#include <bits/stdc++.h>
using namespace std;
/*{{{*/  //template
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define rrep(i,n) for(int i=(n)-1;i>=0;i--)
constexpr int INF = numeric_limits<int>::max()/2;
constexpr long long LINF = numeric_limits<long long>::max()/3;
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define all(v) (v).begin(),(v).end()
#define sz(x) (int)(x).size()
#define debug(x) cerr<<#x<<":"<<x<<endl
#define debug2(x,y) cerr<<#x<<","<<#y":"<<x<<","<<y<<endl
//struct fin{ fin(){ cin.tie(0); ios::sync_with_stdio(false); } } fin_;
struct Double{ double d; explicit Double(double x) : d(x){} };
ostream& operator<<(ostream& os,const Double x){ os << fixed << setprecision(20) << x.d; return os; }
template<typename T> ostream& operator<<(ostream& os,const vector<T>& vec){ os << "["; for(const auto& v : vec){ os << v << ","; } os << "]"; return os; }
template<typename T,typename U> ostream& operator<<(ostream& os, const map<T,U>& mp){ os << "{"; for(auto& p : mp){ os << p << ","; } os << "}"; return os; }
template<typename T,typename U> ostream& operator<<(ostream& os,const pair<T,U>& p){ os << "(" << p.first << ","<< p.second <<")"; return os; }
template<typename T> ostream& operator<<(ostream& os,const set<T>& st){ os<<"{"; for(T v:st) os<<v<<","; os <<"}"; return os; }
template<typename T,typename U> inline void chmax(T &x,U y){ if(y>x) x = y; }
template<typename T,typename U> inline void chmin(T &x,U y){ if(y<x) x = y; }
using ll = long long;
using ull = unsigned long long;
using pii = std::pair<int,int>;
using vi = std::vector<int>;
typedef vector<vi> vvi;
ll gcd(ll a,ll b){ if(b==0) return a; else return gcd(b,a%b); }
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }
//constexpr double eps = 1e-14; 
constexpr double eps = 1e-10; 
constexpr ll mod = 1e9+7;
const int dx[]={1,0,-1,0} ,dy[] = {0,1,0,-1};
/*}}}*/

int main(){
    ll n,k; cin >> n >> k;
    vector<ll> a(n);
    rep(i,n) cin >> a[i];
    sort(all(a));
    ll sum = 0;
    rep(i,n) sum += a[i];

    vector<ll> yakusu;
    for(ll i=1;i*i<=sum;i++){
        if(sum % i == 0){
            yakusu.push_back(i);
            if(sum / i != i){
                yakusu.push_back(sum/i);
            }
        }
    }

    sort(all(yakusu));
    reverse(all(yakusu));
    for(ll& v : yakusu){
        vector<ll> vs(n);
        rep(i,n) vs[i] = v - (a[i]%v);
        sort(all(vs));
        reverse(all(vs));

        vector<ll> sum(n+1,0);
        rep(i,n) sum[i+1] = sum[i] + vs[i];

        for(int m = 1; m < n; m++){
            ll p = sum[n] - sum[m];
            ll q = sum[m] - m * v;
            ll t = p + q;
            if(t%v != 0) continue;
            if(max(abs(p),abs(q))<= k){
                cout << v << endl;
                /* cerr << m << " " << p << " " << q << endl; */
                return 0;
            }
        }
        /* int l,r; */
        /* l = 0; */
        /* r = n; */
        /* while(r-l>1){ */
        /*     int m = (l+r)/2; */
        /*     ll p = sum[n] - sum[m]; */
        /*     ll q = sum[m] - m * v; */

        /*     if(p+q >= 0){ */
        /*         l = m; */
        /*     }else{ */
        /*         r = m; */
        /*     } */
        /* } */

        /* cout << v <<" "  << l << endl; */
        /* if(sum[n] - l * v == 0 and sum[n]-sum[l] <= k){ */
        /*     cout << v << endl; */
        /*     return 0; */
        /* } */
    }
}


Measured memory_bytes: 256