# https://yukicoder.me/problems/no/368

import math

MOD = 10 ** 9 + 7

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

    p_array_map = {}
    for a in A:
        p_map = {}
        sqrt_n = int(math.sqrt(a))
        for p in range(2, sqrt_n + 1):
            while a % p == 0:
                a //= p
                if p not in p_map:
                    p_map[p] = 0
                p_map[p] += 1
        if a > 1:
            p_map[a] = 1
        
        for p, value in p_map.items():
            if p not in p_array_map:
                p_array_map[p] = []
            p_array_map[p].append(value)
    
    answer = 1
    for p, array in p_array_map.items():
        array.sort(reverse=True)

        z = 0
        for i in range(min(K, len(array))):
            z += array[i]
        answer *= pow(p, z, MOD)
        answer %= MOD
    print(answer)
        
        




if __name__ == "__main__":
    main()