04. The kth Factor of n.cpp

/*
The kth Factor of n
===================

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

Hint #1  
The factors of n will be always in the range [1, n].

Hint #2  
Keep a list of all factors sorted. Loop i from 1 to n and add i if n % i == 0. Return the kth factor if it exist in this list.
*/

class Solution
{
public:
  int kthFactor(int n, int k)
  {
    for (int i = 1; i <= n; ++i)
      if (n % i == 0)
        if (--k == 0)
          return i;
    return -1;
  }
};