from collections import defaultdict
mp=defaultdict(list)
def factorize(x):
    for i in range(2,40000):
        ret=0
        while x%i==0:
            ret+=1
            x//=i
        if ret:
            mp[i].append(ret)
    if x>1:
        mp[x].append(1)
N,K=map(int,input().split())
A=list(map(int,input().split()))
for i in range(N):
    factorize(A[i])
mod=1000000007
ans=1
for k,v in mp.items():
    list.sort(v)
    list.reverse(v)
    ret=0
    for i in range(min(len(v),K)):
        ret+=v[i]
    ans=ans*pow(int(k),ret,mod)%mod
print(ans)