#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; namespace { using Integer = long long; //__int128; template istream& operator >> (istream& is, vector& vec){for(T& val: vec) is >> val; return is;} template istream& operator , (istream& is, T& val){ return is >> val;} template ostream& operator << (ostream& os, const vector& vec){for(int i=0; i ostream& operator , (ostream& os, const T& val){ return os << " " << val;} template void print(const H& head){ cout << head; } template void print(const H& head, const T& ... tail){ cout << head << " "; print(tail...); } template void println(const T& ... values){ print(values...); cout << endl; } template void eprint(const H& head){ cerr << head; } template void eprint(const H& head, const T& ... tail){ cerr << head << " "; eprint(tail...); } template void eprintln(const T& ... values){ eprint(values...); cerr << endl; } string operator "" _s (const char* str, size_t size){ return move(string(str)); } constexpr Integer my_pow(Integer x, Integer k, Integer z=1){return k==0 ? z : k==1 ? z*x : (k&1) ? my_pow(x*x,k>>1,z*x) : my_pow(x*x,k>>1,z);} constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z=1){return k==0 ? z%M : k==1 ? z*x%M : (k&1) ? my_pow_mod(x*x%M,k>>1,M,z*x%M) : my_pow_mod(x*x%M,k>>1,M,z);} constexpr unsigned long long operator "" _ten (unsigned long long value){ return my_pow(10,value); } inline int k_bit(Integer x, int k){return (x>>k)&1;} //0-indexed mt19937 mt(chrono::duration_cast(chrono::steady_clock::now().time_since_epoch()).count()); template string join(const vector& v, const string& sep){ stringstream ss; for(int i=0; i0) ss << sep; ss << v[i]; } return ss.str(); } } constexpr long long mod = 9_ten + 7; long long gcd(long long a, long long b){ return (b==0)?a:gcd(b,a%b); } template long long gcd(long long a, long long b, T ... c){ return gcd(gcd(a,b), c...);} long long lcm(long long a, long long b){ if(a long long lcm(long long a, long long b, T ... c){ return lcm(lcm(a,b), c...);} long long extgcd(long long a, long long b, long long &x, long long &y){ long long d=a; if(b!=0){ d = extgcd(b, a%b, y, x); y -= (a/b) * x; }else{ x = 1; y = 0; } return d; } long long mod_inverse(long long a, long long m){ long long x,y; extgcd(a,m,x,y); return (m+x%m)%m; } // nCk mod p, O(1) // precomputation O(size) class combination_mod{ const long long mod; const long long size; vector fact; //n! vector fact_inv; // (n!)^-1 void make_fact(){ fact[0] = 1; for(long long i=1; i divisors(long long N){ if(N==1) return {1LL}; vector ret; ret.push_back(1); ret.push_back(N); for(long long i=2; i*i<=N; i++){ if(N%i==0){ ret.push_back(i); if(i*i != N) ret.push_back(N/i); } } //sort(ret.begin(), ret.end()); return ret; } int main(){ long long k; cin >> k; vector c(k); cin >> c; long long sum = accumulate(c.begin(), c.end(), 0ll); combination_mod comb(mod, sum+1); long long ans = 0; long long g = c[0]; for(auto v : c) g = gcd(g, v); auto d = divisors(g); for(auto v : d){ long long tmp = 1; long long acc = 0; for(int i=0; i