#include using namespace std; using Int = long long; template inline void chmin(T1 &a,T2 b){if(a>b) a=b;} template inline void chmax(T1 &a,T2 b){if(a 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< struct Kitamasa{ using VR = vector; VR cs; vector rs; int m; Kitamasa(const VR &C) :cs(C),rs(1),m(C.size()){ rs[0].assign(2*m+1,R::add_identity()); rs[0][1]=R::mul_identity(); } VR merge(const VR &xs,const VR &ys){ VR zs(2*m+1,R::add_identity()); for(int i=1;i<=m;i++) for(int j=1;j<=m;j++) zs[i+j]=zs[i+j]+(xs[i]*ys[j]); for(int i=2*m;i>m;zs[i--]=R::add_identity()) for(int j=1;j<=m;j++) zs[i-j]=zs[i-j]+(cs[m-j]*zs[i]); return zs; } R calc(const VR &A,long long n){ assert((int)A.size()==m); VR res(rs[0]); for(int i=0;n;i++,n>>=1){ if(i>=(int)rs.size()) rs.emplace_back(merge(rs[i-1],rs[i-1])); if(~n&1) continue; res=merge(res,rs[i]); } R ans=R::add_identity(); for(int i=1;i<=m;i++) ans=ans+(res[i]*A[i-1]); return ans; } }; // construct a charasteristic equation from sequence // return a monic polynomial in O(n^2) template vector berlekamp_massey(const 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>n>>p>>c; using M = Mint; const int d = 1500; const int MAX = p+c+1; vector> cf(MAX,vector(d,0)); cf[0][0]=M(1); for(int v:{2,3,5,7,11,13}){ vector> nx(MAX,vector(d,0)); for(int t=0;t<=p;t++) for(int i=0;i> nx(MAX,vector(d,0)); for(int t=p;t<=p+c;t++) for(int i=0;i 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 kt(cs); as.resize(cs.size()); cout<