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:
# Author: Maharshi Gor
import math


def read(type=int):
    return type(input())


def read_arr(type=int):
    return [type(token) for token in input().split()]


def solution(n, k):
    small = []
    large = []
    s = int(math.sqrt(n))
    for i in range(1, s + 1):
        if n % i == 0:
            small.append(i)
            if n // i != i:
                large.append(n // i)
    f = small + list(reversed(large))
    return f[k-1] if k <= len(f) else -1


def run():
    n, k = read_arr()
    ans = solution(n, k)
    if ans is None: ans = -1
    print(ans)

run()