Problem: You are given two integers n and k. Find k-th smallest divisor of n, or report that it doesn't exist.

Divisor of n is any such natural number, that n can be divided by it without remainder.

Input

The first line contains two integers n and k (1 ≤ n ≤ 1015, 1 ≤ k ≤ 109).

Output

If n has less than k divisors, output -1.

Otherwise, output the k-th smallest divisor of n.

Examples

Input

4 2


Output

2


Input

5 3


Output

-1


Input

12 5


Output

6

Note

In the first example, number 4 has three divisors: 1, 2 and 4. The second one is 2.

In the second example, number 5 has only two divisors: 1 and 5. The third divisor doesn't exist, so the answer is -1.

Solution (in PYTHON3):

Solution:
import math

def divisors(n):
    sq = math.ceil(math.sqrt(n))
    d = set()
    for i in range(1, sq+1):
        if n % i == 0:
            d.add(i)
            d.add(n//i)
    d.add(n)
    return sorted(d)

n, k = input().split(" ")
n, k = int(n), int(k)

d = divisors(n)
if k > len(d):
    print(-1)
else:
    print(d[k-1])