#include using namespace std; #define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++) #define ALL(v) (v).begin(),(v).end() using ll=long long int; 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;} templatestruct fp { int v; static int 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(int 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){return is>>x.v;} friend ostream& operator<<(ostream& os,const fp& x){return 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(n<0)return 0; return (inv?Finv[n]:Fact[n]);} T inv(int n){if(n<0)return 0; return Inv[n];} T nPr(int n,int r,bool inv=0){if(n<0||n lo; vector hi; PrimeCount(const ll& _N):N(_N),M(int(sqrt(N))),lo(M+1),hi(M+1){ rep(i,1,M+1)lo[i]=i-1,hi[i]=N/i-1; int cnt=0; for(int p=2;p<=M;p++){ if(lo[p-1]==lo[p])continue; const ll n=N/p; const ll q=ll(p)*p; const int w=M/p; const ll L=min(M,N/q); for(int i=1;i<=w;i++)hi[i]-=hi[i*p]-cnt; const int t=min(sqrt(n),L); for(int i=w+1;i<=t;i++)hi[i]-=lo[n/i]-cnt; for(int i=L,j=n/L;i>t;j++){ int c=lo[j]; while(j+1<=M and lo[j+1]==c)j++; c-=cnt; for(int e=max(t,n/(j+1));i>e;i--)hi[i]-=c; } for(int i=M,j=M/p;j>=p;j--){ const int c=lo[j]-cnt; for(int e=j*p;i>=e;i--)lo[i]-=c; } cnt++; } } ll pi(ll x){ if(x<=M)return lo[x]; else return hi[N/x]; } }; const int L=401010; bitset isp; int main(){ ll n,m; cin>>n>>m; PrimeCount pi(m); rep(p,2,L)isp[p]=1; vector ps; for(int p=2;p*p<=L;p++)if(isp[p]){ for(int q=p*p;q<=L;q+=p)isp[q]=0; } rep(p,2,L)if(isp[p])ps.push_back(p); Fp pw[50],ret; rep(x,1,50)pw[x]=Fp(x).pow(n); auto dfs=[&](auto& f,ll x,int i,int e,Fp sigma)->void{ // x*(prime>=ps[i]) まで確定 ret+=sigma*pw[e+2]; // x*ps[i] ret+=sigma*pw[e+1]*pw[2]*(pi.pi(m/x)-i-1); // x*(prime>ps[i]) if(x*ps[i]*ps[i]<=m){ f(f,x*ps[i],i,e+1,sigma); } rep(j,i+1,ps.size()){ if(x*ps[j]*ps[j]>m)break; f(f,x*ps[j],j,1,sigma*pw[e+1]); } }; ret+=1; // 1 ret+=pw[2]*pi.pi(m); // only prime rep(i,0,ps.size()){ if(ps[i]*ps[i]>m)break; dfs(dfs,ps[i],i,1,1); } cout<