec<T>::vec;
  using fps=formal_power_series;
  static constexpr ll SPARSE_THRESHOLD=20;
  static inline arbitrary_mod_convolution<T>fft;
  static fps mul(const fps&a,const fps&b){
    if constexpr(!modulary<T>){ }
    else if constexpr(is_same_v<T,atcoder::modint998244353>){ }
    else return fft.multiply(a,b);
  }
  auto&shrink(){while(this->size()>1&&this->back()==T{})this->pop_back();return*this;}
  fps pre(ll deg)const{fps r(this->begin(),this->begin()+min(this->size(),deg));r.resize(deg);return r;}
  fps&operator-=(const fps&g){if(g.size()>this->size())this->resize(g.size());fo(i,g.size())(*this)[i]-=g[i];return*this;}
  fps&operator*=(const fps&g){return*this=(this->size()&&g.size()?mul(*this,g):fps{});}
  fps&operator>>=(ll sz){if(this->size()<=sz)return*this=fps{};this->erase(this->begin(),this->begin()+sz);return*this;}
  fps&operator<<=(ll sz){this->insert(this->begin(),sz,T{});return*this;}
  base_operator(-,fps)
  base_operator(*,fps)
  fps operator>>(ll sz)const{return fps{*this}>>=sz;}
  fps operator<<(ll sz)const{return fps{*this}<<=sz;}
  fps&operator+=(const T&c){if(!this->size())this->resize(1);(*this)[0]+=c;return*this;}
  fps&operator*=(const T&c){fo(i,this->size())(*this)[i]*=c;return*this;}
  base_operator(+,T)
  base_operator(*,T)
  fps differential()const{
    assert(this->size());
    fps r(this->size()-1);
    fo(i,r.size())r[i]=(*this)[i+1]*T{i+1};
    return r;
  }
  fps integral()const{
    fps r(this->size()+1);
    auto iv=inv_enumerate<T>(r.size());
    fo(i,r.size()-1)r[i+1]=(*this)[i]*iv[i+1];
    return r;
  }
  fps inv_sparse(ll deg=-1)const{
    assert((*this)[0]!=T{});
    ll n=this->size();
    if(deg==-1)deg=n;
    vec<pair<ll,T>>p;
    fo(i,1,n)if((*this)[i]!=T{})p.eb(i,(*this)[i]);
    fps r(deg);
    r[0]=T{1}/(*this)[0];
    fo(i,1,deg){
      T t{};
      fe(p,k,fk){
        if(i-k<0)break;
        t-=fk*r[i-k];
      }
      r[i]=r[0]*t;
    }
    return r;
  }
  fps exp_sparse(ll deg=-1)const{
    assert((*this)[0]==T{});
    ll n=this->size();
    if(deg==-1)deg=n;

    vec<pair<ll,T>>p;
    fo(i,1,n)if((*this)[i]!=T{})p.eb(i-1,T{i}*(*this)[i]);
    auto iv=inv_enumerate<T>(deg);
    fps r(deg);
    r[0]=1;
    fo(i,1,deg){
      T t{};
      fe(p,k,fk){
        if(i-k-1<0)break;
        t+=fk*r[i-k-1];
      }
      r[i]=t*iv[i];
    }
    return r;
  }
  fps pow_sparse(lll P,lll Q,ll deg=-1)const{
    assert((*this)[0]==T{1});
    ll n=this->size();
    if(deg==-1)deg=n;

