#include using namespace std; const int MOD = 1e9 + 7; using ll = long long; using ull = unsigned long long; template struct ModInt { using M = ModInt; const static M G; uint v; ModInt(ll _v = 0) { set_v(_v % MD + MD); } M& set_v(uint _v) { v = (_v < MD) ? _v : _v - MD; return *this; } explicit operator bool() const { return v != 0; } M operator-() const { return M() - *this; } M operator+(const M& r) const { return M().set_v(v + r.v); } M operator-(const M& r) const { return M().set_v(v + MD - r.v); } M operator*(const M& r) const { return M().set_v(ull(v) * r.v % MD); } M operator/(const M& r) const { return *this * r.inv(); } M& operator+=(const M& r) { return *this = *this + r; } M& operator-=(const M& r) { return *this = *this - r; } M& operator*=(const M& r) { return *this = *this * r; } M& operator/=(const M& r) { return *this = *this / r; } bool operator==(const M& r) const { return v == r.v; } M pow(ll n) const { M x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } M inv() const { return pow(MD - 2); } friend ostream& operator<<(ostream& os, const M& r) { return os << r.v; } friend istream& operator>>(istream& is, M& r) { return is >> r.v; } }; using Mint = ModInt; vector divisor(int n) { vector ret; for (int i = 1; i * i <= n; i++) { if (n % i == 0) { ret.push_back(i); if (i * i != n) ret.push_back(n / i); } } sort(begin(ret), end(ret)); return (ret); } int gcd(int a, int b) { while (b) { int c = b; b = a % b; a = c; } return a; } const int MN = 1'000'000; Mint fact[MN], iFac[MN]; void first() { fact[0] = Mint(1); for (int i = 1; i < MN; i++) fact[i] = fact[i - 1] * Mint(i); iFac[MN - 1] = fact[MN - 1].inv(); for (int i = MN - 1; i >= 1; i--) { iFac[i - 1] = iFac[i] * Mint(i); } assert(fact[2345] * iFac[2345] == Mint(1)); } Mint C(int n, int k) { if (n < k || k < 0) return Mint(0); return fact[n] * iFac[k] * iFac[n - k]; } int main() { first(); int K, total = 0; cin >> K; vector C(K); for (int i = 0; i < K; i++) { cin >> C[i]; total += C[i]; } int GCD = C[0]; for (int i = 1; i < K; i++) { GCD = gcd(GCD, C[i]); } auto V = divisor(GCD); vector memo(total + 1); for (auto& x : V) { auto c = C; int SUM = 0; for (auto& a : c) { a /= x; SUM += a; } Mint tmp = fact[SUM]; for (auto& a : c) { tmp *= iFac[a]; } memo[total / x] = tmp; } Mint ans = 0; for (int i = 1; i <= total; i++) { ans += memo[gcd(i, total)]; } ans /= total; cout << ans << endl; }