結果
| 問題 | No.310 2文字しりとり |
| ユーザー |
 tko919
|
| 提出日時 | 2022-02-02 03:13:47 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,037 ms / 6,000 ms |
| コード長 | 19,189 bytes |
| コンパイル時間 | 3,893 ms |
| コンパイル使用メモリ | 244,308 KB |
| 最終ジャッジ日時 | 2025-01-27 18:21:52 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 28 |
ソースコード
#line 1 "library/Template/template.hpp"#include <bits/stdc++.h>using namespace std;#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)#define ALL(v) (v).begin(),(v).end()using ll=long long int;const int inf = 0x3fffffff;const ll INF = 0x1fffffffffffffff;template<typename T>inline bool chmax(T& a,T b){if(a<b){a=b;return 1;}return 0;}template<typename T>inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;}#line 2 "library/Utility/fastio.hpp"#include <unistd.h>class FastIO{static constexpr int L=1<<16;char rdbuf[L];int rdLeft=0,rdRight=0;inline void reload(){int len=rdRight-rdLeft;memmove(rdbuf,rdbuf+rdLeft,len);rdLeft=0,rdRight=len;rdRight+=fread(rdbuf+len,1,L-len,stdin);}inline bool skip(){for(;;){while(rdLeft!=rdRight and rdbuf[rdLeft]<=' ')rdLeft++;if(rdLeft==rdRight){reload();if(rdLeft==rdRight)return false;}else break;}return true;}template<typename T,enable_if_t<is_integral<T>::value,int> =0>inline bool _read(T& x){if(!skip())return false;if(rdLeft+20>=rdRight)reload();bool neg=false;if(rdbuf[rdLeft]=='-'){neg=true;rdLeft++;}x=0;while(rdbuf[rdLeft]>='0' and rdLeft<rdRight){x=x*10+(neg?-(rdbuf[rdLeft++]^48):(rdbuf[rdLeft++]^48));}return true;}template<typename T,enable_if_t<is_floating_point<T>::value,int> =0>inline bool _read(T& x){if(!skip())return false;if(rdLeft+20>=rdRight)reload();bool neg=false;if(rdbuf[rdLeft]=='-'){neg=true;rdLeft++;}x=0;while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft<rdRight){x=x*10+(rdbuf[rdLeft++]^48);}if(rdbuf[rdLeft]!='.')return true;rdLeft++;T base=.1;while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft<rdRight){x+=base*(rdbuf[rdLeft++]^48);base*=.1;}if(neg)x=-x;return true;}inline bool _read(char& x){if(!skip())return false;if(rdLeft+1>=rdRight)reload();x=rdbuf[rdLeft++];return true;}inline bool _read(string& x){if(!skip())return false;for(;;){int pos=rdLeft;while(pos<rdRight and rdbuf[pos]>' ')pos++;x.append(rdbuf+rdLeft,pos-rdLeft);if(rdLeft==pos)break;rdLeft=pos;if(rdLeft==rdRight)reload();else break;}return true;}template<typename T>inline bool _read(vector<T>& v){for(auto& x:v){if(!_read(x))return false;}return true;}char wtbuf[L],tmp[50];int wtRight=0;inline void flush(){fwrite(wtbuf,1,wtRight,stdout);wtRight=0;}inline void _write(const char& x){if(wtRight>L-32)flush();wtbuf[wtRight++]=x;}inline void _write(const string& x){for(auto& c:x)_write(c);}template<typename T,enable_if_t<is_integral<T>::value,int> =0>inline void _write(T x){if(wtRight>L-32)flush();if(x==0){_write('0');return;}else if(x<0){_write('-');if (__builtin_expect(x == std::numeric_limits<T>::min(), 0)) {switch (sizeof(x)) {case 2: _write("32768"); return;case 4: _write("2147483648"); return;case 8: _write("9223372036854775808"); return;}}x=-x;}int pos=0;while(x!