<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 {
public:
    int maximumScore(vector<int>& nums, int k) {
        int n = nums.size(),res=0;
        vector<int> range(n);

        stack<int> st;

        for(int i=0;i<n;i++){
            while(!st.empty() && nums[i]<nums[st.top()]){
                int t = st.top();
                st.pop();
                range[t] = i-1;
            }
            st.push(i);
        }
        while(!st.empty() ){
            int t = st.top();
            st.pop();
            range[t] = n-1;
        }

        // for(int i=n-1;i>=0;i--){
        //     cout<<range[i]<<" ";
        // }cout<<endl;

        for(int i=n-1;i>=0;i--){
            while(!st.empty() && nums[i]<nums[st.top()]){
                int t = st.top();
                st.pop();
                // cout<<t<<" ";
                if(k>i && k<=range[t])
                {
                    int prod = (range[t] - i) * nums[t];
                    res = max(res,prod);
                }
            }
            st.push(i);
        }
        while(!st.empty() ){
            int t = st.top();
            st.pop();
            if(k>=0 && k<=range[t])
            {
                int prod = (range[t] +1) * nums[t];
                res = max(res,prod);
            }
            
        }
        return res;
    }
};
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