def prime_factorize(N): #素因数分解
    exponent = 0
    while N%2 == 0:
        exponent += 1
        N //= 2
    if exponent: factorization = [[2,exponent]]
    else: factorization = []
    i=1
    while i*i <=N:
        i += 2
        if N%i: continue
        exponent = 0
        while N%i == 0:
            exponent += 1
            N //= i
        factorization.append([i,exponent])
    if N!= 1: factorization.append([N,1])
    assert N != 0, "zero"
    return factorization

n,k,*a = map(int,open(0).read().split())
d = {}
for ai in a:
    for p,e in prime_factorize(ai):
        if p in d: d[p].append(e)
        else: d[p] = [e]
ans = 1
MOD = 10**9+7
for p,lst in d.items():
    lst.sort(reverse=True)
    ans *= pow(p,sum(lst[:k]),MOD)
    ans %= MOD
print(ans)