/* -*- coding: utf-8 -*-
 *
 * 368.cc: No.368 LCM of K-products - yukicoder
 */

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<iostream>
#include<string>
#include<vector>
#include<map>
#include<set>
#include<stack>
#include<list>
#include<queue>
#include<deque>
#include<algorithm>
#include<numeric>
#include<utility>
#include<complex>
#include<functional>
 
using namespace std;

/* constant */

const int MAX_N = 1000;
const int MAX_K = 1000;
const int MAX_P = 32000; // >=sqrt(10^9)

typedef long long ll;
const ll MOD = 1000000007;

/* typedef */

typedef vector<int> vi;
typedef pair<int,int> pii;
typedef vector<pii> vpii;
typedef map<int,vi> mivi;

/* global variables */

bool primes[MAX_P + 1];
int as[MAX_N];

/* subroutines */

void gen_primes(int maxp, vi &pnums) {
  memset(primes, true, sizeof(primes));
  primes[0] = primes[1] = false;

  int p;
  for (p = 2; p * p <= maxp; p++)
    if (primes[p]) {
      pnums.push_back(p);
      for (int q = p * p; q <= maxp; q += p) primes[q] = false;
    }
  for (; p <= maxp; p++)
    if (primes[p]) pnums.push_back(p);
}

bool prime_decomp(int n, vi &pnums, vpii& pds) {
  pds.clear();

  int pn = pnums.size();
  for (int i = 0; i < pn; i++) {
    int pi = pnums[i];
    if (pi * pi > n) {
      if (n > 1) pds.push_back(pii(n, 1));
      return true;
    }

    if (n % pi == 0) {
      int fi = 0;
      while (n % pi == 0) n /= pi, fi++;
      pds.push_back(pii(pi, fi));
    }
  }
  return false;
}

ll powmod(ll a, int b) {
  ll pm = 1;
  while (b > 0) {
    if ((b & 1) != 0) pm = (pm * a) % MOD;
    a = (a * a) % MOD;
    b >>= 1;
  }
  return pm;
}

/* main */

int main() {
  vi pnums;
  gen_primes(MAX_P, pnums);

  int n, k;
  cin >> n >> k;

  mivi pvs;
  
  for (int i = 0; i < n; i++) {
    int ai;
    cin >> ai;

    vpii pds;
    prime_decomp(ai, pnums, pds);

    for (vpii::iterator vit = pds.begin(); vit != pds.end(); vit++)
      pvs[vit->first].push_back(vit->second);
  }

  ll lcm = 1;
  for (mivi::iterator mit = pvs.begin(); mit != pvs.end(); mit++) {
    const int &pi = mit->first;
    vi &v = mit->second;
    sort(v.begin(), v.end(), greater<int>());

    //printf("%d:", pi);
    //for (int i = 0; i < v.size(); i++) printf(" %d", v[i]); putchar('\n');
    
    int sum = 0, maxi = min(k, (int)v.size());
    for (int i = 0; i < maxi; i++) sum += v[i];
    lcm = (lcm * powmod((ll)pi, sum)) % MOD;
  }

  printf("%lld\n", lcm);
  return 0;
}