<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:
    def rangeSum(self, nums, n, left, right):
        mod = 10**9 + 7

        def count_and_sum(nums, n, target):
            count = 0
            current_sum = 0
            total_sum = 0
            window_sum = 0
            i = 0
            for j in range(n):
                current_sum += nums[j]
                window_sum += nums[j] * (j - i + 1)
                while current_sum > target:
                    window_sum -= current_sum
                    current_sum -= nums[i]
                    i += 1
                count += j - i + 1
                total_sum += window_sum
            return count, total_sum

        def sum_of_first_k(nums, n, k):
            min_sum = min(nums)
            max_sum = sum(nums)
            left = min_sum
            right = max_sum

            while left <= right:
                mid = left + (right - left) // 2
                if count_and_sum(nums, n, mid)[0] >= k:
                    right = mid - 1
                else:
                    left = mid + 1
            count, total_sum = count_and_sum(nums, n, left)
            # There can be more subarrays with the same sum of left.
            return total_sum - left * (count - k)

        result = (
            sum_of_first_k(nums, n, right) - sum_of_first_k(nums, n, left - 1)
        ) % mod
        # Ensure non-negative result
        return (result + mod) % mod
16272