#include <bits/stdc++.h>

#define _overload(_1,_2,_3,name,...) name
#define _rep(i,n) _range(i,0,n)
#define _range(i,a,b) for(int i=int(a);i<int(b);++i)
#define rep(...) _overload(__VA_ARGS__,_range,_rep,)(__VA_ARGS__)

#define _rrep(i,n) _rrange(i,n,0)
#define _rrange(i,a,b) for(int i=int(a)-1;i>=int(b);--i)
#define rrep(...) _overload(__VA_ARGS__,_rrange,_rrep,)(__VA_ARGS__)

#define _all(arg) begin(arg),end(arg)
#define uniq(arg) sort(_all(arg)),(arg).erase(unique(_all(arg)),end(arg))
#define getidx(ary,key) lower_bound(_all(ary),key)-begin(ary)
#define clr(a,b) memset((a),(b),sizeof(a))
#define bit(n) (1LL<<(n))
#define popcount(n) (__builtin_popcountll(n))

template<class T>bool chmax(T &a, const T &b) { return (a<b)?(a=b,1):0;}
template<class T>bool chmin(T &a, const T &b) { return (b<a)?(a=b,1):0;}

using namespace std;
using ll=long long;
const ll mod=1000000007LL;

inline ll extgcd(ll a,ll b,ll& x,ll& y){x=1,y=0;ll g=a;if(b!=0) g=extgcd(b,a%b,y,x),y-=a/b*x;return g;}
inline ll ADD(const ll &a, const ll &b,const ll &mod) { return a+b<mod?a+b:a+b-mod;}
inline ll SUB(const ll &a, const ll &b,const ll &mod) { return a-b>=0?a-b:a-b+mod;}
inline ll MUL(const ll &a, const ll &b,const ll &mod) { return (1LL*a*b)%mod;}
inline ll INV(ll a,ll mod){ll x,y;extgcd(a,mod,x,y);return (x%mod+mod)%mod;}
inline ll DIV(const ll &a, const ll &b,const ll &mod) {return MUL(a,INV(b,mod),mod);}
inline ll POW(ll a,ll n,ll mod){ll b=1LL;for(a%=mod;n;a=MUL(a,a,mod),n>>=1)if(n&1) b=MUL(b,a,mod); return b;}

const int limit=31607;
bool prime[limit+1];

void init(){
	rep(i,limit+1) prime[i]=true;
	prime[0]=prime[1]=false;
	for(ll i=2;i*i<=limit;++i){
		if(prime[i])
			for(ll j=i*i;j<=limit;j+=i)
				prime[j]=false;
	}
	return;
}

ll a[1010];


int main(void){
	init();

	int n,k;
	cin >> n >> k;
	rep(i,n) cin >> a[i];
	ll ans=1LL;

	ll factor[1010];
	for(int f=2;f<=limit;++f){
		if(prime[f]==false) continue;
		rep(i,n){
			factor[i]=0;
			while(a[i]%f==0) a[i]/=f,factor[i]++;
		}
		sort(factor,factor+n);
		reverse(factor,factor+n);
		ll sum=0LL;
		rep(i,min(999,k)) sum+=factor[i];
		ans=MUL(ans,POW(f,sum,mod),mod);
	}

	map<ll,int> remain;
	rep(i,n){
		if(a[i]==1) continue;
		remain[a[i]]++;
	} 

	for(auto &it:remain){
		ll index=min<ll>(it.second,k);
		ans=MUL(ans,POW(it.first,index,mod),mod);
	}

	cout << ans << endl;
	return 0;
}

// Incorrect solution one  
// mistake processing Line 69