#include using namespace::std; using lint=long long; constexpr lint MOD=1000000007LL; #define rep(i,n) for(int i=0;i struct FPS_BASE:vector{ using vector::vector; inline P operator +(T x)noexcept{return P(*static_cast(this))+=x;} inline P operator -(T x)noexcept{return P(*static_cast(this))-=x;} inline P operator *(T x)noexcept{return P(*static_cast(this))*=x;} inline P operator /(T x)noexcept{return P(*static_cast(this))/=x;} inline P operator <<(int x)noexcept{return P(*static_cast(this))<<=x;} inline P operator >>(int x)noexcept{return P(*static_cast(this))>>=x;} inline P operator +(const P& x)noexcept{return P(*static_cast(this))+=x;} inline P operator -(const P& x)noexcept{return P(*static_cast(this))-=x;} inline P operator -()noexcept{return P(1,T(0))-=P(*static_cast(this));} inline P operator *(const P& x)noexcept{return P(*static_cast(this))*=x;} inline P operator /(const P& x)noexcept{return P(*static_cast(this))/=x;} inline P operator %(const P& x)noexcept{return P(*static_cast(this))%=x;} inline P &operator +=(T x){ if(this->size()==0)this->resize(1,T(0)); (*static_cast(this))[0]+=x; return (*static_cast(this)); } inline P &operator -=(T x){ if(this->size()==0)this->resize(1,T(0)); (*static_cast(this))[0]-=x; return (*static_cast(this)); } inline P &operator *=(T x){ for(int i=0;i<(int)this->size();++i){ (*static_cast(this))[i]*=x; } return (*static_cast(this)); } inline P &operator /=(T x){ return (*static_cast(this))*=(T(1)/x); } inline P &operator <<=(int x){ P ret(x,T(0)); ret.insert(ret.end(),begin(*static_cast(this)),end(*static_cast(this))); return (*static_cast(this))=ret; } inline P &operator >>=(int x){ P ret; ret.insert(ret.end(),begin(*static_cast(this))+x,end(*static_cast(this))); return (*static_cast(this))=ret; } inline P &operator +=(const P& x){ if(this->size()resize(x.size(),T(0)); for(int i=0;i<(int)x.size();++i){ (*this)[i]+=x[i]; } return (*static_cast(this)); } inline P &operator -=(const P& x){ if(this->size()resize(x.size(),T(0)); for(int i=0;i<(int)x.size();++i){ (*static_cast(this))[i]-=x[i]; } return (*static_cast(this)); } inline P &operator *=(const P& x){ return (*static_cast(this))=mul((*static_cast(this)),x); } inline P &operator /=(P x){ if(this->size()clear(); return (*static_cast(this)); } const int n=this->size()-x.size()+1; return (*static_cast(this)) = (rev().pre(n)*x.rev().inv(n)).pre(n).rev(n); } inline P &operator %=(const P& x){ return ((*static_cast(this))-=*static_cast(this)/x*x); } inline P& shrink(){while((*static_cast(this)).back()==0)(*static_cast(this)).pop_back();return (*static_cast(this));} inline P pre(int sz)const{ return P(begin(*this),begin(*this)+min((int)this->size(),sz)); } inline P rev(int deg=-1){ P ret(*static_cast(this)); if(deg!=-1)ret.resize(deg,T(0)); reverse(begin(ret),end(ret)); return ret; } P inv(int deg=-1){ assert((*static_cast(this))[0]!=T(0)); const int n=deg==-1?this->size():deg; P ret({T(1)/(*this)[0]}); for(int i=1;i(this)); for(int i=0;isize(),x.size()));++i){ ret[i]*=x[i]; } return ret; } P diff(){ P ret(*static_cast(this)); for(int i=0;i<(int)ret.size();i++){ ret[i]*=i; } return ret>>1; } P integral(){ P ret(*static_cast(this)); for(int i=0;i<(int)ret.size();i++){ ret[i]/=i+1; } return ret<<1; } P log(int deg=-1){ assert((*this)[0]==T(1)); const int n=deg==-1?this->size():deg; return (diff()*inv(n)).pre(n-1).integral(); } P exp(int deg=-1){ assert((*this)[0]==T(0)); const int n=deg==-1?this->size():deg; P ret({T(1)}); for(int i=1;ilog()*n).exp(); } P sqrt(int deg=-1){ const int n=deg==-1?this->size():deg; if((*this)[0]==T(0)) { for(int i=1;i<(int)this->size();i++) { if((*this)[i]!