#include #include #include using namespace std; #define REP(i, n) for (int i = 0; i < (n); i++) const int MOD = 1e9 + 7; struct mint { int n; mint(int n_ = 0) : n(n_) {} }; mint operator+(mint a, mint b) { a.n += b.n; if (a.n >= MOD) a.n -= MOD; return a; } mint operator-(mint a, mint b) { a.n -= b.n; if (a.n < 0) a.n += MOD; return a; } mint operator*(mint a, mint b) { return (long long)a.n * b.n % MOD; } mint &operator+=(mint &a, mint b) { return a = a + b; } mint &operator-=(mint &a, mint b) { return a = a - b; } mint &operator*=(mint &a, mint b) { return a = a * b; } int phi[1000001]; mint F[1000001] = {1, 1}; mint R[1000001] = {1, 1}; mint I[1000001] = {0, 1}; vector divs(int n) { vector ans; for (int i = 1; i * i <= n; i++) { if (n % i == 0) { ans.push_back(i); if (i != n / i) ans.push_back(n / i); } } return ans; } int main() { for (int i = 2; i <= 1000000; i++) { I[i] = I[MOD % i] * (MOD - MOD / i); F[i] = F[i - 1] * i; R[i] = R[i - 1] * I[i]; } for (int i = 0; i <= 1000000; i++) phi[i] = i; for (int i = 1; i <= 1000000; i++) for (int j = i * 2; j <= 1000000; j += i) phi[j] -= phi[i]; int K; cin >> K; vector C(K); int s = 0; REP(i, K) { cin >> C[i]; s += C[i]; } mint ans = 0; for (int d : divs(s)) { mint x = F[s / d]; REP(i, K) { if (C[i] % d != 0) x = 0; else { x *= R[C[i] / d]; } } ans += x * phi[d]; } ans *= I[s]; cout << ans.n << '\n'; }