<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: List[int], n: int, left: int, right: int) -> int:
        '''heap = [(num,i) for i,num in enumerate(nums)]
        heapq.heapify(heap)
        i = 1
        res = 0
        while i<=right:
            a,c = heapq.heappop(heap)
            if i>=left:
                res=(res+a)%(10**9+7)
            if c<len(nums)-1:
                heapq.heappush(heap,(nums[c+1]+a,c+1))
            i+=1
        return res'''
        def countLessThan(cutoff):
            total = 0
            count = 0
            current = 0
            total_add = 0
            j = 0
            for i in range(len(nums)):
                while j<len(nums) and current+nums[j]<=cutoff:
                    current = current+nums[j]
                    total_add+=current
                    j+=1
                count+=(j-i)
                total=(total+total_add)%(10**9+7)
                total_add-=(j-i)*nums[i]
                if j>i:
                    current -= nums[i]
                else:
                    j = i+1
            return count,total
                
        def topK(k):
            low = min(nums)
            high = sum(nums)
            while low<=high:
                mid = (low+high)//2
                count,total = countLessThan(mid)
                if count>=k:
                    high = mid-1
                elif count<k:
                    low = mid+1
                #print(mid,count,k)
            return total-(count-k)*low
        return topK(right)-topK(left-1)



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