=0){tmp[pos++]=char((x%10)|48);x/=10;}rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i];wtRight+=pos;}template<typename T>inline void _write(const vector<T>& v){rep(i,0,v.size()){if(i)_write(' ');_write(v[i]);}}public:FastIO(){}~FastIO(){flush();}inline void read(){}template <typename Head, typename... Tail>inline void read(Head& head,Tail&... tail){assert(_read(head));read(tail...);}template<bool ln=true,bool space=false>inline void write(){if(ln)_write('\n');}template <bool ln=true,bool space=false,typename Head, typename... Tail>inline void write(const Head& head,const Tail&... tail){if(space)_write(' ');_write(head);write<ln,true>(tail...);}};/*** @brief Fast IO*/#line 3 "sol.cpp"#line 2 "library/Math/modint.hpp"template<int mod=1000000007>struct fp {int v; static int get_mod(){return mod;}int inv() const{int tmp,a=v,b=mod,x=1,y=0;while(b)tmp=a/b,a-=tmp*b,swap(a,b),x-=tmp*y,swap(x,y);if(x<0){x+=mod;} return x;}fp(ll x=0){init(x%mod+mod);}fp& init(int x){v=(x<mod?x:x-mod); return *this;}fp operator-()const{return fp()-*this;}fp pow(ll t){fp res=1,b=*this; while(t){if(t&1)res*=b;b*=b;t>>=1;} return res;}fp& operator+=(const fp& x){return init(v+x.v);}fp& operator-=(const fp& x){return init(v+mod-x.v);}fp& operator*=(const fp& x){v=ll(v)*x.v%mod; return *this;}fp& operator/=(const fp& x){v=ll(v)*x.inv()%mod; return *this;}fp operator+(const fp& x)const{return fp(*this)+=x;}fp operator-(const fp& x)const{return fp(*this)-=x;}fp operator*(const fp& x)const{return fp(*this)*=x;}fp operator/(const fp& x)const{return fp(*this)/=x;}bool operator==(const fp& x)const{return v==x.v;}bool operator!=(const fp& x)const{return v!=x.v;}friend istream& operator>>(istream& is,fp& x){return is>>x.v;}friend ostream& operator<<(ostream& os,const fp& x){return os<<x.v;}};template<typename T>struct factorial {vector<T> Fact,Finv,Inv;factorial(int maxx){Fact.resize(maxx); Finv.resize(maxx); Inv.resize(maxx);Fact[0]=Fact[1]=Finv[0]=Finv[1]=Inv[1]=1;rep(i,2,maxx){Fact[i]=Fact[i-1]*i;} Finv[maxx-1]=Fact[maxx-1].inv();for(int i=maxx-1;i>=2;i--){Finv[i-1]=Finv[i]*i; Inv[i]=Finv[i]*Fact[i-1];}}T fact(int n,bool inv=0){if(n<0)return 0; return (inv?Finv[n]:Fact[n]);}T inv(int n){if(n<0)return 0; return Inv[n];}T nPr(int n,int r,bool inv=0){if(n<0||n<r||r<0)return 0; return fact(n,inv)*fact(n-r,inv^1);}T nCr(int n,int r,bool inv=0){if(n<0||n<r||r<0)return 0; return fact(n,inv)*fact(r,inv^1)*fact(n-r,inv^1);}T nHr(int n,int r,bool inv=0){return nCr(n+r-1,r,inv);}};/*** @brief Modint*/#line 2 "library/Convolution/ntt.hpp"template<typename T,unsigned p=3>struct NTT{vector<T> rt,irt;NTT(int lg=21){unsigned m=T::get_mod()-1; T prt=p;rt.resize(lg); irt.resize(lg);rep(k,0,lg){rt[k]=-prt.pow(m>>(k+2));irt[k]=rt[k].inv();}}void ntt(vector<T>& f,bool inv=0){int n=f.size();if(inv){for(int m=1;m<n;m<<=1){ T w=1;for(int s=0,t=0;s<n;s+=m*2){for(int i=s,j=s+m;i<s+m;i++,j++){auto x=f[i],y=f[j];f[i]=x+y; f[j]=(x-y)*w;} w*=irt[__builtin_ctz(++t)];}} T mul=T(n).inv(); rep(i,0,n)f[i]*=mul;}else{for(int