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.