We partition a row of numbers `nums`

into at most `k`

adjacent (non-empty) groups, then our score is the sum of the average of each group. What is the largest score we can achieve?

Note that our partition must use every number in `nums`

, and that scores are not necessarily integers.

Example:Input:nums = [9,1,2,3,9] k = 3Output:20Explanation:The best choice is to partition nums into [9], [1, 2, 3], [9]. The answer is 9 + (1 + 2 + 3) / 3 + 9 = 20. We could have also partitioned nums into [9, 1], [2], [3, 9], for example. That partition would lead to a score of 5 + 2 + 6 = 13, which is worse.

**Note: **

`1 <= nums.length <= 100`

.`1 <= nums[i] <= 10000`

.`1 <= k <= nums.length`

.- Answers within
`10`

of the correct answer will be accepted as correct.^{-6}

class Solution {
public double largestSumOfAverages(int[] nums, int k) {
}
}