#include <iostream>
#include <vector>
#include <algorithm>
#include <array>
#include <iterator>
#include <string>
#include <cctype>
#include <cstring>
#include <cstdlib>
#include <cassert>
#include <cmath>
#include <ctime>
#include <iomanip>
#include <numeric>
#include <stack>
#include <queue>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <bitset>
#include <random>
#include <utility>
#include <functional>
using namespace std;
vector<long long> Divisors(long long N)
{
	vector<long long> res;
	for(long long i = 1;i * i <= N;i++)
	{
		if(N % i == 0)
		{
			res.push_back(i);
			if(i != N / i) res.push_back(N / i);
		}
	}

	sort(res.begin(),res.end());

	return res;
}

void Main()
{
	int N,K;
	cin >> N >> K;
	vector<long long> A(N);
	for(int i = 0;i < N;i++)
	{
		cin >> A[i];
	}
	sort(A.begin(),A.end());
	long long ans = 0;
	for(int k = 0;k <= K;k++)
	{
		auto divs = Divisors(A[0] + k);
		for(int j = (int)divs.size() - 1;j >= 0;j--)
		{
			long long d = divs[j];
			long long need = 0;
			for(int i = 0;i < N;i++)
			{
				long long cur = min(A[i] - A[i] / d * d,(A[i] + d - 1) / d * d - A[i]);
				need += cur;
				if(need > K)
				{
					break;
				}
			}
			if(need <= K)
			{
				ans = max(ans,d);
			}
		}
	}
	cout << ans << "\n";
}
int main()
{
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	int tt = 1;
	/* cin >> tt; */
	while(tt--) Main();
}