N,K = map(int,input().split())
P = 10 ** 9 + 7
ans = 1
a = list(map(int,input().split()))

C = 4 * 10 ** 4
dat = [0] * C
for i in range(2,C):
    if dat[i] == 0:
        for j in range(2 * i,C,i):
            dat[j] = 1
        l = []
        for j in range(N):
            count = 0
            while a[j] % i == 0:
                count += 1
                a[j] //= i
            if count:
                l.append(count)
        l.sort(reverse = True)
        _sum = 0
        for j in l[:K]:
            _sum += j
        ans = ans * pow(i,_sum,P) % P
from collections import defaultdict
d = defaultdict(int)
for i in a:
    if i > 1:
        d[i] += 1
for i in d:
    if d[i] > K:
        ans = ans * pow(i,K,P) % P
    else:
        ans = ans * pow(i,d[i],P) % P
print(ans)