#include using namespace std; using Int = long long; const char newl = '\n'; template inline void chmin(T1 &a,T2 b){if(a>b) a=b;} template inline void chmax(T1 &a,T2 b){if(a void drop(const T &x){cout< vector read(size_t n){ vector ts(n); for(size_t i=0;i>ts[i]; return ts; } #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< 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(); 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; } bool is_zero(Poly as){ return as==Poly(as.size(),0); } void shrink(Poly &as){ assert(not is_zero(as)); while(as.back()==M(0)) as.pop_back(); } // 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); }; template vector FormalPowerSeries::inv(Poly as,int deg){ assert(as[0]!=M(0)); Poly rs({M(1)/as[0]}); for(int i=1;i vector FormalPowerSeries::div(Poly as,Poly bs){ shrink(as);shrink(bs); if(as.size() vector FormalPowerSeries::mod(Poly as,Poly bs){ if(is_zero(as)) return Poly({0}); shrink(as);shrink(bs); as=sub(as,mul(div(as,bs),bs)); if(is_zero(as)) return Poly({0}); shrink(as); return as; } template vector FormalPowerSeries::sqrt(Poly as,int deg){ assert(as[0]==M(1)); M inv2=M(1)/M(2); Poly ss({M(1)}); for(int i=1;i vector FormalPowerSeries::diff(Poly as){ int n=as.size(); Poly rs(n); for(int i=1;i vector FormalPowerSeries::integral(Poly as){ super::init(as.size()+1); int n=as.size(); Poly rs(n+1); rs[0]=M(0); for(int i=0;i vector FormalPowerSeries::log(Poly as,int deg){ return pre(integral(mul(diff(as),inv(as,deg))),deg); } template vector FormalPowerSeries::exp(Poly as,int deg){ Poly fs({M(1)}); as[0]+=M(1); for(int i=1;i vector FormalPowerSeries::pow(Poly as,long long k,int deg){ if(is_zero(as)) return Poly(deg,M(0)); shrink(as); int cnt=0; while(as[cnt]==M(0)) cnt++; if(cnt*k>=deg) return Poly(deg,M(0)); as.erase(as.begin(),as.begin()+cnt); deg-=cnt*k; M c=as[0]; Poly zs(cnt*k,M(0)); Poly rs=mul(exp(mul(log(mul(as,c.inv()),deg),M(k)),deg),c.pow(k)); zs.insert(zs.end(),rs.begin(),rs.end()); return pre(zs,deg+cnt*k); } template vector FormalPowerSeries::shift(Poly as,M c){ super::init(as.size()+1); int n=as.size(); for(int i=0;i struct NTT{ static constexpr int md = bmds(X); static constexpr int rt = brts(X); using M = Mint; vector< vector > rts,rrts; void ensure_base(int n){ if((int)rts.size()>=n) return; rts.resize(n);rrts.resize(n); for(int i=1;i &as,bool f){ int n=as.size(); assert((n&(n-1))==0); ensure_base(n); for(int i=0,j=1;j+1>1;k>(i^=k);k>>=1); if(i>j) swap(as[i],as[j]); } for(int i=1;i multiply(vector as,vector bs){ int need=as.size()+bs.size()-1; int sz=1; while(sz multiply(vector as,vector bs){ vector am(as.size()),bm(bs.size()); for(int i=0;i<(int)am.size();i++) am[i]=M(as[i]); for(int i=0;i<(int)bm.size();i++) bm[i]=M(bs[i]); vector cm=multiply(am,bm); vector cs(cm.size()); for(int i=0;i<(int)cs.size();i++) cs[i]=cm[i].v; return cs; } }; template constexpr int NTT::md; template constexpr int NTT::rt; //INSERT ABOVE HERE signed main(){ cin.tie(0); ios::sync_with_stdio(0); NTT<2> ntt; using M = decltype(ntt)::M; auto conv=[&](auto as,auto bs){return ntt.multiply(as,bs);}; FormalPowerSeries FPS(conv); int n,m,k; cin>>n>>m>>k; auto ps=FPS.exp({M(0),M(1)},n+1); ps[0]-=M(1); auto qs=FPS.pow(ps,k,n+1); M ans{0}; using E = Enumeration; E::init(n+m); vector po(n+1,1); for(int i=0;i+1<(int)po.size();i++) po[i+1]=po[i]*M(m); for(int l=k;l<=n;l++) ans+=E::C(m,k)*E::C(n,l)*E::Fact(l)*qs[l]*po[n-l]; cout<