A number is called lucky if it comprises only the digits $4$ and $7$. Your task is to return the k-th lucky number as a string for a given integer k. 

Constraints:

• $1 <=$ k $<= 10^9$

The essence of this solution lies in using bitwise manipulation to generate the k-th lucky number. The solution uses an approach by transforming the given integer k into a binary-like representation to determine the k-th lucky number. The key idea is to convert k into a string of digits composed of $4s$ ...