Kth Smallest Prime Fraction

Statement

You are given a sorted array of unique integers, arr, which includes the number $1$ and other prime numbers. You are also given an integer $k$.

For every index $i$ and $j$ where $0 \leq i < j <$ arr.length, you can form a fraction by taking the number at index $i$ as the numerator and the number at index $j$ as the denominator, resulting in the fraction arr[i] / arr[j].

Your task is to return the $k^{th}$ smallest fraction among these fractions. The answer should be returned as an array of two integers, where the first element, answer[0], is the numerator (arr[i]), and the second element, answer[1], is the denominator (arr[j]) corresponding to the $k^{th}$ smallest fraction.

Constraints:

• $2 \leq$ arr.length $\leq 10^3$

• $1 \leq arr[i] \leq 3 \times 10^4$

• $arr[0] = 1$

• $arr[i]$ is a prime number for $i > 0.$

• All the numbers of arr are unique and sorted in strictly increasing order.

• $1 \leq k \leq$ arr.length $\times$ (arr.length $- 1$)

Examples