from heapq import heappop, heappush
from collections import defaultdict

n, k = map(int, input().split())
A = list(map(int, input().split()))
mod = 10**9 + 7

P = defaultdict(list)
C = defaultdict(int)
for i in range(n):
    a = A[i]
    f = 2
    while f * f <= a:
        cnt = 0
        while a % f == 0:
            cnt += 1
            a //= f
        if cnt > 0:
            if len(P[f]) < k:
                heappush(P[f], cnt)
                C[f] += cnt
            else:
                d = heappop(P[f])
                C[f] -= d
                res = max(d, cnt)
                heappush(P[f], res)
                C[f] += res
        f += 1
    if a != 1:
        if len(P[a]) < k:
            heappush(P[a], 1)
            C[a] += 1
        else:
            d = heappop(P[a])
            C[a] -= d
            res = max(d, 1)
            heappush(P[a], res)
            C[a] += res
ans = 1
for val, cnt in C.items():
    ans *= pow(val, cnt, mod)
    ans %= mod
print(ans)