<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 backtrack(self, nums, k, idx):
        if k == 1:
            self.dp[idx][k] = sum(nums[idx:])
            return self.pSum[len(nums)] - self.pSum[idx]
        elif self.dp[idx][k] != -1:
            return self.dp[idx][k]

        minMaxSubVal = math.inf

        for i in range(idx, len(nums) - k + 1):
            newVal = max(self.pSum[i+1] - self.pSum[idx], self.backtrack(nums, k-1, i+1))
            minMaxSubVal = min(newVal, minMaxSubVal)
            if self.pSum[i+1] - self.pSum[idx] > self.backtrack(nums, k-1, i+1):
                break
        
        self.dp[idx][k] = minMaxSubVal
        return minMaxSubVal

    def splitArray(self, nums: List[int], k: int) -> int:
        self.pSum = [0]
        for num in nums:
            self.pSum.append(self.pSum[-1] + num)

        self.dp = [[-1 for _ in range(k+1)] for _ in range(len(nums)+1)]
        return self.backtrack(nums, k, 0)
17300