<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>

from typing import List, Tuple

class Solution:
    # MODULUS = 10**9 + 7

    # def count_and_sum_subarrays(self, array, threshold):
    #     count, total_sum, running_sum, current_window_sum = 0, 0, 0, 0
    #     start = 0

    #     for end, num in enumerate(array):
    #         running_sum += num * (end - start + 1)
    #         current_window_sum += num
    #         while running_sum > threshold:
    #             running_sum -= current_window_sum
    #             current_window_sum -= array[start]
    #             start += 1
    #         count += end - start + 1
    #         total_sum += running_sum

    #     return count, total_sum

    # def calculate_sum_of_first_k_subarrays(self, array, k):
    #     low, high = min(array), sum(array)
    #     while low < high:
    #         mid = low + (high - low) // 2
    #         if self.count_and_sum_subarrays(array, mid)[0] < k:
    #             low = mid + 1
    #         else:
    #             high = mid
    #     count, total_sum = self.count_and_sum_subarrays(array, low)
    #     return total_sum - (count - k) * low

    # def rangeSum(self, nums: List[int], n: int, left: int, right: int) -> int:
    #     res = (self.calculate_sum_of_first_k_subarrays(nums, right) -
    #             self.calculate_sum_of_first_k_subarrays(nums, left - 1))
    #     return res % self.MODULUS

        
        # Find the maximum possible sum

    def rangeSum(self, nums: List[int], n: int, left: int, right: int) -> int:
        MOD = 10**9 + 7
        maxSum = sum(nums)
        
        # Count the frequency of each sum
        count = [0] * (maxSum + 1)
        for i in range(n):
            current_sum = 0
            for j in range(i, n):
                current_sum += nums[j]
                count[current_sum] += 1
        
        # Calculate prefix sum of frequencies
        for i in range(1, maxSum + 1):
            count[i] += count[i - 1]
        
        result = 0
        k = 1
        for current_sum in range(1, maxSum + 1):
            while k <= count[current_sum]:
                if left <= k <= right:
                    result = (result + current_sum) % MOD
                k += 1
        
        return result
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