Given an integer array nums, sort the integers in ascending order based on their binary reflection.

The binary reflection of a positive integer is formed by taking its binary representation without leading zeros, reversing the bits, and converting the reversed binary string back to an integer.

If two or more integers share the same binary reflection value, arrange them in ascending order according to their original values.

Return the sorted array.

Note: If multiple elements have identical reflected values, their relative order is resolved by comparing their original values in ascending order.

Constraints:

• $1 \leq$ nums.length $\leq 100$

• $1 \leq$ nums[i] $\leq 10^9$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.