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 sys
import math

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

divisors = []

limit = math.sqrt(n)
d = 1

while d <= limit:
    if n % d == 0:
        if d == n // d:
            divisors.append(d)
        else:
            divisors.append(d)
            divisors.append(n // d)
    d += 1

divisors.sort()

if k > len(divisors):
    ans = -1
else:
    ans = divisors[k - 1]

print(ans)