// verification-helper: PROBLEM https://yukicoder.me/problems/444 #include using namespace std; #define call_from_test 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< 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 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 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 struct BostanMori{ using Poly = vector; using Conv = function; 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]; } }; #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; cin>>n; n--; int p,c; cin>>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<