<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:
        n = len(nums)
        left_bound, right_bound = [0] * n, [0] * n
        st = []
        for i in range(0, n):
            while st and nums[st[-1]] >= nums[i]: st.pop()
            if len(st) > 0:
                left_bound[i] = st[-1] + 1
            else:
                left_bound[i] = 0
            st.append(i)

        st = []
        for i in range(n - 1, -1, -1):
            while st and nums[st[-1]] >= nums[i]: st.pop()
            if len(st) > 0:
                right_bound[i] = st[-1] - 1
            else:
                right_bound[i] = n - 1
            st.append(i)

        preSum = [0] * (n + 1)
        for i in range(n):
            preSum[i + 1] = preSum[i] + nums[i]

        def getSum(left, right):  # left, right inclusive
            return preSum[right + 1] - preSum[left]

        maxProduct = 0
        for i in range(n):
            maxProduct = max(maxProduct, nums[i] * getSum(left_bound[i], right_bound[i]))
        return maxProduct % 1000_000_007
36500