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Problem

You are given a sorted integer array arr containing 1 and prime numbers, where all the integers of arr are unique. You are also given an integer k.

For every i and j where 0 <= i < j < arr.length, we consider the fraction arr[i] / arr[j].

Return the $k^{th}$ smallest fraction considered. Return your answer as an array of integers of size 2, where answer[0] == arr[i] and answer[1] == arr[j].

Example 1:

Input: arr = [1,2,3,5], k = 3
Output: [2,5]
Explanation: The fractions to be considered in sorted order are:
1/5, 1/3, 2/5, 1/2, 3/5, and 2/3.
The third fraction is 2/5.

Example 2:

Input: arr = [1,7], k = 1
Output: [1,7]

Constraints:

  • 2 <= arr.length <= 1000
  • $1 <= arr[i] <= 3 * 10^4$
  • arr[0] == 1
  • arr[i] is a prime number for i > 0.
  • All the numbers of arr are unique and sorted in strictly increasing order.
  • 1 <= k <= arr.length * (arr.length - 1) / 2

Code