結果
問題 | No.1112 冥界の音楽 |
ユーザー | tko919 |
提出日時 | 2022-02-02 03:29:27 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 7 ms / 2,000 ms |
コード長 | 18,505 bytes |
コンパイル時間 | 3,375 ms |
コンパイル使用メモリ | 253,844 KB |
実行使用メモリ | 5,376 KB |
最終ジャッジ日時 | 2024-06-11 09:18:38 |
合計ジャッジ時間 | 4,403 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge1 |
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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 | 2 ms
5,248 KB |
testcase_01 | AC | 2 ms
5,248 KB |
testcase_02 | AC | 2 ms
5,376 KB |
testcase_03 | AC | 2 ms
5,376 KB |
testcase_04 | AC | 2 ms
5,376 KB |
testcase_05 | AC | 2 ms
5,376 KB |
testcase_06 | AC | 2 ms
5,376 KB |
testcase_07 | AC | 1 ms
5,376 KB |
testcase_08 | AC | 2 ms
5,376 KB |
testcase_09 | AC | 2 ms
5,376 KB |
testcase_10 | AC | 2 ms
5,376 KB |
testcase_11 | AC | 2 ms
5,376 KB |
testcase_12 | AC | 2 ms
5,376 KB |
testcase_13 | AC | 2 ms
5,376 KB |
testcase_14 | AC | 4 ms
5,376 KB |
testcase_15 | AC | 2 ms
5,376 KB |
testcase_16 | AC | 2 ms
5,376 KB |
testcase_17 | AC | 3 ms
5,376 KB |
testcase_18 | AC | 3 ms
5,376 KB |
testcase_19 | AC | 2 ms
5,376 KB |
testcase_20 | AC | 2 ms
5,376 KB |
testcase_21 | AC | 4 ms
5,376 KB |
testcase_22 | AC | 4 ms
5,376 KB |
testcase_23 | AC | 2 ms
5,376 KB |
testcase_24 | AC | 1 ms
5,376 KB |
testcase_25 | AC | 2 ms
5,376 KB |
testcase_26 | AC | 2 ms
5,376 KB |
testcase_27 | AC | 2 ms
5,376 KB |
testcase_28 | AC | 4 ms
5,376 KB |
testcase_29 | AC | 2 ms
5,376 KB |
testcase_30 | AC | 6 ms
5,376 KB |
testcase_31 | AC | 3 ms
5,376 KB |
testcase_32 | AC | 7 ms
5,376 KB |
testcase_33 | AC | 2 ms
5,376 KB |
testcase_34 | AC | 2 ms
5,376 KB |
testcase_35 | AC | 3 ms
5,376 KB |
testcase_36 | AC | 2 ms
5,376 KB |
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 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).rev(); Poly<T> cs({T(1)}),base({T(0),T(1)}); while(t){ if(t&1){ cs*=base; cs%=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 8 "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); } FastIO io; int main(){ int k,m; ll n; io.read(k,m,n); SparseMatrix<Fp> mat(k*k); int p,q,r; rep(_,0,m){ io.read(p,q,r); p--; q--; r--; mat.add(p*k+q,q*k+r,1); } Poly<Fp> b(k*k); rep(i,0,k)b[i*k]=1; auto c=FastPow(mat,b,n-2); Fp ret; rep(i,0,k)ret+=c[i]; io.write(ret.v); return 0; }