human
Give me a the Python program you requested given the following:
Solve in Python:
Given an integer array arr, you should partition the array into (contiguous) subarrays of length at most k. After partitioning, each subarray has their values changed to become the maximum value of that subarray.
Return the largest sum of the given array after partitioning.
 
Example 1:
Input: arr = [1,15,7,9,2,5,10], k = 3
Output: 84
Explanation: arr becomes [15,15,15,9,10,10,10]

Example 2:
Input: arr = [1,4,1,5,7,3,6,1,9,9,3], k = 4
Output: 83

Example 3:
Input: arr = [1], k = 1
Output: 1

 
Constraints:

1 <= arr.length <= 500
0 <= arr[i] <= 109
1 <= k <= arr.length
assistant
#Here is the Python program you requested.

class Solution:
    def maxSumAfterPartitioning(self, arr: List[int], k: int) -> int:
        return self.recur(arr, len(arr)-1, k, {})

    def recur(self, arr, index, k, hashMap):
        if index < 0:
            return 0
        
        if index in hashMap:
            return hashMap[index]
        result = 0
        maxV = 0
        for i in range(k):
            if index - i < 0:
                continue
            maxV = max(maxV, arr[index-i])
            result = max(result, maxV * (i +1 ) + self.recur(arr, index-i-1, k, hashMap))
        
        hashMap[index] =  result
        return result