#include using namespace std; using Int = long long; template inline void chmin(T1 &a,T2 b){if(a>b) a=b;} template inline void chmax(T1 &a,T2 b){if(a struct NTT{ static constexpr int md = bmds(X); static constexpr int rt = brts(X); inline int add(int a,int b){ a+=b; if(a>=md) a-=md; return a; } inline int mul(int a,int b){ return 1LL*a*b%md; } inline int pow(int a,int b){ int res=1; while(b){ if(b&1) res=mul(res,a); a=mul(a,a); b>>=1; } return res; } inline int inv(int x){ return pow(x,md-2); } 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 &a,bool f,int n=-1){ if(n==-1) n=a.size(); assert((n&(n-1))==0); for(int i=0,j=1;j+1>1;k>(i^=k);k>>=1); if(i>j) swap(a[i],a[j]); } for(int i=1;i multiply(const vector &a,const vector &b){ int need=a.size()+b.size()-1; int sz=1; while(sz f(sz),g(sz); for(int i=0;i<(int)a.size();i++) f[i]=a[i]; for(int i=0;i<(int)b.size();i++) g[i]=b[i]; ntt(f,0);ntt(g,0); for(int i=0;i ntt0; static NTT<1> ntt1; static NTT<2> ntt2; int MOD; ArbitraryModConvolution(int MOD):MOD(MOD){} 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(vector< vector > &cs){ 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); int m01 =(ll)ntt0.md*ntt1.md%MOD; size_t sz=cs[0].size(); for(size_t i=0;i=MOD) cs[0][i]-=MOD; cs[0][i]+=(ll)cs[2][i]*m01%MOD; if(cs[0][i]>=MOD) cs[0][i]-=MOD; } } vector multiply(vector a,vector b){ for(int& x:a) x%=MOD; for(int& x:b) x%=MOD; vector< vector > cs(3); cs[0]=ntt0.multiply(a,b); cs[1]=ntt1.multiply(a,b); cs[2]=ntt2.multiply(a,b); size_t sz=a.size()+b.size()-1; for(auto& v:cs) v.resize(sz); garner(cs); return cs[0]; } }; NTT<0> ArbitraryModConvolution::ntt0; NTT<1> ArbitraryModConvolution::ntt1; NTT<2> ArbitraryModConvolution::ntt2; //BEGIN CUT HERE int factorial(int n,int MOD){ if(n>=MOD) return 0; ArbitraryModConvolution arb(MOD); auto inv=[&](int a){return ArbitraryModConvolution::inv(a,MOD);}; using ll = long long; auto add=[&](int a,int b){return a+b>=MOD?a+b-MOD:a+b;}; auto sub=[&](int a,int b){return a-b<0?a-b+MOD:a-b;}; auto mul=[&](int a,int b){return (ll)a*b%MOD;}; auto div=[&](int a,int b){return mul(a,inv(b));}; 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]=mul(fact[i-1],i); finv[d*2]=inv(fact[d*2]); for(int i=d*2-1;i>=0;i--) finv[i]=mul(finv[i+1],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]=mul(mul(finv[i],finv[sz-i]),seq[i]); if(((sz+i)&1)&&(f[i]!=0)) f[i]=MOD-f[i]; } vector pf(f); vector as; as.emplace_back(sz+1); as.emplace_back(div(sz,d)); as.emplace_back(add(div(sz,d),sz+1)); for(int idx=0;idx<3;idx++){ for(int i=0;i>n; cout<