import sys
from collections import Counter
sys.setrecursionlimit(10**7)
def I(): return int(sys.stdin.readline().rstrip())
def MI(): return map(int,sys.stdin.readline().rstrip().split())
def LI(): return list(map(int,sys.stdin.readline().rstrip().split()))
def LI2(): return list(map(int,sys.stdin.readline().rstrip()))
def S(): return sys.stdin.readline().rstrip()
def LS(): return list(sys.stdin.readline().rstrip().split())
def LS2(): return list(sys.stdin.readline().rstrip())


def sieve_of_eratosthenes(n):  # n以下の素数の全列挙
    prime_list = []
    A = [1]*(n+1)  # A[i] = iが素数なら1,その他は0
    A[0] = A[1] = 0
    for i in range(2,int(n**.5)+1):
        if A[i]:
            prime_list.append(i)
            for j in range(i**2,n+1,i):
                A[j] = 0
    for i in range(int(n**.5)+1,n+1):
        if A[i] == 1:
            prime_list.append(i)
    return prime_list


N,K = MI()
A = LI()
mod = 10**9+7

prime_list = sieve_of_eratosthenes(int(10**4.5))

ans = 1
for p in prime_list:
    X = []
    for i in range(N):
        r = 0
        while A[i] % p == 0:
            r += 1
            A[i] //= p
        X.append(r)
    X.sort(reverse=True)
    ans *= pow(p,sum(X[:K]))
    ans %= mod

count = Counter(A)
for p in count.keys():
    if p != 1:
        ans *= pow(p,min(count[p],K))
        ans %= mod

print(ans)