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// verification-helper: PROBLEM https://yukicoder.me/problems/104 #include <bits/stdc++.h> using namespace std; #define call_from_test #include "../../mod/mint.cpp" #include "../../polynomial/berlekampmassey.cpp" #include "../../convolution/naive.cpp" #include "../../math/bostanmori.cpp" #undef call_from_test signed main(){ cin.tie(0); ios::sync_with_stdio(0); long long n; int p,c; cin>>n>>p>>c; using M = Mint<int>; using Poly = vector<M>; const int d = 1500; const int MAX = p+c+1; vector<Poly> cf(MAX,Poly(d,0)); cf[0][0]=M(1); for(int v:{2,3,5,7,11,13}){ vector<Poly> nx(MAX,Poly(d,0)); for(int t=0;t<=p;t++) for(int i=0;i<d;i++) for(int j=0;t+j<=p&&i+v*j<d;j++) nx[t+j][i+v*j]+=cf[t][i]; swap(cf,nx); } for(int v:{4,6,8,9,10,12}){ vector<Poly> nx(MAX,Poly(d,0)); for(int t=p;t<=p+c;t++) for(int i=0;i<d;i++) for(int j=0;t+j<=p+c&&i+v*j<d;j++) nx[t+j][i+v*j]+=cf[t][i]; swap(cf,nx); } Poly dp(d*3,0),as(d*3,0); dp[0]=M(1); for(int i=0;i<(int)dp.size();i++){ for(int j=0;j<d&&i+j<(int)dp.size();j++) dp[i+j]+=dp[i]*cf[p+c][j]; for(int j=1;i+j<(int)dp.size();j++) as[i]+=dp[i+j]; } as.resize(d*2); BostanMori<M> bm(naive<M>()); cout<<bm.build(n-1,as,berlekamp_massey(as))<<endl; return 0; }
#line 1 "test/yukicoder/0104.test.cpp" // verification-helper: PROBLEM https://yukicoder.me/problems/104 #include <bits/stdc++.h> using namespace std; #define call_from_test #line 1 "mod/mint.cpp" #line 3 "mod/mint.cpp" using namespace std; #endif //BEGIN CUT HERE template<typename T, T MOD = 1000000007> struct Mint{ inline static constexpr T mod = MOD; T v; Mint():v(0){} Mint(signed v):v(v){} Mint(long long t){v=t%MOD;if(v<0) v+=MOD;} Mint pow(long long k){ Mint res(1),tmp(v); while(k){ if(k&1) res*=tmp; tmp*=tmp; k>>=1; } return res; } static Mint add_identity(){return Mint(0);} static Mint mul_identity(){return Mint(1);} Mint inv(){return pow(MOD-2);} Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;} Mint& operator/=(Mint a){return (*this)*=a.inv();} Mint operator+(Mint a) const{return Mint(v)+=a;} Mint operator-(Mint a) const{return Mint(v)-=a;} Mint operator*(Mint a) const{return Mint(v)*=a;} Mint operator/(Mint a) const{return Mint(v)/=a;} Mint operator+() const{return *this;} Mint operator-() const{return v?Mint(MOD-v):Mint(v);} bool operator==(const Mint a)const{return v==a.v;} bool operator!=(const Mint a)const{return v!=a.v;} static Mint comb(long long n,int k){ Mint num(1),dom(1); for(int i=0;i<k;i++){ num*=Mint(n-i); dom*=Mint(i+1); } return num/dom; } }; template<typename T, T MOD> ostream& operator<<(ostream &os,Mint<T, MOD> m){os<<m.v;return os;} //END CUT HERE #ifndef call_from_test signed main(){ return 0; } #endif #line 1 "polynomial/berlekampmassey.cpp" #line 3 "polynomial/berlekampmassey.cpp" using namespace std; #endif //BEGIN CUT HERE // construct a charasteristic equation from sequence // return a monic polynomial in O(n^2) template<typename