=T(0)) { if(i&1)return{}; if(n-i/2<=0)break; auto ret=(*this>>i).sqrt(n-i/2)<<(i/2); if((int)ret.size()size()-1;i>=0;--i){ res*=x; res+=(*this)[i]; } return res; } vector multipoint_eval(const vector&x){ const int n=x.size(); P* v=new P[2*n-1]; for(int i=0;i=0;i--){v[i]=v[i*2+1]*v[i*2+2];} v[0]=P(*static_cast(this))%v[0];v[0].shrink(); for(int i=1;ires(n); for(int i=0;i struct fps1:FPS_BASE>{ class mint_fps; using FPS_BASE>::FPS_BASE; using P=fps1; P mul(P s,P t)override{ lint n=s.size()+t.size()-1; lint h=1; while((1<a(1< ntt(vector v,const int& h,const bool& inv){ int n=v.size(),mask=n-1; vector tmp(n); vector table(n,1); mint_fps theta=mint_fps(3).base(h); if(inv)theta=theta.inv(); for(int i=1;i>1,t=h-1;j>=1;j>>=1,--t){ for(int k=0;k>t; tmp[k]=v[((i<<(t+1))|s)&mask]+table[i*j]*v[((i<<(t+1))|j|s)&mask]; } swap(v,tmp); } if(inv)for(int i=0;i=0?x%get_mod():get_mod()-(-x)%get_mod(); } } constexpr u64 value() noexcept { return garner(); } constexpr mint_fps operator+(const mint_fps rhs)const noexcept{return mint_fps(*this) += rhs;} constexpr mint_fps operator-(const mint_fps rhs)const noexcept{return mint_fps(*this)-=rhs;} constexpr mint_fps operator*(const mint_fps rhs) const noexcept {return mint_fps(*this) *= rhs;} constexpr mint_fps operator/(const mint_fps rhs) const noexcept {return mint_fps(*this) /= rhs;} constexpr mint_fps &operator+=(const mint_fps rhs) noexcept { for(int i=0;i<3;++i){ a[i]+=rhs.a[i]; if (a[i]>=mods[i])a[i]-=mods[i]; } return *this; } constexpr bool operator==(mint_fps x) noexcept { return a==x.a; } constexpr bool operator!=(mint_fps x) noexcept { return a!=x.a; } constexpr mint_fps &operator-=(const mint_fps rhs) noexcept { for(int i=0;i<3;++i){ a[i]-=rhs.a[i]; if (a[i]>=mods[i])a[i]-=mods[i]; } return *this; } constexpr mint_fps &operator*=(const mint_fps rhs) noexcept { for(int i=0;i<3;++i){ a[i]=a[i]*rhs.a[i]%mods[i]; } return *this; } constexpr mint_fps &operator/=(mint_fps rhs)noexcept{ for(int i=0;i<3;i++){ u64 ret =rhs.a[i]; u64 exp=mods[i]-2; while (exp) { if (exp %2) { (a[i]*=ret)%=mods[i]; } (ret *= ret)%=mods[i]; exp /= 2; } } return *this; } constexpr mint_fps operator++(int n) noexcept { return *this+=1; } constexpr mint_fps operator--(int n) noexcept { return *this-=1; } constexpr mint_fps base(int h)noexcept{ for(int i=0;i<3;i++){ u64 ret =3; a[i]=1; u64 exp=((mods[i]-1)>>h); while (exp) { if (exp %2) { (a[i]*=ret)%=mods[i]; } (ret *= ret)%=mods[i]; exp /= 2; } } return *this; } constexpr mint_fps inv(){ return mint_fps(1)/(*this); } constexpr static u64 get_mod(){return MOD;} constexpr u64 garner(){ const int sz=3; using u64 = long long; const u64 mods[4]={1224736769,1045430273,1007681537,get_mod()}; u64 coeffs[sz+1]={1,1,1,1}; u64 constants[sz+1]={}; auto modinv=[](u64 x,u64 mod){ u64 y=mod-2; u64 ret=1; while(y>0) { if(y&1)(ret*=x)%=mod; (x*=x)%=mod; y>>=1; } return ret; }; for(int i=0;i=0?x%get_mod():get_mod()-(-x)%get_mod()){} constexpr u64 &value()noexcept{return a;} constexpr const u64 &value() const noexcept {return a;} constexpr mint operator+(const mint rhs)const noexcept{return mint(*this) += rhs;} constexpr mint operator-(const mint rhs)const noexcept{return mint(*this)-=rhs;} constexpr mint operator*(const mint rhs) const noexcept {return mint(*this) *= rhs;} constexpr mint operator/(const mint rhs) const noexcept {return mint(*this) /= rhs;} constexpr mint &operator+=(const mint rhs) noexcept { a += rhs.a; if (a >= get_mod())a -= get_mod(); return *this; } constexpr mint &operator-=(const mint rhs) noexcept { if (a= get_mod())a -= get_mod(); return *this; } constexpr mint operator--(int n) noexcept { if (a<1)a += get_mod(); a -= 1; return *this; } constexpr mint &operator/=(mint rhs) noexcept { u64 exp=get_mod()-2; while (exp) { if (exp % 2) { *this *= rhs; } rhs *= rhs; exp /= 2; } return *this; } constexpr bool operator==(mint x) noexcept { return a==x.a; } constexpr bool operator!=(mint x) noexcept { return a!=x.a; } constexpr static int root(){ mint root = 2; while(root.pow((get_mod()-1)>>1).a==1)root++; return root.a; } constexpr mint pow(long long n){ long long x=a; mint ret = 1; while(n>0) { if(n&1)(ret*=x); (x*=x)%=get_mod(); n>>=1; } return ret; } constexpr mint inv(){ return pow(get_mod()-2); } static vector fac,ifac; static bool init; void build(){ init=0; fac.resize(10101011); ifac.resize(10101011); fac[0]=1,ifac[0]=1; for(int i=1;i<10101011;i++)fac[i]=fac[i-1]*i; ifac[10101010]=fac[10101010].inv(); for(int i=10101009;i>=0;i--)ifac[i]=ifac[i+1]*(i+1); } mint comb(lint b){ if(init)build(); if(a==0&&b==0)return 1; if((lint)a>(istream& lhs,mint& rhs) noexcept { lhs >> rhs.a; return lhs; } constexpr static u64 get_mod(){return MOD;} }; vector mint::fac; vector mint::ifac; bool mint::init=1; int main(){ lint n,d,k; cin>>n>>d>>k; fps1v(k); rep(i,min(k,d))v[i]=1; v=v.pow(n)<