#define _USE_MATH_DEFINES #include using namespace std; //template #define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++) #define ALL(v) (v).begin(),(v).end() typedef long long int ll; const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; const double eps=1e-12; templateinline bool chmax(T& a,T b){if(ainline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;} //end templatestruct fp { using uint=unsigned; uint v; static uint get_mod(){return mod;} int inv() const{ int tmp,a=v,b=mod,x=1,y=0; while(b)tmp=a/b,a-=tmp*b,swap(a,b),x-=tmp*y,swap(x,y); if(x<0){x+=mod;} return x; } fp(ll x=0){init(x%mod+mod);} fp& init(uint x){v=(x>=1;} return res;} fp& operator+=(const fp& x){return init(v+x.v);} fp& operator-=(const fp& x){return init(v+mod-x.v);} fp& operator*=(const fp& x){v=ll(v)*x.v%mod; return *this;} fp& operator/=(const fp& x){v=ll(v)*x.inv()%mod; return *this;} fp operator+(const fp& x)const{return fp(*this)+=x;} fp operator-(const fp& x)const{return fp(*this)-=x;} fp operator*(const fp& x)const{return fp(*this)*=x;} fp operator/(const fp& x)const{return fp(*this)/=x;} bool operator==(const fp& x)const{return v==x.v;} bool operator!=(const fp& x)const{return v!=x.v;} friend istream& operator>>(istream& is,fp& x){is>>x.v; return is;} friend ostream& operator<<(ostream& os,fp x){os<; templatestruct factorial { vector Fact,Finv,Inv; factorial(int maxx){ Fact.resize(maxx); Finv.resize(maxx); Inv.resize(maxx); Fact[0]=Fact[1]=Finv[0]=Finv[1]=Inv[1]=1; rep(i,2,maxx){Fact[i]=Fact[i-1]*i;} Finv[maxx-1]=Fact[maxx-1].inv(); for(int i=maxx-1;i>=2;i--){Finv[i-1]=Finv[i]*i; Inv[i]=Finv[i]*Fact[i-1];} } T fact(int n,bool inv=0){if(inv)return Finv[n];else return Fact[n];} T inv(int n){return Inv[n];} T nPr(int n,int r){if(n<0||nstruct NTT{ vector rt,irt; NTT(int lg=21){ unsigned m=T::get_mod()-1; T prt=p; rt.resize(lg); irt.resize(lg); rep(k,0,lg){ rt[k]=-prt.pow(m>>(k+2)); irt[k]=rt[k].inv(); } } void ntt(vector& f,bool inv=0){ int n=f.size(); if(inv){ for(int m=1;m>=1;){ T w=1; for(int s=0,t=0;s mult(const vector& a,const vector& b,bool same=0){ if(a.empty() and b.empty())return vector(); int n=a.size()+b.size()-1,m=1<<__lg(n*2-1); vector res(m); rep(i,0,a.size()){res[i]=a[i];} ntt(res); if(same)rep(i,0,m)res[i]*=res[i]; else{ vector c(m); rep(i,0,b.size())c[i]=b[i]; ntt(c); rep(i,0,m)res[i]*=c[i]; } ntt(res,1); return res; } }; NTT ntt; vector mult(const vector& a,const vector& b,bool same){ return ntt.mult(a,b,same); } factorial fact(2010101); templatestruct Poly:vector{ Poly(int n=0){this->assign(n,T());} Poly(const vector& f){this->assign(ALL(f));} T eval(const T& x){T res; for(auto& v:*this)res*=x,res+=v; return res;} Poly rev()const{Poly res=*this; reverse(ALL(res)); return res;} void shrink(){while(!this->empty() and this->back()==0)this->pop_back();} Poly inv()const{ assert(this->front()!