Maximum Average Subarray II

You are given an integer array nums consisting of n elements, and an integer k.

Find a contiguous subarray whose length is greater than or equal to k that has the maximum average value and return this value. Any answer with a calculation error less than 10⁻⁵ will be accepted.

Example 1:

Input: nums = [1,12,-5,-6,50,3], k = 4

Output: 12.75000

Explanation:

• When the length is 4, averages are [0.5, 12.75, 10.5] and the maximum average is 12.75
• When the length is 5, averages are [10.4, 10.8] and the maximum average is 10.8
• When the length is 6, averages are [9.16667] and the maximum average is 9.16667

The maximum average is when we choose a subarray of length 4 (i.e., the sub array [12, -5, -6, 50]) which has the max average 12.75, so we return 12.75

Note that we do not consider the subarrays of length < 4.

Example 2:

Input: nums = [5], k = 1

Output: 5.00000

Constraints:

• n == nums.length
• 1 <= k <= n <= 10⁴
• -10⁴ <= nums[i] <= 10⁴