Random Pick with Weight

Question

## Problem

Given an array `w` of positive weights, implement `pickIndex()` that returns index `i` with probability proportional to `w[i]`.

## Example
```
w = [1,3] -> index 0 ~25%, index 1 ~75%
```

## Constraints
- 1 ≤ w.length ≤ 10^4

## Approach
Prefix sums + binary search on a random target in [1, total]. Classic Meta question.