#include #define show(x) std::cerr << #x << " = " << x << std::endl using ll = long long; constexpr ll MOD = 1000000007; template class ModCombination { public: ModCombination(const std::size_t n) : fact(n + 1, 1), inv(n + 1, 1), inv_fact(n + 1, 1) { for (ll i = 2; i <= (ll)n; i++) { fact[i] = (fact[i - 1] * i) % mod, inv[i] = ((mod - (mod / i)) * inv[mod % i]) % mod, inv_fact[i] = (inv_fact[i - 1] * inv[i]) % mod; } } ll factorial(const std::size_t n) const { return fact[n]; } ll inverse(const std::size_t n) const { return inv[n]; } ll inverseFactorial(const std::size_t n) const { return inv_fact[n]; } ll permutation(const std::size_t n, const std::size_t k) const { return (fact[n] * inv_fact[n - k]) % mod; } ll combination(const std::size_t n, const std::size_t k) const { return (((fact[n] * inv_fact[k]) % mod) * inv_fact[n - k]) % mod; } private: std::vector fact, inv, inv_fact; }; template std::ostream& operator<<(std::ostream& os, const std::vector& v) { os << "["; for (const auto& p : v) { os << p << ","; } return (os << "]\n"); } int main() { int K; std::cin >> K; std::vector C(K); for (int i = 0; i < K; i++) { std::cin >> C[i]; } ll G = C[0]; for (int i = 1; i < K; i++) { G = std::gcd(G, C[i]); } std::vector d; for (int i = 1; i * i <= G; i++) { if (G % i == 0) { d.push_back(i); if (i * i != G) { d.push_back(G / i); } } } std::sort(d.begin(), d.end()); const int S = d.size(); std::vector dnum(S, -1); for (int i = 0; i < S; i++) { for (int j = i; j < S; j++) { if (d[j] % d[i] == 0) { dnum[j]++; } } } ModCombination<> mod(1000000); const ll CS = std::accumulate(C.begin(), C.end(), 0LL); std::vector p(S, 1); ll ans = 0; for (int i = S - 1; i >= 0; i--) { for (int j = 0, sum = CS / d[i]; j < K; j++) { (p[i] *= mod.combination(sum, C[j] / d[i])) %= MOD, sum -= C[j] / d[i]; } for (int j = i + 1; j < S; j++) { if (d[j] % d[i] == 0) { (p[i] += MOD - p[j]) %= MOD; } } (ans += (mod.inverse(CS / d[i]) * p[i])) %= MOD; } std::cout << ans << std::endl; return 0; }