#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <queue>
#include <string>
#include <map>
#include <set>
#include <stack>
#include <tuple>
#include <deque>
#include <array>
#include <numeric>
#include <bitset>
#include <iomanip>
#include <cassert>
#include <chrono>
#include <random>
#include <limits>
#include <iterator>
#include <functional>
#include <sstream>
#include <fstream>
#include <complex>
#include <cstring>
#include <unordered_map>
#include <unordered_set>
using namespace std;

using ll = long long;
constexpr int INF = 1001001001;
constexpr int mod = 1000000007;
// constexpr int mod = 998244353;

template<class T>
inline bool chmax(T& x, T y){
    if(x < y){
        x = y;
        return true;
    }
    return false;
}
template<class T>
inline bool chmin(T& x, T y){
    if(x > y){
        x = y;
        return true;
    }
    return false;
}

struct mint {
    int x;
    mint() : x(0) {}
    mint(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
    mint& operator+=(const mint& p){
        if((x += p.x) >= mod)   x -= mod;
        return *this;
    }
    mint& operator-=(const mint& p){
        if((x -= p.x) < 0)  x += mod;
        return *this;
    }
    mint& operator*=(const mint& p){
        x = (int)(1LL * x * p.x % mod);
        return *this;
    }
    mint& operator/=(const mint& p){
        *this *= p.inverse();
        return *this;
    }
    mint operator-() const { return mint(-x); }
    mint operator+(const mint& p) const { return mint(*this) += p; }
    mint operator-(const mint& p) const { return mint(*this) -= p; }
    mint operator*(const mint& p) const { return mint(*this) *= p; }
    mint operator/(const mint& p) const { return mint(*this) /= p; }
    bool operator==(const mint& p) const { return x == p.x; }
    bool operator!=(const mint& p) const { return x != p.x; }
    mint pow(int64_t n) const {
        mint res = 1, mul = x;
        while(n > 0){
            if(n & 1)   res *= mul;
            mul *= mul;
            n >>= 1;
        }
        return res;
    }
    mint inverse() const { return pow(mod - 2); }
    friend ostream& operator<<(ostream& os, const mint& p){
        return os << p.x;
    }
    friend istream& operator>>(istream& is, mint& p){
        int64_t val;
        is >> val;
        p = mint(val);
        return is;
    }
};

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int N, K;
    cin >> N >> K;
    vector<map<int, int>> prime_factor(N);
    set<int> primes;
    vector<int> A(N);
    for(int i = 0; i < N; ++i){
        cin >> A[i];
        int X = A[i];
        for(int j = 2; j * j <= X; ++j){
            if(X % j == 0){
                primes.emplace(j);
                while(X % j == 0){
                    prime_factor[i][j] += 1;
                    X /= j;
                }
            }
        }
        if(X != 1){
            primes.emplace(X);
            prime_factor[i][X] = 1;
        }
    }
    map<int, vector<int>> cnt;
    for(int i = 0; i < N; ++i){
        for(auto& p : primes){
            cnt[p].emplace_back(prime_factor[i][p]);
        }
    }
    mint ans = 1;
    for(auto& [p, v] : cnt){
        sort(rbegin(v), rend(v));
        int S = accumulate(begin(v), begin(v) + K, 0);
        for(int i = 0; i < S; ++i)  ans *= p;
    }
    cout << ans << endl;

    return 0;
}