<p>The <strong>min-product</strong> of an array is equal to the <strong>minimum value</strong> in the array <strong>multiplied by</strong> the array&#39;s <strong>sum</strong>.</p>

<ul>
	<li>For example, the array <code>[3,2,5]</code> (minimum value is <code>2</code>) has a min-product of <code>2 * (3+2+5) = 2 * 10 = 20</code>.</li>
</ul>

<p>Given an array of integers <code>nums</code>, return <em>the <strong>maximum min-product</strong> of any <strong>non-empty subarray</strong> of </em><code>nums</code>. Since the answer may be large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>Note that the min-product should be maximized <strong>before</strong> performing the modulo operation. Testcases are generated such that the maximum min-product <strong>without</strong> modulo will fit in a <strong>64-bit signed integer</strong>.</p>

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

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

<pre>
<strong>Input:</strong> nums = [1,<u>2,3,2</u>]
<strong>Output:</strong> 14
<strong>Explanation:</strong> The maximum min-product is achieved with the subarray [2,3,2] (minimum value is 2).
2 * (2+3+2) = 2 * 7 = 14.
</pre>

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

<pre>
<strong>Input:</strong> nums = [2,<u>3,3</u>,1,2]
<strong>Output:</strong> 18
<strong>Explanation:</strong> The maximum min-product is achieved with the subarray [3,3] (minimum value is 3).
3 * (3+3) = 3 * 6 = 18.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [3,1,<u>5,6,4</u>,2]
<strong>Output:</strong> 60
<strong>Explanation:</strong> The maximum min-product is achieved with the subarray [5,6,4] (minimum value is 4).
4 * (5+6+4) = 4 * 15 = 60.
</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;= 10<sup>7</sup></code></li>
</ul>

class Solution:
    def maxSumMinProduct(self, nums: List[int]) -> int:
        prefix = [0]
        n = len(nums)
        for i in nums:
            prefix.append(prefix[-1]+i)
        
        stack = []
        left, right = [0]*n, [0]*n
        for i in range(n):
            while stack and nums[stack[-1]] >= nums[i]:
                stack.pop()
            if stack:
                left[i] = stack[-1]+1
            else:
                left[i] = 0
            stack.append(i)
        
        stack = []
        for i in range(n-1, -1, -1):
            while stack and nums[stack[-1]] >= nums[i]:
                stack.pop()
            if stack:
                right[i] = stack[-1]-1
            else:
                right[i] = n-1
            stack.append(i)
        
        res = 0

        for i in range(n):
            l, r = left[i], right[i]
            res = max(res, (prefix[r+1]-prefix[l])*nums[i])

        return res%(10**9+7)
            

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