C_HSE

#include <bits/stdc++.h>
#define FOR(i, a, b) for (int i = a; i < b; ++i)
#define RFOR(i, a, b) for (int i = a; i >= b; --i)
#define ll long long
#pragma GCC optimize("O3,unroll-loops")

#define int long long

using namespace std;

int erat[1500001];

signed main() {
    // O(n log n)
    ios_base::sync_with_stdio(false); cin.tie(0);
    int n, k; cin >> n >> k;
    int mx = 0;
    int a[n];
    FOR(i, 0, n) {
        cin >> a[i];
        mx = max(mx, a[i]);
    }
    vector <int> d[mx + 1];
    for (int i = 2; i <= mx; ++i) {
        if (!erat[i]) {
            erat[i] = i;
            d[i] = {i};
            for (int j = i; j <= mx; j += i) if (!erat[j]) erat[j] = i;
        }
        else {
            int c = i;
            while (c != 1) {
                d[i].push_back(erat[c]);
                c /= erat[c];
            }
        }
    }
    priority_queue <int> cur;
    cur.push(1);
    FOR(i, 0, n) cur.push(a[i]);
    while (true) { // O(n log^2 n)
        int now = cur.top();
        cur.pop();
        int nx = cur.top();
        if (now == 1 || k < d[now][0]) {
            cout << now;
            return 0;
        }
        if (now / d[now][0] <= nx) {
            k -= d[now][0];
            now /= d[now][0];
            cur.push(now);
            continue;
        }
        int l = 0, r = d[now].size();
        while (l < r - 1) {
            int m = (l + r) / 2;
            if (d[now][m] <= k && now / d[now][m] > nx) l = m;
            else r = m;
        }
        if (r != d[now].size()) {
            k -= d[now][r];
            now /= d[now][r];
        }
        else {
            k -= d[now][l];
            now /= d[now][l];
        }
        cur.push(now);
    }
}