"""
1492. The kth Factor of n
Medium

Given two positive integers n and k.

A factor of an integer n is defined as an integer i where n % i == 0.

Consider a list of all factors of n sorted in ascending order, return the kth factor in this list or return -1 if n has less than k factors.

 

Example 1:

Input: n = 12, k = 3
Output: 3
Explanation: Factors list is [1, 2, 3, 4, 6, 12], the 3rd factor is 3.

Example 2:

Input: n = 7, k = 2
Output: 7
Explanation: Factors list is [1, 7], the 2nd factor is 7.

Example 3:

Input: n = 4, k = 4
Output: -1
Explanation: Factors list is [1, 2, 4], there is only 3 factors. We should return -1.

Example 4:

Input: n = 1, k = 1
Output: 1
Explanation: Factors list is [1], the 1st factor is 1.

Example 5:

Input: n = 1000, k = 3
Output: 4
Explanation: Factors list is [1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000].

 

Constraints:

    1 <= k <= n <= 1000

"""


class Solution:
    def kthFactor(self, n: int, k: int) -> int:
        factors = set()
        if n == 1:
            if k == 1:
                return 1
            else:
                return -1
        for i in range(1, int(n ** 0.5) + 1):
            if n % i == 0:
                factors.add(i)
                factors.add(n // i)
        factors = list(factors)
        factors.sort()
        try:
            return factors[k - 1]
        except:
            return -1
