// verification-helper: PROBLEM https://yukicoder.me/problems/444 #include using namespace std; #define call_from_test #ifndef call_from_test #include using namespace std; #endif //BEGIN CUT HERE template struct Mint{ 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 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;} bool operator <(const Mint a)const{return v constexpr T Mint::mod; template ostream& operator<<(ostream &os,Mint m){os< using namespace std; #endif //BEGIN CUT HERE namespace FFT{ using dbl = double; struct num{ dbl x,y; num(){x=y=0;} num(dbl x,dbl y):x(x),y(y){} }; inline num operator+(num a,num b){ return num(a.x+b.x,a.y+b.y); } inline num operator-(num a,num b){ return num(a.x-b.x,a.y-b.y); } inline num operator*(num a,num b){ return num(a.x*b.x-a.y*b.y,a.x*b.y+a.y*b.x); } inline num conj(num a){ return num(a.x,-a.y); } int base=1; vector rts={{0,0},{1,0}}; vector rev={0,1}; const dbl PI=asinl(1)*2; void ensure_base(int nbase){ if(nbase<=base) return; rev.resize(1<>1]>>1)+((i&1)<<(nbase-1)); rts.resize(1< &as){ int n=as.size(); assert((n&(n-1))==0); int zeros=__builtin_ctz(n); ensure_base(zeros); int shift=base-zeros; for(int i=0;i>shift)) swap(as[i],as[rev[i]>>shift]); for(int k=1;k vector multiply(vector &as,vector &bs){ int need=as.size()+bs.size()-1; int nbase=0; while((1< fa(sz); for(int i=0;i>1);i++){ int j=(sz-i)&(sz-1); num z=(fa[j]*fa[j]-conj(fa[i]*fa[i]))*r; if(i!=j) fa[j]=(fa[i]*fa[i]-conj(fa[j]*fa[j]))*r; fa[i]=z; } fft(fa); vector res(need); for(int i=0;i using namespace std; #define call_from_test #include "fastfouriertransform.cpp" #undef call_from_test #endif //BEGIN CUT HERE template struct ArbitraryMod{ using dbl=FFT::dbl; using num=FFT::num; vector multiply(vector as,vector bs){ int need=as.size()+bs.size()-1; int sz=1; while(sz fa(sz),fb(sz); for(int i=0;i<(int)as.size();i++) fa[i]=num(as[i].v&((1<<15)-1),as[i].v>>15); for(int i=0;i<(int)bs.size();i++) fb[i]=num(bs[i].v&((1<<15)-1),bs[i].v>>15); fft(fa);fft(fb); dbl ratio=0.25/sz; num 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); num a1=(fa[i]+conj(fa[j])); num a2=(fa[i]-conj(fa[j]))*r2; num b1=(fb[i]+conj(fb[j]))*r3; num b2=(fb[i]-conj(fb[j]))*r4; if(i!=j){ num c1=(fa[j]+conj(fa[i])); num c2=(fa[j]-conj(fa[i]))*r2; num d1=(fb[j]+conj(fb[i]))*r3; num d2=(fb[j]-conj(fb[i]))*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(fa);fft(fb); vector cs(need); using ll = long long; for(int i=0;i using namespace std; #endif //BEGIN CUT HERE // construct a charasteristic equation from sequence // return a monic polynomial in O(n^2) template vector berlekamp_massey(vector &as){ using Poly = vector; 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 using namespace std; #endif //BEGIN CUT HERE template class Enumeration{ using M = M_; protected: static vector fact,finv,invs; public: static void init(int n){ n=min(n,M::mod-1); int m=fact.size(); if(n=m;i--) finv[i-1]=finv[i]*M(i); for(int i=m;i<=n;i++) invs[i]=finv[i]*fact[i-1]; } static M Fact(int n){ init(n); return fact[n]; } static M Finv(int n){ init(n); return finv[n]; } static M Invs(int n){ init(n); return invs[n]; } static M C(int n,int k){ if(n vector Enumeration::fact=vector(); template vector Enumeration::finv=vector(); template vector Enumeration::invs=vector(); //END CUT HERE #ifndef call_from_test //INSERT ABOVE HERE signed main(){ return 0; } #endif #ifndef call_from_test #include using namespace std; #define call_from_test #include "../combinatorics/enumeration.cpp" #undef call_from_test #endif // http://beet-aizu.hatenablog.com/entry/2019/09/27/224701 //BEGIN CUT HERE template struct FormalPowerSeries : Enumeration { using M = M_; using super = Enumeration; using super::fact; using super::finv; using super::invs; using Poly = vector; using Conv = function; Conv conv; FormalPowerSeries(Conv conv):conv(conv){} Poly pre(const Poly &as,int deg){ return Poly(as.begin(),as.begin()+min((int)as.size(),deg)); } Poly add(Poly as,Poly bs){ int