#include #define REP_(i, a_, b_, a, b, ...) for (int i = (a), END_##i = (b); i < END_##i; ++i) #define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__) #define ALL(x) std::begin(x), std::end(x) using Int = long long; using Uint = unsigned long long; using Real = long double; #include using Mint = atcoder::modint1000000007; std::ostream &operator<<(std::ostream &os, const Mint &m) { return os << m.val(); } template inline bool chmax(T &a, U b) { return a < b and ((a = b), true); } template inline bool chmin(T &a, U b) { return a > b and ((a = b), true); } template inline int ssize(const T &a) { return (int) a.size(); } template constexpr T kBigVal = std::numeric_limits::max() / 2; template inline std::ostream &print_one(const T &x, char endc) { if constexpr (std::is_same::value) { return std::cout << (x ? "Yes" : "No") << endc; } else { return std::cout << x << endc; } } template inline std::ostream &print(const T &x) { return print_one(x, '\n'); } template std::ostream &print(const T &head, Ts... tail) { return print_one(head, ' '), print(tail...); } inline std::ostream &print() { return std::cout << '\n'; } template std::ostream &print_seq(const Container &seq, const char *sep = " ", const char *ends = "\n", std::ostream &os = std::cout) { const auto itl = std::begin(seq), itr = std::end(seq); for (auto it = itl; it != itr; ++it) { if (it != itl) os << sep; os << *it; } return os << ends; } struct CastInput { template operator T() const { T x; std::cin >> x; return x; } struct Sized { int n; template operator T() const { T xs(n); for (auto &x: xs) std::cin >> x; return xs; } }; Sized operator()(int n) const { return {n}; } } in; #ifdef MY_DEBUG #include "debug_dump.hpp" #include "backward.hpp" backward::SignalHandling kSignalHandling; #else #define DUMP(...) #define cerr if(false)cerr #endif // mod: prime template struct Factorials { // factorials and inverse factorials. std::vector fact, ifact; // n: max cached value. explicit Factorials(int n) : fact(n + 1), ifact(n + 1) { assert(n >= 0); assert(n < T::mod()); fact[0] = 1; for (int i = 1; i <= n; ++i) { fact[i] = fact[i - 1] * i; } ifact[n] = fact[n].inv(); for (int i = n; i >= 1; --i) { ifact[i - 1] = ifact[i] * i; } } // Combination (binomial coefficients) T C(Int n, Int k) const { if (k < 0 || k > n) return 0; return fact[n] * ifact[k] * ifact[n - k]; } }; using namespace std; std::vector divisors(Int n) { std::vector res; for (Int k = 1; k * k <= n; ++k) { if (n % k != 0) continue; res.push_back(k); Int q = n / k; if (q != k) res.push_back(q); } std::sort(res.begin(), res.end()); return res; } auto solve() { int n = in; vector C = in(n); int N = accumulate(ALL(C), 0); auto divs = divisors(N); Factorials fs(N); map memo; auto f = [&](Int d) -> Mint { if (n > N / d) return 0; if (auto it = memo.find(d); it != memo.end()) { return it->second; } Mint ret = 1; int r = 0; for (Int c: C) { if (c % d != 0) return 0; ret *= fs.C(N / d - r, c / d); r += c / d; } memo[d] = ret; return ret; }; Mint ans = 0; for (int d = 1; d <= N; ++d) { ans += f(N / gcd(d, N)); } ans /= N; print(ans); } int main() { std::ios::sync_with_stdio(false), cin.tie(nullptr); cout << std::fixed << std::setprecision(18); const int T = 1;//in; REP(t, T) { (solve()); } }