    vec<pair<ll,T>>p;
    fo(i,1,n)if((*this)[i]!=T{})p.eb(i,(*this)[i]);
    auto iv=inv_enumerate<T>(deg);
    fps r(deg);
    r[0]=1;
    T Q_inv=T{1}/Q;
    fo(i,deg-1){
      T t{};
      fe(p,k,fk){
        if(i-k+1<0)break;
        t+=fk*r[i-k+1]*(P*Q_inv*k-(i-k+1));
      }
      r[i+1]=t*iv[i+1];
    }
    return r;
  }
  ll nonzero_terms_count()const{ll r=0;fe(*this,e)r+=(e!=T{});return r;}
  fps inv(ll deg=-1)const{
    assert((*this)[0]!=T{});
    if(deg==-1)deg=this->size();
    if(nonzero_terms_count()<SPARSE_THRESHOLD)return inv_sparse(deg);
    fps r{T{1}/(*this)[0]};
    for(ll i=1;i<deg;i<<=1)r=(r*2-this->pre(i<<1)*(r*r)).pre(i<<1);
    return r.pre(deg);
  }
  fps log(ll deg=-1)const{
    assert((*this)[0]==T{1});
    if(deg==-1)deg=this->size();
    return(differential()*inv(deg)).integral().pre(deg);
  }
  fps exp(ll deg=-1)const{
    assert((*this)[0]==T{});
    if(deg==-1)deg=this->size();
    if(nonzero_terms_count()<SPARSE_THRESHOLD)return exp_sparse(deg);
    fps r{1};
    for(ll i=1;i<deg;i<<=1)r=(r*(this->pre(i<<1)+T{1}-r.log(i<<1))).pre(i<<1);
    return r.pre(deg);
  }
  fps pow(lll K,ll deg=-1)const{
    ll n=this->size();
    if(deg==-1)deg=(n-1)*K+1;
    if(K==0)return fps{1}.pre(deg);
    if(K==1)return this->pre(deg);

    bool is_negative=(K<0);
    K=abs(K);

    ll a;
    for(a=0;a<n&&(*this)[a]==T{};++a);
    if(a==n)return fps(deg);
    if(a*K>=deg)return fps(deg);

    T fa_inv=T{1}/(*this)[a];
    fps g=(*this*fa_inv)>>a;
    T faK=((*this)[a].pow(K));

    if(ll C=nonzero_terms_count();C==1){
      if(is_negative)assert(a==0);
      if(is_negative)faK=faK.inv();
      return fps{faK}<<a*K;
    }else if(C==2){
      if(is_negative)assert(a==0);

      ll b;
      for(b=a+1;b<n&&(*this)[b]==T{};++b);

      T t=1;
      fps r(deg-a*K);
      for(ll i=0;(b-a)*i<deg-a*K;++i){
        r[(b-a)*i]=(is_negative?comb<T>(i+K-1,K-1):comb<T>(K,i))*t;
        t*=g[b-a]*(1-is_negative*2);
      }

      if(is_negative)faK=faK.inv();
      return r*faK<<a*K;
    }

    fps r;
    if(nonzero_terms_count()<SPARSE_THRESHOLD)r=g.pow_sparse(K,1,deg-a*K);
    else r=(g.log(deg)*K).exp(deg-a*K);

    r=r*faK<<a*K;
    return is_negative?r.inv():r;
  }
  fps rev()const{fps r{*this};ranges::reverse(r);return r;}
  static auto polynomial_division(const fps&f,const fps&g){
    ll n=f.size()-g.size()+1;
    fps q=n>0?(f.rev().pre(n)*g.rev().inv(n)).pre(n).rev():fps{};
    fps r=(f-g*q).shrink();
    return pair{q,r};
  }
};
template<class T>using fps=formal_power_series<T>;
template<class T>T bostan_mori(ll n,fps<T>P,fps<T>Q){
  if(P.shrink().size()>=Q.shrink().size()){
    auto[q,r]=fps<T>::polynomial_division(P,Q);
    return(n<q.size()?q[n]:0)+bostan_mori(n,r,Q);
  }

  P.resize(Q.size());
  while(n){
    fps<T>Qsym=Q;
    fo(i,1,Qsym.size(),2)Qsym[i]=-Qsym[i];

    fps<T>PQ=P*Qsym;
    fps<T>QQ=Q*Qsym;
    bool f=n&1;
    fo(i,f,PQ.size(),2)P[i>>1]=PQ[i];
    fo(i,0,QQ.size(),2)Q[i>>1]=QQ[i];
    n>>=1;
  }
  return P[0]/Q[0];
}
}
namespace my{entry
void main(){
  LL(N);
  use_ml1000000007
  if(even(N)){
    pp(bostan_mori(N/2,fps<ml>{1},fps<ml>{1,-1,-1}));
  }else{
    pp(bostan_mori((N-1)/2,fps<ml>{1,1},fps<ml>{1,-1,-1}.pow(2)));
  }
}}