<p>Given an integer array <code>nums</code> and two integers <code>lower</code> and <code>upper</code>, return <em>the number of range sums that lie in</em> <code>[lower, upper]</code> <em>inclusive</em>.</p>

<p>Range sum <code>S(i, j)</code> is defined as the sum of the elements in <code>nums</code> between indices <code>i</code> and <code>j</code> inclusive, where <code>i &lt;= j</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [-2,5,-1], lower = -2, upper = 2
<strong>Output:</strong> 3
<strong>Explanation:</strong> The three ranges are: [0,0], [2,2], and [0,2] and their respective sums are: -2, -1, 2.
</pre>

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

<pre>
<strong>Input:</strong> nums = [0], lower = 0, upper = 0
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-2<sup>31</sup> &lt;= nums[i] &lt;= 2<sup>31</sup> - 1</code></li>
	<li><code>-10<sup>5</sup> &lt;= lower &lt;= upper &lt;= 10<sup>5</sup></code></li>
	<li>The answer is <strong>guaranteed</strong> to fit in a <strong>32-bit</strong> integer.</li>
</ul>

from sortedcontainers import SortedSet

class Solution:
    def countRangeSum(self, nums: List[int], lower: int, upper: int) -> int:
        n = len(nums)
        prefixes = [0]
        for num in nums:
            prefixes.append(prefixes[-1] + num)
        
        def get_less(bound, strict):
            ss = SortedSet()
            ss.add((0, 0))
            ans = 0
            for i in range(1, n+1):
                cur_prefix = prefixes[i]
                val_to_check = cur_prefix - bound
                delimiter = float('inf') if strict else -1
                idx = ss.bisect_left((val_to_check, delimiter))
                ans += i - idx
                ss.add((cur_prefix, i))
            return ans

        return get_less(upper, False) - get_less(lower, True)
43373