#include <bits/stdc++.h>
// created [2019/11/18] 15:19:42
#pragma GCC diagnostic ignored "-Wsign-compare"
#pragma GCC diagnostic ignored "-Wsign-conversion"

using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
using uint = unsigned int;
using usize = std::size_t;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
template<typename T> constexpr T popcount(const T u) { return u ? static_cast<T>(__builtin_popcountll(static_cast<u64>(u))) : static_cast<T>(0); }
template<typename T> constexpr T log2p1(const T u) { return u ? static_cast<T>(64 - __builtin_clzll(static_cast<u64>(u))) : static_cast<T>(0); }
template<typename T> constexpr T msbp1(const T u) { return log2p1(u); }
template<typename T> constexpr T lsbp1(const T u) { return __builtin_ffsll(u); }
template<typename T> constexpr T clog(const T u) { return u ? log2p1(u - 1) : static_cast<T>(u); }
template<typename T> constexpr bool ispow2(const T u) { return u and (static_cast<u64>(u) & static_cast<u64>(u - 1)) == 0; }
template<typename T> constexpr T ceil2(const T u) { return static_cast<T>(1) << clog(u); }
template<typename T> constexpr T floor2(const T u) { return u == 0 ? static_cast<T>(0) : static_cast<T>(1) << (log2p1(u) - 1); }
template<typename T> constexpr bool btest(const T mask, const usize ind) { return static_cast<bool>((static_cast<u64>(mask) >> ind) & static_cast<u64>(1)); }
template<typename T> void bset(T& mask, const usize ind) { mask |= (static_cast<T>(1) << ind); }
template<typename T> void breset(T& mask, const usize ind) { mask &= ~(static_cast<T>(1) << ind); }
template<typename T> void bflip(T& mask, const usize ind) { mask ^= (static_cast<T>(1) << ind); }
template<typename T> void bset(T& mask, const usize ind, const bool b) { (b ? bset(mask, ind) : breset(mask, ind)); }
template<typename T> constexpr T bcut(const T mask, const usize ind) { return ind == 0 ? static_cast<T>(0) : static_cast<T>((static_cast<u64>(mask) << (64 - ind)) >> (64 - ind)); }
template<typename T> bool chmin(T& a, const T& b) { return (a > b ? a = b, true : false); }
template<typename T> bool chmax(T& a, const T& b) { return (a < b ? a = b, true : false); }
constexpr unsigned int mod                  = 1000000007;
template<typename T> constexpr T inf_v      = std::numeric_limits<T>::max() / 4;
template<typename Real> constexpr Real pi_v = Real{3.141592653589793238462643383279502884};

template<typename T>
T read()
{
    T v;
    return std::cin >> v, v;
}
template<typename T, typename... Args>
auto read(const usize size, Args... args)
{
    std::vector<decltype(read<T>(args...))> ans(size);
    for (usize i = 0; i < size; i++) { ans[i] = read<T>(args...); }
    return ans;
}
template<typename... Types>
auto reads() { return std::tuple<std::decay_t<Types>...>{read<Types>()...}; }
#    define SHOW(...) static_cast<void>(0)

template<typename T>
std::vector<T> make_v(const usize size, const T v) { return std::vector<T>(size, v); }
template<typename... Args>
auto make_v(const usize size, Args... args) { return std::vector<decltype(make_v(args...))>(size, make_v(args...)); }
template<typename T>
std::vector<T> divisors(const T n)
{
    std::vector<T> head, tail;
    for (T i = 1; i * i <= n; i++) {
        if (n % i == 0) {
            head.push_back(i);
            if (i * i != n) { tail.push_back(n / i); }
        }
    }
    for (auto it = tail.rbegin(); it != tail.rend(); it++) { head.push_back(*it); }
    return head;
}
int main()
{
    const auto n = read<int>();
    const auto k = read<ll>();
    const auto a = read<ll>(n);
    const ll A   = std::accumulate(a.begin(), a.end(), 0LL);
    auto ds      = divisors(A);
    std::reverse(ds.begin(), ds.end());
    for (const ll d : ds) {
        std::vector<ll> m(n), p(n);
        for (int i = 0; i < n; i++) { m[i] = a[i] % d; }
        std::sort(m.begin(), m.end());
        for (int i = 0; i < n; i++) { p[i] = (d - m[i]) % d; }
        auto l = m, r = p;
        for (int i = 1; i < n; i++) { l[i] += l[i - 1]; }
        for (int i = n - 2; i >= 0; i--) { r[i] += r[i + 1]; }
        ll min = d * n;
        for (int i = 0; i < n; i++) {
            const ll minus = l[i];
            const ll plus  = (i == n - 1 ? 0LL : r[i + 1]);
            const ll sub   = std::abs(plus - minus);
            if (sub % d != 0) { continue; }
            chmin(min, std::max(plus, minus));
        }
        if (min <= k) { return std::cout << d << std::endl, 0; }
    }
    return 0;
}


Measured memory_bytes: 256