def factorization(n):
    arr = []
    temp = n
    for i in range(2, int(-(-n**0.5 // 1)) + 1):
        if temp % i == 0:
            cnt = 0
            while temp % i == 0:
                cnt += 1
                temp //= i
            arr.append([i, cnt])
 
    if temp != 1:
        arr.append([temp, 1])

    return arr


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

from collections import *
D = defaultdict(list)
for a in A:
    for k, v in factorization(a):
        D[k].append(v)

ans = 1
mod = 10 ** 9 + 7
for k, v in D.items():
    if len(v) <= K:
        ans *= pow(k, sum(v), mod)
        ans %= mod
    else:
        v.sort(reverse=True)
        ans *= pow(k, sum(v[:K]), mod)
        ans %= mod

print(ans)