<p>You are given the array <code>nums</code> consisting of <code>n</code> positive integers. You computed the sum of all non-empty continuous subarrays from the array and then sorted them in non-decreasing order, creating a new array of <code>n * (n + 1) / 2</code> numbers.</p>

<p><em>Return the sum of the numbers from index </em><code>left</code><em> to index </em><code>right</code> (<strong>indexed from 1</strong>)<em>, inclusive, in the new array. </em>Since the answer can be a huge number return it modulo <code>10<sup>9</sup> + 7</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [1,2,3,4], n = 4, left = 1, right = 5
<strong>Output:</strong> 13 
<strong>Explanation:</strong> All subarray sums are 1, 3, 6, 10, 2, 5, 9, 3, 7, 4. After sorting them in non-decreasing order we have the new array [1, 2, 3, 3, 4, 5, 6, 7, 9, 10]. The sum of the numbers from index le = 1 to ri = 5 is 1 + 2 + 3 + 3 + 4 = 13. 
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,2,3,4], n = 4, left = 3, right = 4
<strong>Output:</strong> 6
<strong>Explanation:</strong> The given array is the same as example 1. We have the new array [1, 2, 3, 3, 4, 5, 6, 7, 9, 10]. The sum of the numbers from index le = 3 to ri = 4 is 3 + 3 = 6.
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,2,3,4], n = 4, left = 1, right = 10
<strong>Output:</strong> 50
</pre>

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

<ul>
	<li><code>n == nums.length</code></li>
	<li><code>1 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 100</code></li>
	<li><code>1 &lt;= left &lt;= right &lt;= n * (n + 1) / 2</code></li>
</ul>

class Solution {
public:
    int rangeSum(vector<int>& nums, int n, int left, int right) {
        
        int size = nums.size ();
        int mod = 1e9 + 7;

        vector <vector <int> > dp (size, vector <int> (size));

        priority_queue <int> pq;

        for (int i = 0; i < size; i++)
        {
            dp[i][i] = nums[i];
                            if (pq.size () < right)
                {
                    pq.push (dp[i][i]);
                }

                else
                {
                    if (pq.top() > dp[i][i])
                    {
                        pq.pop();
                        pq.push (dp[i][i]);
                    }
                }
        }

        for (int i = 1; i < size; i++)
        {
            dp[i - 1][i] = (nums[i - 1] + nums[i]) % mod;
                            if (pq.size () < right)
                {
                    pq.push (dp[i - 1][i]);
                }

                else
                {
                    if (pq.top() > dp[i - 1][i])
                    {
                        pq.pop();
                        pq.push (dp[i - 1][i]);
                    }
                }
        }

        for (int gap = 2; gap < size; gap++)
        {
            for (int i = 0; i < size - gap; i++)
            {
                dp[i][i + gap] = (nums[i]%mod + nums[i + gap]%mod + dp[i + 1][i + gap - 1]%mod)%mod;

                if (pq.size () < right)
                {
                    pq.push (dp[i][i + gap]);
                }

                else
                {
                    if (pq.top() > dp[i][i + gap])
                    {
                        pq.pop();
                        pq.push (dp[i][i+ gap]);
                    }
                }
            }
        }

        // for (int i = 0; i < size; i++)
        // {
        //     for (int j = 0; j < size; j++)
        //     {
        //         cout << dp[i][j] <<" ";
        //     }
        //     cout<<endl;
        // }

        int sum = 0;
        int cnt = right - left + 1;

        // cout << pq.size();

        while (cnt > 0 && pq.size())
        {
            sum += pq.top();
            sum %= mod;
            pq.pop();
            --cnt;
        }

        return sum;
    }
};
35559