Support Dynamic Range Sums

Implement a data structure over an integer array `nums`. Part 1: If the array never changes, support `sumRange(left, right)` that returns the sum of elements from index `left` to `right`, inclusive. Part 2 (follow-up): Now the array is mutable. Support both: - `update(index, value)`: set `nums[index] = value` - `sumRange(left, right)`: return the inclusive range sum Design the mutable version so that both operations are efficient when the array length and number of operations can each be up to 100,000. Be prepared to discuss multiple approaches and their tradeoffs.