m=n;m>>=1;){ T w=1;for(int s=0,t=0;s<n;s+=m*2){for(int i=s,j=s+m;i<s+m;i++,j++){auto x=f[i],y=f[j]*w;f[i]=x+y; f[j]=x-y;} w*=rt[__builtin_ctz(++t)];}}}}vector<T> mult(const vector<T>& a,const vector<T>& b,bool same=0){if(a.empty() or b.empty())return vector<T>();int n=a.size()+b.size()-1,m=1<<__lg(n*2-1);vector<T> res(m); rep(i,0,a.size()){res[i]=a[i];} ntt(res);if(same)rep(i,0,m)res[i]*=res[i];else{vector<T> c(m); rep(i,0,b.size())c[i]=b[i];ntt(c); rep(i,0,m)res[i]*=c[i];} ntt(res,1); res.resize(n); return res;}};/*** @brief Number Theoretic Transform*/#line 4 "library/Convolution/arbitrary.hpp"using M1=fp<1045430273>; using M2=fp<1051721729>; using M3=fp<1053818881>;NTT<fp<1045430273>,3> N1; NTT<fp<1051721729>,6> N2; NTT<fp<1053818881>,7> N3;template<typename T>vector<T> ArbitraryMult(const vector<T>& a,const vector<T>& b,bool same=0){if(a.empty() or b.empty())return vector<T>();int n=a.size()+b.size()-1; vector<T> res(n); vector<int> vals[3];vector<int> aa(a.size()),bb(b.size());rep(i,0,a.size())aa[i]=a[i].v; rep(i,0,b.size())bb[i]=b[i].v;vector<M1> a1(ALL(aa)),b1(ALL(bb)),c1=N1.mult(a1,b1,same);vector<M2> a2(ALL(aa)),b2(ALL(bb)),c2=N2.mult(a2,b2,same);vector<M3> a3(ALL(aa)),b3(ALL(bb)),c3=N3.mult(a3,b3,same);for(M1 x:c1)vals[0].push_back(x.v);for(M2 x:c2)vals[1].push_back(x.v);for(M3 x:c3)vals[2].push_back(x.v);M2 r_12=M2(M1::get_mod()).inv();M3 r_13=M3(M1::get_mod()).inv(),r_23=M3(M2::get_mod()).inv();M3 r_1323=r_13*r_23;T w1(M1::get_mod()),w2=w1*T(M2::get_mod());rep(i,0,n){ll p=vals[0][i];ll q=(vals[1][i]+M2::get_mod()-p)*r_12.v%M2::get_mod();ll r=((vals[2][i]+M3::get_mod()-p)*r_1323.v+(M3::get_mod()-q)*r_23.v)%M3::get_mod();res[i]=(p+q*w1.v+r*w2.v);} return res;}/*** @brief Arbitrary Mod Convolution*/#line 2 "library/FPS/arbitraryfps.hpp"template<typename T>struct Poly:vector<T>{Poly(int n=0){this->assign(n,T());}Poly(const vector<T>& f){this->assign(ALL(f));}T eval(const T& x){T res;for(int i=this->size()-1;i>=0;i--)res*=x,res+=this->at(i);return res;}Poly rev()const{Poly res=*this; reverse(ALL(res)); return res;}void shrink(){while(!this->empty() and this->back()==0)this->pop_back();}Poly inv()const{assert(this->front()!=0); const int n=this->size();Poly res(1); res.front()=T(1)/this->front();for(int k=1;k<n;k<<=1){Poly g=res,h=*this; h.resize(k*2); res.resize(k*2);g=(g.square()*h); g.resize(k*2);rep(i,k,min(k*2,n))res[i]-=g[i];}res.resize(n); return res;}Poly square()const{return Poly(mult(*this,*this,1));}Poly operator+(const Poly& g)const{return Poly(*this)+=g;}Poly operator+(const T& g)const{return Poly(*this)+=g;}Poly operator-(const Poly& g)const{return Poly(*this)-=g;}Poly operator-(const T& g)const{return Poly(*this)-=g;}Poly operator*(const Poly& g)const{return Poly(*this)*=g;}Poly operator*(const T& g)const{return Poly(*this)*=g;}Poly operator/(const Poly& g)const{return Poly(*this)/=g;}Poly operator%(const Poly& g)const{return Poly(*this)%=g;}Poly& operator+=(const Poly& g){if(g.size()>this->size())this->resize(g.size());rep(i,0,g.size()){(*this)[i]+=g[i];} return *this;}Poly& operator+=(const T& g){if(this->empty())this->push_back(0);(*this)[0]+=g; return *this;}Poly& operator-=(const Poly& g){if(g.size()>this->size())this->resize(g.size());rep(i,0,g.size()){(*this)[i]-=g[i];} return *this;}Poly& operator-=(const T& g){if(this->empty())this->push_back(0);(*this)[0]-=g; return *this;}Poly& operator*=(const Poly& g){*this=mult(*this,g,0);return *this;}Poly& operator*=(const T& g){rep(i,0,this->size())(*this)[i]*=g;return *this;}Poly& operator/=(const Poly& g){if(g.size()>this->size()){this->clear(); return *this;}Poly g2=g;reverse(ALL(*this));reverse(ALL(g2));int n=this->size()-g2.size()+1;this->resize(n); g2.resize(n);*this*=g2.inv(); this->resize(n);reverse(ALL(*this));shrink();return *this;}Poly& operator%=(const Poly& g){*this-=*this/g*g; shrink(); return *this;}Poly diff()const{Poly res(this->size()-1);rep(i,0,res.size())res[i]=(*this)[i+1]*(i+1);return res;}Poly inte()const{Poly res(this->size()+1);for(int i=res.size()-1;i;i--)res[i]=(*this)[i-1]/i;return res;}Poly log()const{assert(this->front()==1); const int n=this->size();Poly res=diff()*inv(); res=res.inte();res.resize(n); return res;}Poly exp()const{assert(this->front()==0); const int n=this->size();Poly res(1),g(1); res.front()=g.front()=1;for(int k=1;k<n;k<<=1){g=(g+g-g.square()*res); g.resize(k);Poly q=*this; q.resize(k); q=q.diff();Poly w=(q+g*(res.diff()-res*q)),t=*this;w.resize(k*2-1); t.resize(k*2);res=(res+res*(t-w.inte())); res.resize(k*2);} res.resize(n); return res;}Poly shift(const int& c)const{const int n=this->size();Poly res=*this,g(n); g[0]=1; rep(i,1,n)g[i]=g[i-1]*c/i;vector<T> fact(n,1);rep(i,0,n){if(i)fact[i]=fact[i-1]*i;res[i]*=fact[i];}res=res.rev();res*=g;res.resize(n);res=res.rev();rep(i,0,n)res[i]/=fact[i];return res;}Poly pow(ll t){int n=this->size(),k=0; while(k<n and (*this)[k]==0)k++;Poly res(n); if(t*k>=n)return res;n-=t*k; Poly g(n); T c=(*this)[k],ic=T(1)/c;rep(i,0,n)g[i]=(*this)[i+k]*ic;g=g.log(); for(auto& x:g)x*=t; g=g.exp();c=c.pow(t); rep(i,0,n)res[i+t*k]=g[i]*c; return res;}vector<T> mult(const vector<T>& a,const vector<T>& b,bool same)const;};/*** @brief Formal Power Series (Arbitrary mod)*/#line 7 "sol.cpp"using Fp=fp<>;template<>vector<Fp> Poly<Fp>::mult(const vector<Fp>& a,const vector<Fp>& b,bool same)const{return ArbitraryMult(a,b,same);}#line 2 "library/Math/bbla.hpp"#line 2 "library/FPS/berlekampmassey.hpp"template<typename T>vector<T> BerlekampMassey(vector<T>& a){int n=a.size(); T d=1;vector<T> b(1),c(1);b[0]=c[0]=1;rep(j,1,n+1){int l=c.size(),m=b.size();T x=0;rep(i,0,l)x+=c[i]*a[j-l+i];b.push_back(0);m++;if(x==0)continue;T coeff=-x/d;if(l<m){auto tmp=c;c.insert(c.begin(),m-l,0);rep(i,0,m)c[m-1-i]+=coeff*b[m-1-i];b=tmp; d=x;}else rep(i,0,m)c[l-1-i]+=coeff*b[m-1-i];}return c;}/*** @brief Berlekamp Massey Algorithm*/#line 2 "library/Utility/random.hpp"struct Random{random_device rnd;unsigned x=123456789,y=362436069,z=521288629,w=rnd();Random(){}unsigned get(){unsigned t=x^(x<<11);x=y,y=z,z=w;return w=(w^(w<<19))^(t^(t>>8));}unsigned get(unsigned L){return get()%(L+1);}template<typename T>T get(T L,T R){return get(R-L)+L;}double uniform(){return double(get())/UINT_MAX;}string str(int n){string ret;rep(i,0,n)ret+=get('a','z');return ret;}template<typename Iter>void shuffle(Iter first,Iter last){if(first==last)return;int len=1;for(auto it=first+1;it!