Problem - Count of Range Sum

Given an integer array nums and two integers lower and upper, return the number of range sums that lie in $[\text{lower}, \text{upper}]$ inclusive.

Range sum $S(i, j)$ is the sum of elements from index $i$ to $j$ where $i \leq j$. Example: nums $= [-2, 5, -1]$, lower $= -2$, upper $= 2$. Range sums: $-2, 3, 2, 5, 4, -1$.

In range: $-2, 2, -1$. Answer: $3$. This you can solve with segment tree + coordinate compression on prefix sums. Constraints: up to $10^5$ elements, values up to $10^9$.