from collections import defaultdict


def prime_factorization(n):  # 素因数分解
    res = []
    cnt = 0
    while n % 2 == 0:
        while n % 2 == 0:
            cnt += 1
            n //= 2
    if cnt:
        res.append((2, cnt))
    i = 1
    while i * i <= n:
        i += 2
        if n % i == 0:
            cnt = 0
            while n % i == 0:
                cnt += 1
                n //= i
            res.append((i, cnt))
    if n > 1:
        res.append((n, 1))
    return res


N, K = map(int, input().split())
A = list(map(int, input().split()))

dp = [defaultdict(int) for _ in range(K+1)]
for a in A:
    pf = prime_factorization(a)
    for i in reversed(range(K)):
        for p, f in pf:
            dp[i+1][p] = max(dp[i+1][p], dp[i][p] + f)

mod = 10 ** 9 + 7
ans = 1
for k, v in dp[K].items():
    ans *= pow(k, v, mod)
    ans %= mod
print(ans)