#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{ 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 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; struct Garner{ using ll = long long; static NTT<0> ntt0; static NTT<1> ntt1; static NTT<2> ntt2; static constexpr int pow(int a,int b,int md){ int res=1; a=a%md; while(b){ if(b&1) res=(ll)res*a%md; a=(ll)a*a%md; b>>=1; } return res; } static constexpr int inv(int x,int md){ return pow(x,md-2,md); } inline void garner(int &c0,int c1,int c2,int m01,int MOD){ static constexpr int r01=inv(ntt0.md,ntt1.md); static constexpr int r02=inv(ntt0.md,ntt2.md); static constexpr int r12=inv(ntt1.md,ntt2.md); c1=(ll)(c1-c0)*r01%ntt1.md; if(c1<0) c1+=ntt1.md; c2=(ll)(c2-c0)*r02%ntt2.md; c2=(ll)(c2-c1)*r12%ntt2.md; if(c2<0) c2+=ntt2.md; c0%=MOD; c0+=(ll)c1*ntt0.md%MOD; if(c0>=MOD) c0-=MOD; c0+=(ll)c2*m01%MOD; if(c0>=MOD) c0-=MOD; } inline void garner(vector< vector > &cs,int MOD){ int m01 =(ll)ntt0.md*ntt1.md%MOD; int sz=cs[0].size(); for(int i=0;i multiply(vector as,vector bs,int MOD){ vector< vector > cs(3); cs[0]=ntt0.multiply(as,bs); cs[1]=ntt1.multiply(as,bs); cs[2]=ntt2.multiply(as,bs); size_t sz=as.size()+bs.size()-1; for(auto& v:cs) v.resize(sz); garner(cs,MOD); return cs[0]; } template decltype(auto) multiply(vector am, vector bm){ vector as(am.size()),bs(bm.size()); for(int i=0;i<(int)as.size();i++) as[i]=am[i].v; for(int i=0;i<(int)bs.size();i++) bs[i]=bm[i].v; vector cs=multiply(as,bs,T::mod); vector cm(cs.size()); for(int i=0;i<(int)cm.size();i++) cm[i]=T(cs[i]); return cm; } }; NTT<0> Garner::ntt0; NTT<1> Garner::ntt1; NTT<2> Garner::ntt2; template struct Rint{ static T mod; static void set_mod(T nmod){mod=nmod;} T v; Rint():v(0){} Rint(signed v):v(v){} Rint(long long t){v=t%mod;if(v<0) v+=mod;} Rint pow(long long k){ Rint res(1),tmp(v); while(k){ if(k&1) res*=tmp; tmp*=tmp; k>>=1; } return res; } static Rint add_identity(){return Rint(0);} static Rint mul_identity(){return Rint(1);} Rint inv(){return pow(mod-2);} Rint& operator+=(Rint a){v+=a.v;if(v>=mod)v-=mod;return *this;} Rint& operator-=(Rint a){v+=mod-a.v;if(v>=mod)v-=mod;return *this;} Rint& operator*=(Rint a){v=1LL*v*a.v%mod;return *this;} Rint& operator/=(Rint a){return (*this)*=a.inv();} Rint operator+(Rint a) const{return Rint(v)+=a;} Rint operator-(Rint a) const{return Rint(v)-=a;} Rint operator*(Rint a) const{return Rint(v)*=a;} Rint operator/(Rint a) const{return Rint(v)/=a;} Rint operator-() const{return v?Rint(mod-v):Rint(v);} bool operator==(const Rint a)const{return v==a.v;} bool operator!=(const Rint a)const{return v!=a.v;} bool operator <(const Rint a)const{return v T Rint::mod; template ostream& operator<<(ostream &os,Rint m){os<=MOD) return 0; Garner arb; using R = Rint; R::set_mod(MOD); int d=1<<15; vector fact(d*2+1,1),finv(d*2+1,1); for(int i=1;i<=d*2;i++) fact[i]=fact[i-1]*R(i); finv[d*2]=fact[d*2].inv(); for(int i=d*2-1;i>=0;i--) finv[i]=finv[i+1]*R(i+1); vector seq({1,d+1}); seq.reserve(d+1); int sz=1; while(sz aux(sz,1); vector f(sz*4,0),g(sz*4,0); for(int i=0;i<=sz;i++){ f[i]=finv[i]*finv[sz-i]*seq[i]; if(((sz+i)&1) and (f[i].v!=0)) f[i]=-f[i]; } vector pf(f); vector as; as.emplace_back(R(sz+1)); as.emplace_back(R(sz)/R(d)); as.emplace_back(R(sz)/R(d)+R(sz+1)); for(int idx=0;idx<3;idx++){ for(int i=0;i>str; if(str.size()>10) drop(0); long long n=stoll(str); if(n-1>=MOD) drop(0); long long ans=factorial(n-1,MOD); if(~n&1) ans=(MOD-ans)%MOD; cout<