#include<bits/stdc++.h>
#include<atcoder/all>
#define rep(i,n) for(int i=0;i<n;i++)
using namespace std;
using namespace atcoder;
typedef long long ll;
typedef vector<int> vi;
typedef vector<long long> vl;
typedef vector<vector<int>> vvi;
typedef vector<vector<long long>> vvl;
typedef long double ld;
typedef pair<int, int> P;

ostream& operator<<(ostream& os, const modint& a) {os << a.val(); return os;}
template <int m> ostream& operator<<(ostream& os, const static_modint<m>& a) {os << a.val(); return os;}
template<typename T> istream& operator>>(istream& is, vector<T>& v){int n = v.size(); assert(n > 0); rep(i, n) is >> v[i]; return is;}
template<typename U, typename T> ostream& operator<<(ostream& os, const pair<U, T>& p){os << p.first << ' ' << p.second; return os;}
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v){int n = v.size(); rep(i, n) os << v[i] << (i == n - 1 ? "\n" : " "); return os;}
template <typename T> ostream& operator<<(ostream& os, const vector<vector<T>>& v){int n = v.size(); rep(i, n) os << v[i] << (i == n - 1 ? "\n" : ""); return os;}

// Sieve of Eratosthenes
// https://youtu.be/UTVg7wzMWQc?t=2774
struct Sieve {
  int n;
  vector<int> f, primes;
  Sieve(int n=1):n(n), f(n+1) {
    f[0] = f[1] = -1;
    for (ll i = 2; i <= n; ++i) {
      if (f[i]) continue;
      primes.push_back(i);
      f[i] = i;
      for (ll j = i*i; j <= n; j += i) {
        if (!f[j]) f[j] = i;
      }
    }
  }
  bool isPrime(int x) { return f[x] == x;}
  vector<int> factorList(int x) {
    vector<int> res;
    while (x != 1) {
      res.push_back(f[x]);
      x /= f[x];
    }
    return res;
  }
  vector<pair<ll,int>> factor(ll x) {
    vector<pair<ll,int>> res;
    for (int p : primes) {
      int y = 0;
      while (x%p == 0) x /= p, ++y;
      if (y != 0) res.emplace_back(p,y);
    }
    if (x != 1) res.emplace_back(x,1);
    return res;
  }
	vector<long long> devisor(long long x){
		vector<pair<long long, int>> f = factor(x);
		vector<long long> res;
		res.push_back(1);
		for(auto [p, num] : f){
			vector<long long> old;
			swap(res, old);
			for(auto x : old){
				long long tmp = 1;
				rep(i, num + 1){
					res.push_back(x * tmp);
					tmp *= p;
				}
			}
		}
		return res;
	}
};


int main(){
	int n, k;
	cin >> n >> k;
	vl a(n);
	cin >> a;
	Sieve sieve(1001001);
	unordered_set<long long> devisor;
	rep(i, n){
		auto res = sieve.devisor(a[i]);
		for(long long x : res) devisor.insert(x);
	}
	long long ans = 0;
	for(long long x : devisor){
		long long cnt = 0;
		rep(i, n) cnt += min(a[i] - a[i] / x * x, (a[i] / x + 1) * x - a[i]);
		if(cnt <= k) ans = max(ans, x);
	}
	cout << ans << "\n";
	return 0;
}