sz=max(as.size(),bs.size()); Poly cs(sz,M(0)); for(int i=0;i<(int)as.size();i++) cs[i]+=as[i]; for(int i=0;i<(int)bs.size();i++) cs[i]+=bs[i]; return cs; } Poly sub(Poly as,Poly bs){ int sz=max(as.size(),bs.size()); Poly cs(sz,M(0)); for(int i=0;i<(int)as.size();i++) cs[i]+=as[i]; for(int i=0;i<(int)bs.size();i++) cs[i]-=bs[i]; return cs; } Poly mul(Poly as,Poly bs){ return conv(as,bs); } Poly mul(Poly as,M k){ for(auto &a:as) a*=k; return as; } // F(0) must not be 0 Poly inv(Poly as,int deg); // not zero Poly div(Poly as,Poly bs); // not zero Poly mod(Poly as,Poly bs); // F(0) must be 1 Poly sqrt(Poly as,int deg); Poly diff(Poly as); Poly integral(Poly as); // F(0) must be 1 Poly log(Poly as,int deg); // F(0) must be 0 Poly exp(Poly as,int deg); // not zero Poly pow(Poly as,long long k,int deg); // x <- x + c Poly shift(Poly as,M c); }; //END CUT HERE #ifndef call_from_test //INSERT ABOVE HERE signed main(){ return 0; } #endif #ifndef call_from_test #include using namespace std; #define call_from_test #include "../combinatorics/enumeration.cpp" #include "base.cpp" #undef call_from_test #endif //BEGIN CUT HERE template vector FormalPowerSeries::inv(Poly as,int deg){ assert(as[0]!=M(0)); Poly rs({M(1)/as[0]}); for(int i=1;i using namespace std; #define call_from_test #include "../combinatorics/enumeration.cpp" #include "base.cpp" #include "inv.cpp" #undef call_from_test #endif //BEGIN CUT HERE template vector FormalPowerSeries::div(Poly as,Poly bs){ while(as.back()==M(0)) as.pop_back(); while(bs.back()==M(0)) bs.pop_back(); if(bs.size()>as.size()) return Poly(); reverse(as.begin(),as.end()); reverse(bs.begin(),bs.end()); int need=as.size()-bs.size()+1; Poly ds=pre(mul(as,inv(bs,need)),need); reverse(ds.begin(),ds.end()); return ds; } //END CUT HERE #ifndef call_from_test //INSERT ABOVE HERE signed main(){ return 0; } #endif #ifndef call_from_test #include using namespace std; #define call_from_test #include "../combinatorics/enumeration.cpp" #include "base.cpp" #include "inv.cpp" #include "div.cpp" #undef call_from_test #endif //BEGIN CUT HERE template vector FormalPowerSeries::mod(Poly as,Poly bs){ if(as==Poly(as.size(),0)) return Poly({0}); as=sub(as,mul(div(as,bs),bs)); if(as==Poly(as.size(),0)) return Poly({0}); while(as.back()==M(0)) as.pop_back(); return as; } //END CUT HERE #ifndef call_from_test //INSERT ABOVE HERE signed main(){ return 0; } #endif #ifndef call_from_test #include using namespace std; #define call_from_test #include "../combinatorics/enumeration.cpp" #include "../formalpowerseries/base.cpp" #include "../polynomial/berlekampmassey.cpp" #undef call_from_test #endif //BEGIN CUT HERE template struct Sequence : FormalPowerSeries{ using FormalPowerSeries::FormalPowerSeries; using Poly = vector; struct Calculator{ const Poly as,cs; Sequence* seq; Calculator(const Poly as_,const Poly cs_,Sequence *seq_): as(as_),cs(cs_),seq(seq_){} M operator()(long long n){ Poly rs({M(1)}),ts({M(0),M(1)}); n--; while(n){ if(n&1) rs=seq->mod(seq->mul(rs,ts),cs); ts=seq->mod(seq->mul(ts,ts),cs); n>>=1; } M res(0); rs.resize(cs.size(),M(0)); for(int i=0;i<(int)cs.size();i++) res+=as[i]*rs[i]; return res; } }; Calculator build(vector as){ return Calculator(as,berlekamp_massey(as),this); } }; //END CUT HERE #ifndef call_from_test //INSERT ABOVE HERE signed main(){ return 0; } #endif #undef call_from_test signed main(){ cin.tie(0); ios::sync_with_stdio(0); using M = Mint; using Poly = vector; ArbitraryMod arb; auto conv=[&](auto as,auto bs){return arb.multiply(as,bs);}; long long n; int p,c; cin>>n>>p>>c; const int d = 606 * 13; auto calc=[&](int l,vector vs){ int m=vs.size(); vector dp(m,Poly(d)); for(int i=0;i=0;j--){ dp[i][j]=0; if(i) dp[i][j]+=dp[i-1][j]; if(j>=vs[i]) dp[i][j]+=dp[i][j-vs[i]]; } } } return dp.back(); }; Poly cf({M(1)}); cf=conv(cf,calc(p,vector({2,3,5,7,11,13}))); cf=conv(cf,calc(c,vector({4,6,8,9,10,12}))); cf.resize(d,M(0)); 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 seq(conv); cout<