=last;it++){len++;int j=get(0,len-1);if(j!=len-1)iter_swap(it,first+j);}}template<typename T>vector<T> select(int n,T L,T R){set<T> ret;while(ret.size()<n)ret.insert(get(L,R));return {ALL(ret)};}};/*** @brief Random*/#line 5 "library/Math/bbla.hpp"Random genBBLA;template<typename T>Poly<T> RandPoly(int n){Poly<T> ret(n);for(auto& x:ret)x=genBBLA.get(1,T::get_mod()-1);return ret;}template<typename T>struct SparseMatrix{vector<T> base;vector<map<int,T>> extra;SparseMatrix(int n,T v=0):base(n,v),extra(n){}int size()const{return base.size();}inline void add(int i,int j,T x){extra[i][j]+=x;}friend Poly<T> operator*(const SparseMatrix<T>& A,const Poly<T>& b){int n=A.size();Poly<T> ret(n);T sum;for(auto& v:b)sum+=v;rep(i,0,n){T add=sum;for(auto& [j,v]:A.extra[i]){ret[i]+=v*b[j];add-=b[j];}ret[i]+=add*A.base[i];}return ret;}void mul(int i,T x){base[i]*=x;for(auto& [_,v]:extra[i])v*=x;}};template<typename T>Poly<T> MinPolyforVector(const vector<Poly<T>>& b){int n=b.size(),m=b[0].size();Poly<T> base=RandPoly<T>(m),a(n);rep(i,0,n)rep(j,0,m)a[i]+=base[j]*b[i][j];return Poly<T>(BerlekampMassey(a)).rev();}template<typename T>Poly<T> MinPolyforMatrix(const SparseMatrix<T>& A){int n=A.size();Poly<T> base=RandPoly<T>(n);vector<Poly<T>> b(n*2+1);rep(i,0,n*2+1)b[i]=base,base=A*base;return MinPolyforVector(b);}template<typename T>Poly<T> FastPow(const SparseMatrix<T>& A,Poly<T> b,ll t){int n=A.size();auto mp=MinPolyforMatrix(A);Poly<T> cs({T(1)}),base({T(0),T(1)});while(t){if(t&1)cs=(cs*base)%mp;base=base.square();base%=mp;t>>=1;}Poly<T> ret(n);for(auto& c:cs)ret+=b*c,b=A*b;return ret;}template<typename T>T FastDet(const SparseMatrix<T>& A){int n=A.size();for(;;){Poly<T> d=RandPoly<T>(n);SparseMatrix<T> AD=A;rep(i,0,n)AD.mul(i,d[i]);auto mp=MinPolyforMatrix(AD);if(mp.back()==0)return 0;if(int(mp.size())!=n+1)continue;T ret=mp.back(),base=1;if(n&1)ret=-ret;for(auto& v:d)base*=v;return ret/base;}}/*** @brief Black Box Linear Algebra*/#line 13 "sol.cpp"factorial<Fp> fact(8020);int g[4010][4010]={},in[4010],out[4010];void fail(){puts("0"); exit(0);}FastIO io;int main(){int n,m;io.read(n,m);if(n*n==m){puts("1"); return 0;}rep(i,0,n){g[i][i]=in[i]=out[i]=n;rep(j,0,n)g[i][j]--;}rep(_,0,m){int x,y;io.read(x,y);x--; y--;in[y]--; out[x]--;g[x][y]++; g[y][y]--;}int s=-1,t=-1,N=0,v[4010];rep(i,0,n){if(in[i]==0 and out[i]==0)continue;v[N++]=i;if(abs(in[i]-out[i])>1)fail();if(out[i]==in[i]+1){if(s!=-1)fail(); s=i;}if(out[i]+1==in[i]){if(t!=-1)fail(); t=i;}}Fp ret=n*n-m;if(s!=-1 and t!=-1){in[s]++; out[t]++;g[t][s]--; g[s][s]++;ret=1;}rep(i,0,N)ret*=fact.fact(in[v[i]]-1);SparseMatrix<Fp> mat(N-1,-1);rep(i,0,N-1)rep(j,0,N-1)if(g[v[i]][v[j]]!=-1 or i==j){mat.add(i,j,g[v[i]][v[j]]);}ret*=FastDet(mat);io.write(ret.v);return 0;}