You are given a $0$ indexed integer array nums of length n, and an integer k.

The $k$ radius average for a subarray centered at index i with radius k is the average of all elements in nums spanning from index i - k to i + k inclusive. If there are fewer than k elements before or after index i, then the $k$ radius average is $-1$.

Return an array avgs of length n where avgs[i] is the $k$ radius average for the subarray centered at index i.

Note: The average of $x$ elements is the sum of the $x$ elements divided by $x$, using integer division which rounds down to the nearest integer.

Constraints:

• n == nums.length

• $1 \leq$ n $\leq 10^5$

• $0 \leq$ nums[i], k $\leq 10^5$

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.