#include <bits/stdc++.h>

#define REP(i,n) for(int i=0;i<(int)(n);i++)
#define ALL(x) (x).begin(),(x).end()

using namespace std;

using ll = long long;

vector<pair<int,int>> prime_factorization(int n) {
  vector<pair<int,int>> res;
  for (int i = 2; i * i <= n; ++i) {
    int cnt = 0;
    while (n % i == 0) { ++cnt; n /= i; }
    if (cnt > 0) res.emplace_back(i, cnt);
  }
  if (n > 1) res.emplace_back(n, 1);
  return res;
}

const int mod = 1e9 + 7;

int main() {
  int N, K;
  cin >> N >> K;
  map<int,vector<int>> vec;
  REP(i,N) {
    int a; cin >> a;
    for (auto p: prime_factorization(a))
      vec[p.first].push_back(p.second);
  }
  ll res = 1;
  for (auto p: vec) {
    int i = p.first;
    vector<int> v = p.second;
    sort(v.rbegin(), v.rend());
    REP(j,min((int)v.size(), K))
      REP(k,v[j]) res = (res * i) % mod;
  }
  cout << res << endl;
  return 0;
}