#ifdef OJ_MISC_OFFLINE

#include "prolog.h"

#else
#define LOG
#define PRINT
#define LCERR
#include <iostream>
auto optimize_cpp_stdio = []() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    std::cout.tie(nullptr);
    std::setvbuf(stdout, nullptr, _IOFBF, BUFSIZ);
    return 0;
}();
#endif

#include <algorithm>
#include <array>
#include <cassert>
#include <cstdio>
#include <cstdlib>
#include <iostream>
#include <numeric>
#include <string>
#include <vector>

namespace {

using namespace std;

class Solution {
public:
    int max_gcd(const vector<int>& A, int64_t K) {
        const int N = A.size();
        int sum_A = accumulate(A.begin(), A.end(), 0);
        vector<int> cand;
        for (int i = 1; i * i <= sum_A; ++i) {
            if (sum_A % i == 0) {
                cand.emplace_back(i);
                if (sum_A / i != i) {
                    cand.emplace_back(sum_A / i);
                }
            }
        }
        // Binary search is incorrect, because the `cost` function is not continuous (involves lots
        // of mods). Each candidate must be checked separately.
        int best = -1;
        for (int cur_cand : cand) {
            if (validate(cur_cand, A, K)) {
                best = max(best, cur_cand);
            }
        }
        return best;
    }
private:
    bool validate(int cand_gcd, const vector<int>& A, int64_t K) {
        LOG("Validating candidate {}\n", cand_gcd);
        const int N = A.size();
        static vector<int> remainders;
        remainders.clear();
        for (int i = 0; i < N; ++i) {
            int rem = A[i] % cand_gcd;
            if (rem > 0) {
                remainders.emplace_back(rem);
            }
        }
        sort(remainders.begin(), remainders.end());
        int sum_remainder = accumulate(remainders.begin(), remainders.end(), 0);
        int t = sum_remainder / cand_gcd;
        int64_t sum_abs_diff = 0;
        for (int i = 0; i < remainders.size() - t; ++i) {
            sum_abs_diff += remainders[i];
        }
        for (int i = remainders.size() - t; i < remainders.size(); ++i) {
            sum_abs_diff += cand_gcd - remainders[i];
        }
        if (sum_abs_diff > 2 * K) {
            return false;
        } else {
            return true;
        }

        // Another way of doing validation, learned from another participant
//        int l = 0;
//        int r = remainders.size() - 1;
//        int cost = 0;
//        while(l < r) {
//            int diff = min(remainders[l], cand_gcd - remainders[r]);
//            cost += diff;
//            remainders[l] -= diff;
//            remainders[r] += diff;
//            if (remainders[l] == 0){
//                ++l;
//            }
//            if (remainders[r] == cand_gcd) {
//                --r;
//            }
//        }
//        return cost <= K;
    }
};

int solve() {
    Solution solution;
    // handle IO here
    int N;
    int64_t K;
    cin >> N >> K;
    vector<int> A(N);
    for (int i = 0; i < N; ++i) {
        cin >> A[i];
    }
    cout << solution.max_gcd(A, K) << '\n';
    return 0;
}

} // anonymous namespace

#ifdef OJ_MISC_OFFLINE

#include "epilog.h"

#else

int main() {
    return solve();
}

#endif


Measured memory_bytes: 256