You are given an integer array nums and an integer k.

In a single operation, you can select any index i and either increase or decrease nums[i] by $1$.

The frequency score of the array is defined as the maximum frequency of any value present in nums.

Return the maximum possible frequency score of nums after applying at most k operations.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 10^9$

• $0 \leq$ k $\leq 10^{14}$

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.