T> vector<T> berlekamp_massey(vector<T> &as){ using Poly = vector<T>; int n=as.size(); Poly bs({-T(1)}),cs({-T(1)}); T y(1); for(int ed=1;ed<=n;ed++){ int l=cs.size(),m=bs.size(); T x(0); for(int i=0;i<l;i++) x+=cs[i]*as[ed-l+i]; bs.emplace_back(0); m++; if(x==T(0)) continue; T freq=x/y; if(m<=l){ for(int i=0;i<m;i++) cs[l-1-i]-=freq*bs[m-1-i]; continue; } auto ts=cs; cs.insert(cs.begin(),m-l,T(0)); for(int i=0;i<m;i++) cs[m-1-i]-=freq*bs[m-1-i]; bs=ts; y=x; } for(auto &c:cs) c/=cs.back(); return cs; } //END CUT HERE #ifndef call_from_test signed main(){ return 0; } #endif #line 1 "convolution/naive.cpp" #line 3 "convolution/naive.cpp" using namespace std; #endif //BEGIN CUT HERE // O(N M) template<typename T> decltype(auto) naive(){ using Poly = vector<T>; auto conv=[](Poly as, Poly bs){ Poly cs(as.size()+bs.size()-1,0); for(int i=0;i<(int)as.size();i++) for(int j=0;j<(int)bs.size();j++) cs[i+j]+=as[i]*bs[j]; return cs; }; return +conv; } //END CUT HERE #ifndef call_from_test signed main(){ return 0; } #endif #line 1 "math/bostanmori.cpp" #line 3 "math/bostanmori.cpp" using namespace std; #endif // ref. https://qiita.com/ryuhe1/items/da5acbcce4ac1911f47a //BEGIN CUT HERE // Find k-th term of linear recurrence // execute `conv` O(\log k) times template<typename T> struct BostanMori{ using Poly = vector<T>; using Conv = function<Poly(Poly, Poly)>; Conv conv; BostanMori(Conv conv_):conv(conv_){} Poly sub(Poly as,int odd){ Poly bs((as.size()+!odd)/2); for(int i=odd;i<(int)as.size();i+=2) bs[i/2]=as[i]; return bs; } // as: initial values // cs: monic polynomial T build(long long k,Poly as,Poly cs){ reverse(cs.begin(),cs.end()); assert(cs[0]==T(1)); int n=cs.size()-1; as.resize(n,0); Poly bs=conv(as,cs); bs.resize(n); while(k){ Poly ds(cs); for(int i=1;i<(int)ds.size();i+=2) ds[i]=-ds[i]; bs=sub(conv(bs,ds),k&1); cs=sub(conv(cs,ds),0); k>>=1; } return bs[0]; } }; //END CUT HERE #ifndef call_from_test //INSERT ABOVE HERE signed main(){ return 0; } #endif #line 11 "test/yukicoder/0104.test.cpp" #undef call_from_test signed main(){ cin.tie(0); ios::sync_with_stdio(0); long long n; int p,c; cin>>n>>p>>c; using M = Mint<int>; using Poly = vector<M>; const int d = 1500; const int MAX = p+c+1; vector<Poly> cf(MAX,Poly(d,0)); cf[0][0]=M(1); for(int v:{2,3,5,7,11,13}){ vector<Poly> nx(MAX,Poly(d,0)); for(int t=0;t<=p;t++) for(int i=0;i<d;i++) for(int j=0;t+j<=p&&i+v*j<d;j++) nx[t+j][i+v*j]+=cf[t][i]; swap(cf,nx); } for(int v:{4,6,8,9,10,12}){ vector<Poly> nx(MAX,Poly(d,0)); for(int t=p;t<=p+c;t++) for(int i=0;i<d;i++) for(int j=0;t+j<=p+c&&i+v*j<d;j++) nx[t+j][i+v*j]+=cf[t][i]; swap(cf,nx); } Poly dp(d*3,0),as(d*3,0); dp[0]=M(1); for(int i=0;i<(int)dp.size();i++){ for(int j=0;j<d&&i+j<(int)dp.size();j++) dp[i+j]+=dp[i]*cf[p+c][j]; for(int j=1;i+j<(int)dp.size();j++) as[i]+=dp[i+j]; } as.resize(d*2); BostanMori<M> bm(naive<M>()); cout<<bm.build(n-1,as,berlekamp_massey(as))<<endl; return 0; }