<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:
    static constexpr int m = 10e8 + 7;

    uint32_t rangeSum(const vector<int> &nums, size_t size, uint32_t left, uint32_t right) {

        left--;
        right--;

        uint32_t leadSum[size + 1];
        leadSum[0] = 0;

        for (size_t i = 0; i < size; i++) {

            leadSum[i + 1] = leadSum[i] + nums[i];
        }

        uint16_t stackCounters[size];
        uint16_t stackSums[size];

        for (uint16_t i = 0; i < size; i++) {

            stackCounters[i] = i + 1;
            stackSums[i] = leadSum[i + 1] - leadSum[i];
        }

        auto compFunc = [&stackSums](uint16_t iIndexA, uint16_t iIndexB) {
            return stackSums[iIndexA] > stackSums[iIndexB];
        };

        vector<uint16_t> iIndexHeap(size);

        for (uint16_t i = 0; i < size; i++) {iIndexHeap[i] = i;}

        make_heap(iIndexHeap.begin(), iIndexHeap.end(), compFunc);

        uint32_t result = 0;

        for (uint32_t index = 0; index <= right; index++) {

            pop_heap(iIndexHeap.begin(), iIndexHeap.end(), compFunc);

            uint16_t iIndex = iIndexHeap.back();
            uint16_t jIndex = stackCounters[iIndex];

            if (index >= left) {
                
                result += leadSum[jIndex] - leadSum[iIndex];

                if (result >= m) {result -= m;}
            }

            if (jIndex < size) {

                stackCounters[iIndex]++;

                stackSums[iIndex] += nums[jIndex];

                push_heap(iIndexHeap.begin(), iIndexHeap.end(), compFunc);
            }
            else {

                iIndexHeap.pop_back();
            }
        }

        return result;
    }
};
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