from collections import defaultdict
import sys
readline=sys.stdin.readline

def Factorize(N):
    assert N>=1
    factors=defaultdict(int)
    for p in range(2,N):
        if p**2>N:
            break
        while N%p==0:
            factors[p]+=1
            N//=p
    if N!=1:
        factors[N]+=1
    return factors

N,K=map(int,readline().split())
A=list(map(int,readline().split()))
dct=defaultdict(list)
for a in A:
    for p,e in Factorize(a).items():
        dct[p].append(e)
ans=1
mod=10**9+7
for p,lst in dct.items():
    lst.sort(reverse=True)
    ans*=pow(p,sum(lst[:K]),mod)
    ans%=mod
print(ans)