//#define _GLIBCXX_DEBUG #include #define rep(i, n) for(int i=0; i; using vs = vector; using vi = vector; using vvi = vector; template using PQ = priority_queue; template using PQG = priority_queue, greater >; const int INF = 0xccccccc; const ll LINF = 922337203685477580LL; template inline bool chmax(T1 &a, T2 b) {return a < b && (a = b, true);} template inline bool chmin(T1 &a, T2 b) {return a > b && (a = b, true);} template istream &operator>>(istream &is, pair &p) { return is >> p.first >> p.second;} template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second;} const int mod = 1000000007; //const int mod = 998244353; struct mint { int64_t x; mint(int64_t x=0):x((x%mod+mod)%mod){} mint operator-() const { return mint(-x);} mint& operator+=(const mint a) { if ((x += a.x) >= mod) x -= mod; return *this; } mint& operator-=(const mint a) { if ((x += mod-a.x) >= mod) x -= mod; return *this; } mint& operator*=(const mint a) { (x *= a.x) %= mod; return *this;} mint operator+(const mint a) const { return mint(*this) += a;} mint operator-(const mint a) const { return mint(*this) -= a;} mint operator*(const mint a) const { return mint(*this) *= a;} mint pow(int64_t t) const { if (!t) return 1; mint a = pow(t>>1); a *= a; if (t&1) a *= *this; return a; } //for prime mod mint inv() const { return pow(mod-2);} mint& operator/=(const mint a) { return *this *= a.inv();} mint operator/(const mint a) {return mint(*this) /= a;} }; istream& operator>>(istream& is, mint& a) { return is >> a.x;} ostream& operator<<(ostream& os, const mint& a) { return os << a.x;} struct combination { vector frac, ifrac; combination(int n):frac(n+1), ifrac(n+1) { assert(n < mod); frac[0] = 1; for (int i = 1; i <= n; ++i) frac[i] = frac[i-1]*i; ifrac[n] = frac[n].inv(); for (int i = n; i >= 1; --i) ifrac[i-1] = ifrac[i]*i; } mint operator()(int n, int k) { if (k < 0 || k > n) return 0; return frac[n]*ifrac[k]*ifrac[n-k]; } } c(1000000); struct Sieve { int n; vector f, primes; Sieve(int n=1):n(n), f(n+1) { f[0] = f[1] = -1; for(int64_t i=2; i<=n; ++i) { if(f[i]) continue; primes.push_back(i); f[i] = i; for(int64_t j = i*i; j <= n; j += i) { if(!f[j]) f[j] = i; } } } //素数判定 bool isPrime(int x) {return f[x] == x;} //素数判定(1つ用)(宣言はsqrt(x)のサイズで) bool isPrime1(int64_t x) { bool m = true; for(int z:primes) { if(!(x%z)) { m = false; break; } } return m; } //素数列挙 vector factorList(int x) { assert(x <= n); vector res; while(x != 1) { res.emplace_back(f[x]); x /= f[x]; } return res; } //素因数分解 pair(素数, 素因数の数) vector > factor(int x) { vector fl = factorList(x); if(fl.size() == 0) return {}; vector > res(1, pair(fl[0], 0)); for(int p : fl) { if(res.back().first == p) { ++res.back().second; } else { res.emplace_back(p, 1); } } return res; } //素数列挙(1つ用)(宣言はsqrt(x)のサイズで) vector factorList1(int64_t x) { vector vec; for(int z:primes) { while(!(x%z)) { vec.emplace_back(z); x /= z; } } if(x != 1) vec.emplace_back(x); return vec; } //素数列挙(1つ用)(宣言はsqrt(x)のサイズで) pair(素数, 素因数の数) vector > factor1(int64_t x) { vector vec = factorList1(x); vector > vecc; for(vector::iterator itr = vec.begin(); itr != vec.end(); ++itr) { if(itr != vec.begin() && *itr == *(itr-1)) { (vecc.end()-1)->second++; } else { vecc.emplace_back(pair(*itr, 1)); } } return vecc; } //約数列挙 vector div1(int64_t x) { vector res(1, 1); vector > fac = factor1(x); for(int i = 0; i < fac.size(); ++i) { int si = res.size(); for(int j = 0; j < fac[i].second; ++j) { for(int k = 0; k < si; ++k) { res.emplace_back(res[k+j*si]*fac[i].first); } } } sort(res.begin(), res.end()); return res; } }pp(1e6); const int N = 1e5+10; //head int k; int cc[N]; mint ans; int gc; int sum; map mp; int main() { ios::sync_with_stdio(false); cin.tie(0); cin >> k; rep(i, k) cin >> cc[i]; rep(i, k) gc = gcd(gc, cc[i]); auto vec = pp.div1(gc); sum = accumulate(cc, cc+k, 0); rep(i, vec.size()) { mint now = c.frac[sum/vec[i]-1]; rep(j, k) { int u = cc[j]/vec[i]; if(!j) u--; now *= c.ifrac[u]; } int su = vec[i]-mp[vec[i]]; rep(j, vec.size()) if(vec[j]%vec[i] == 0) mp[vec[j]] += su; ans += now*su; } cout << ans/cc[0] << endl; }