#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; } template struct Mint{ inline 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 *this;} 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;} static Mint comb(long long n,Int k){ Mint num(1),dom(1); for(Int i=0;i ostream& operator<<(ostream &os,Mint m){os< struct NTT{ inline static constexpr Int md = bmds(X); inline 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 class Enumeration{ using M = M_; protected: inline 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>n>>m>>k; NTT<2> ntt; using M = decltype(ntt)::M; using E = Enumeration; using Poly = vector; E::init(2e5+10); chmax(m,1); chmax(k,1); if(!(m<=k)) swap(m,k); if(k==1) drop(E::Fact(n)); if(m==1){ const Int len=n-k; Poly ps(len+1); for(Int i=0;i<(Int)ps.size();i++) ps[i]=E::Fact(i); Poly rs(1,1); for(Int i=0;i<20;i++){ if((k>>i)&1){ rs=ntt.multiply(rs,ps); rs.resize(len+1); } ps=ntt.multiply(ps,ps); ps.resize(len+1); } M ans{0}; for(Int i=0;i<=len;i++){ ans+=rs[i]*E::P(len,i)*E::Fact(i)*E::Fact(len); //cout<