<p>You are given an array of integers <code>nums</code> <strong>(0-indexed)</strong> and an integer <code>k</code>.</p>

<p>The <strong>score</strong> of a subarray <code>(i, j)</code> is defined as <code>min(nums[i], nums[i+1], ..., nums[j]) * (j - i + 1)</code>. A <strong>good</strong> subarray is a subarray where <code>i &lt;= k &lt;= j</code>.</p>

<p>Return <em>the maximum possible <strong>score</strong> of a <strong>good</strong> subarray.</em></p>

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

<pre>
<strong>Input:</strong> nums = [1,4,3,7,4,5], k = 3
<strong>Output:</strong> 15
<strong>Explanation:</strong> The optimal subarray is (1, 5) with a score of min(4,3,7,4,5) * (5-1+1) = 3 * 5 = 15. 
</pre>

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

<pre>
<strong>Input:</strong> nums = [5,5,4,5,4,1,1,1], k = 0
<strong>Output:</strong> 20
<strong>Explanation:</strong> The optimal subarray is (0, 4) with a score of min(5,5,4,5,4) * (4-0+1) = 4 * 5 = 20.
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 2 * 10<sup>4</sup></code></li>
	<li><code>0 &lt;= k &lt; nums.length</code></li>
</ul>

class Solution:
    def maximumScore(self, nums: List[int], k: int) -> int:
        """Monotonic stack to find prefix: next smaller element to the left,
        next smaller element to the right"""
        prefix_l = [0] + [i+1 for i in range(len(nums) - 1)]
        prefix_r = [i+1 for i in range(len(nums) - 1)][::-1] + [0]
        
        stack = []
        for i in range(len(nums)):
            while stack and nums[i] < stack[-1][1]:
                indx, n = stack.pop()
                prefix_r[indx] = i - indx - 1
            stack.append((i, nums[i]))

        stack = []
        for j in range(len(nums)-1, -1, -1):
            while stack and nums[j] < stack[-1][1]:
                indx, n = stack.pop()
                prefix_l[indx] = indx - j - 1
            stack.append((j, nums[j]))

        res = float('-inf')
        for i in range(len(nums)):
            if i < k and i+prefix_r[i] < k or i > k and i - prefix_l[i] > k:
                continue
            else:
                res = max(res, nums[i] * (prefix_r[i] + prefix_l[i] + 1))
        return res
1072