=0); const int n=this->size(); Poly res(1); res.front()=T(1)/this->front(); for(int k=1;kthis->size())this->resize(g.size()); rep(i,0,g.size()){(*this)[i]+=g[i];} shrink(); return *this; } Poly& operator-=(const Poly& g){ if(g.size()>this->size())this->resize(g.size()); rep(i,0,g.size()){(*this)[i]-=g[i];} shrink(); return *this; } Poly& operator*=(const Poly& g){ *this=mult(*this,g,0); shrink(); return *this; } Poly& operator/=(const Poly& g){ if(g.size()>this->size()){ this->clear(); return *this; } *this=this->rev(); g=g.rev(); int n=this->size()-g.size()+1; this->resize(n); g.resize(n); *this*=g.inv_fast(); this->resize(n); // *this=this->rev(); shrink(); return *this; } Poly& operator%=(Poly& g){*this-=*this/g*g; shrink(); return *this;} Poly diff()const{ Poly res(this->size()-1); rep(i,0,res.size())res[i]=(*this)[i+1]*(i+1); return res; } Poly inte()const{ Poly res(this->size()+1); for(int i=res.size()-1;i;i--)res[i]=(*this)[i-1]*fact.inv(i); return res; } Poly log()const{ assert(this->front()==1); const int n=this->size(); Poly res=diff()*inv_fast(); res=res.inte(); // res.resize(n); return res; } Poly exp()const{ assert(this->front()==0); const int n=this->size(); Poly res(1),g(1); res.front()=g.front()=1; for(int k=1;ksize(); Poly res=*this,g(n); g[1]=c; g=g.exp(); rep(i,0,n){res[i]*=fact.fact(i);} res=res.rev(); res*=g; res.resize(n); res=res.rev(); rep(i,0,n){res[i]*=fact.fact(i,1);} return res; } Poly inv_fast()const{ const int n=this->size(); Poly res(1); res.front()=T(1)/this->front(); for(int k=1;ksize(); if(n==1)return Poly({T(1)}); Poly b(2),c(1),z1,z2(2); b[0]=c[0]=z2[0]=z2[1]=1; b[1]=(*this)[1]; for(int k=2;k>1)z[i]=0; ntt.ntt(z); rep(i,0,k)z[i]*=-z1[i]; ntt.ntt(z,1); c.insert(c.end(),z.begin()+(k>>1),z.end()); z2=c; z2.resize(k*2); ntt.ntt(z2); Poly x=*this; x.resize(k); x=x.diff(); x.resize(k); ntt.ntt(x); rep(i,0,k)x[i]*=y[i]; ntt.ntt(x,1); Poly bb=b.diff(); rep(i,0,k-1)x[i]-=bb[i]; x.resize(k*2); rep(i,0,k-1){x[k+i]=x[i]; x[i]=0;} ntt.ntt(x); rep(i,0,k*2)x[i]*=z2[i]; ntt.ntt(x,1); x.pop_back(); x=x.inte(); rep(i,k,min(n,k*2))x[i]+=(*this)[i]; rep(i,0,k)x[i]=0; ntt.ntt(x); rep(i,0,k*2)x[i]*=y[i]; ntt.ntt(x,1); b.insert(b.end(),x.begin()+k,x.end()); } b.resize(n); return b; } Poly pow(ll t){ int n=this->size(),k=0; while(k=n)return res; n-=t*k; Poly g(n); T c=(*this)[k],ic=T(1)/c; rep(i,0,n)g[i]=(*this)[i+k]*ic; g=g.log(); for(auto& x:g)x*=t; g=g.exp_fast(); // c=c.pow(t); rep(i,0,n)res[i+t*k]=g[i]*c; return res; } }; Fp nth(Poly p,Poly q,ll n){ while(n){ Poly ref(q),np,nq; for(int i=1;i<(int)q.size();i+=2)ref[i]*=-1; p*=ref; q*=ref; for(int i=n&1;i<(int)p.size();i+=2)np.emplace_back(p[i]); for(int i=0;i<(int)q.size();i+=2)nq.emplace_back(q[i]); swap(p,np); swap(q,nq); n>>=1; } return p[0]/q[0]; } /* [x^N*y^K] N! * e^{Mx}((e^x-1)y+1)^M =N!*nCr(M,K)* [x^N] e^{Mx}(e^x-1)^K */ int main(){ int n,m,k; cin>>n>>m>>k; Poly f(n+1),g(n+1); Fp pw=1; rep(i,0,n+1){ f[i]=pw*fact.fact(i,1); g[i]=fact.fact(i,1); pw*=m; } g[0]=0; f*=g.pow(k); Fp res=fact.fact(n)*fact.nCr(m,k)*f[n]; cout<