#include #pragma GCC optimize("Ofast") #define _GLIBCXX_DEBUG using namespace std; using std::cout; using std::cin; using std::endl; using ll=long long; using ld=long double; ll ILL=2167167167167167167; const int INF=2100000000; const ll mod=1e9+7; #define rep(i,a) for (ll i=0;i using _pq = priority_queue, greater>; template ll LB(vector &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();} template ll UB(vector &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();} template bool chmin(T &a,const T &b){if(a>b){a=b;return 1;}else return 0;} template bool chmax(T &a,const T &b){if(a void So(vector &v) {sort(v.begin(),v.end());} template void Sore(vector &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});} void yneos(bool a){if(a) cout<<"Yes\n"; else cout<<"No\n";} template void vec_out(vector &p){for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout<> Prime_factorization(long long val){ assert(val>=1); if(val==1){ return {}; } int ind=0; std::vector> ans; for(long long i=2;i*i<=val;i++){ if(val%i!=0) continue; ans.push_back({i,0}); while(val%i==0){ ans[ind].second++; val/=i; } ind++; } if(val!=1) ans.push_back({val,1}); return ans; } template using square_matrix=std::vector>; template square_matrix mul_matrix(square_matrix l,square_matrix r){ int n=l.size(); assert((int)l[0].size()==n&&(int)r.size()==n&&(int)r[0].size()==n); square_matrix val(n,std::vector(n,add_e())); for(int i=0;i square_matrix pow_matrix(square_matrix l,long long times){ int n=l.size(); square_matrix val(n,std::vector(n,add_e())); for(int i=0;i(val,l); } l=mul_matrix(l,l); times>>=1; } return val; } using mat_F=ll; mat_F add_op(mat_F a,mat_F b){ return (a+b)%mod; } mat_F add_e(){ return 0; } mat_F mul_op(mat_F a,mat_F b){ return (a*b)%mod; } mat_F mul_e(){ return 1; } #define calc mat_F,add_op,add_e,mul_op,mul_e void solve(); // oddloop int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int t=1; //cin>>t; rep(i,t) solve(); } void solve(){ ll N,M; cin>>N>>M; auto p=Prime_factorization(M); ll ans=1; for(auto x:p){ if(x.first==1) continue; vector> base(x.second+1,vector(x.second+1)); rep(i,x.second+1) rep(j,x.second+1){ if(i+j<=x.second){ base[i][j]=1; } } auto q=pow_matrix(base,N); ll tmp=0; rep(i,x.second+1) tmp+=q[0][i]; tmp%=mod; ans=(ans*tmp)%mod; } cout<