#include #include #include #include #include #include intmax_t gcd(intmax_t m, intmax_t n) { while (n) std::swap(m %= n, n); return m; } std::vector divisor(intmax_t n) { std::vector res; for (intmax_t i = 1; i*i <= n; ++i) { if (n % i == 0) { res.push_back(i); if (i != n/i) res.push_back(n/i); } } std::sort(res.begin(), res.end()); return res; } constexpr intmax_t operator ""_jd(unsigned long long n) { return n; } constexpr uintmax_t operator ""_ju(unsigned long long n) { return n; } constexpr size_t operator ""_zu(unsigned long long n) { return n; } // constexpr ptrdiff_t operator ""_td(unsigned long long n) { return n; } template Tp gcd(Tp a, Tp b, Tp& x, Tp& y) { x = Tp(0); y = Tp(1); for (Tp u = y, v = x; a;) { Tp q = b/a; std::swap(x -= q*u, u); std::swap(y -= q*v, v); std::swap(b -= q*a, a); } return b; } template Tp modinv(Tp a, Tp mod) { Tp x, y; gcd(a, mod, x, y); x %= mod; if (x < 0) x += mod; return x; } template Tp modadd(Tp a, Tp b, Tp mod) { a += b % mod; if (a < 0) a += mod; if (a >= mod) a -= mod; return a; } template Tp modadd(std::initializer_list const& adds, Tp mod) { Tp res = 0; for (auto const& add: adds) { res += add % mod; if (res < 0) res += mod; if (res >= mod) res -= mod; } return res; } template Tp modsub(Tp a, Tp b, Tp mod) { a -= b % mod; if (a < 0) a += mod; if (a >= mod) a -= mod; return a; } template Tp modmul(std::initializer_list const& muls, Tp mod) { Tp res = 1; for (auto const& mul: muls) (res *= mul) %= mod; return res; } template Tp modpow(Tp base, intmax_t iexp, Tp mod) { Tp res = 1; for (Tp dbl = base; iexp; iexp >>= 1) { if (iexp & 1) res = res * dbl % mod; dbl = dbl * dbl % mod; } return res; } class modfactorial { std::vector fact, fact_inv; intmax_t mod; public: modfactorial(intmax_t N, intmax_t mod): mod(mod) { fact.resize(N+1); fact_inv.resize(N+1); fact[0] = 1; for (intmax_t i = 1; i <= N; ++i) fact[i] = fact[i-1] * i % mod; fact_inv[N] = modinv(fact[N], mod); for (intmax_t i = N; i--;) fact_inv[i] = fact_inv[i+1] * (i+1) % mod; } intmax_t operator ()(intmax_t k) const { return fact[k]; } intmax_t inverse(intmax_t k) const { return fact_inv[k]; } }; constexpr intmax_t mod = 1e9+7; int main() { size_t K; scanf("%zu", &K); std::vector C(K); for (auto& ci: C) scanf("%jd", &ci); intmax_t cs = std::accumulate(C.begin(), C.end(), 0_jd); intmax_t cg = std::accumulate(C.begin(), C.end(), 0_jd, [](auto x, auto y) { return gcd(x, y); }); modfactorial mf(cs, mod); auto ds = divisor(cg); std::vector f(ds.size()); for (size_t i = 0; i < ds.size(); ++i) { intmax_t d = ds[i]; f[i] = mf(cs/d); for (size_t j = 0; j < K; ++j) (f[i] *= mf.inverse(C[j] / d)) %= mod; } intmax_t res = 0; for (size_t i = 0; i < ds.size(); ++i) { for (size_t j = i+1; j < ds.size(); ++j) { if (ds[j] % ds[i] == 0) f[i] = (f[i]+mod-f[j]) % mod; } (res += f[i] * modinv(cs/ds[i], mod)) %= mod; } printf("%jd\n", res); }