<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 splitArray(self, nums: List[int], m: int) -> int:       
        sums, maxs = [0], [0]
        for x in nums:
            sums.append(sums[-1] + x)
            maxs.append(max(maxs[-1], x))
        dp = [[float('inf') for _ in range(len(nums) + 1)] for _ in range(m + 1)]
        for i in range(1, len(nums) + 1):
            dp[1][i] = sums[i]
        for m1 in range(1, m + 1):
            dp[m1][m1] = maxs[m1]
        for m1 in range(2, m + 1):
            for i in range(m1 + 1, len(nums) + 1):
                low, high = m1 - 1, i - 1
                while low < high:
                    mid = low + (high - low) // 2
                    a, b = dp[m1-1][mid], sums[i] - sums[mid]
                    dp[m1][i] = min(dp[m1][i], max(a, b))
                    if b >= a:
                        low = mid + 1
                    else:
                        high = mid
                a, b = dp[m1-1][low], sums[i] - sums[low]
                dp[m1][i] = min(dp[m1][i], max(a, b))
        return dp[m][len(nums)]
18600