<p>Given an integer array <code>nums</code> and an integer <code>k</code>, split <code>nums</code> into <code>k</code> non-empty subarrays such that the largest sum of any subarray is <strong>minimized</strong>.</p>

<p>Return <em>the minimized largest sum of the split</em>.</p>

<p>A <strong>subarray</strong> is a contiguous part of the array.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [7,2,5,10,8], k = 2
<strong>Output:</strong> 18
<strong>Explanation:</strong> There are four ways to split nums into two subarrays.
The best way is to split it into [7,2,5] and [10,8], where the largest sum among the two subarrays is only 18.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3,4,5], k = 2
<strong>Output:</strong> 9
<strong>Explanation:</strong> There are four ways to split nums into two subarrays.
The best way is to split it into [1,2,3] and [4,5], where the largest sum among the two subarrays is only 9.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>
	<li><code>1 &lt;= k &lt;= min(50, nums.length)</code></li>
</ul>

class Solution:
    def __init__(self):
        self.prefixSumArray = []

    def splitArray(self, nums: List[int], k: int) -> int:
        numsLen = len(nums)
        dp = [[10 ** 9 for i in range(k)] for _ in range(numsLen)]
        self.__calculate_prefix_subarray(nums)

        for i in range(numsLen-1,-1,-1):
            dp[i][0] = self.__calculate_ranged_sum(i,numsLen-1)

        for subarrayCount in range(1,k):
            for currentIndex in range(numsLen-1,-1,-1):
                for i in range(currentIndex, numsLen - subarrayCount + 1):
                    sumFromCurrentIndexToSplit = self.__calculate_ranged_sum(currentIndex,i)
                    if i + 1 >= numsLen:
                        break
                    recursiveSplitDP = dp[i+1][subarrayCount-1]
                    maxSubarraySum = max(sumFromCurrentIndexToSplit, recursiveSplitDP)
                    dp[currentIndex][subarrayCount] = min(dp[currentIndex][subarrayCount], maxSubarraySum)

                    if sumFromCurrentIndexToSplit >= dp[currentIndex][subarrayCount]:
                        break

        return dp[0][k-1]
        
    def __calculate_prefix_subarray(self, nums: List[int]) -> None:
        self.prefixSumArray = [0] * len(nums)
        self.prefixSumArray[0] = nums[0]
        for i in range(1,len(nums)):
            self.prefixSumArray[i] = nums[i] + self.prefixSumArray[i-1]

    def __calculate_ranged_sum(self, fromIndex: int, endIndex: int) -> int:
        if fromIndex == 0:
            return self.prefixSumArray[endIndex]
        return self.prefixSumArray[endIndex] - self.prefixSumArray[fromIndex - 1]

        
            

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