Shuffle array using random integer API

You are given an array `nums` of length `n` representing a deck of distinct cards. You **do not** have access to a built-in shuffle function, but you are given the following API: ```python rand_int(l, r) # returns a uniformly random integer in [l, r], inclusive ``` ### Task Implement a function `shuffle(nums)` that randomly permutes the array **in place** such that **every one of the `n!` permutations is equally likely**. ### Requirements - You may only use `rand_int(l, r)` as your source of randomness. - The algorithm should run in `O(n)` time and `O(1)` extra space. - You may assume `rand_int` itself is perfectly uniform and independent between calls. Describe your algorithm, argue why the resulting permutation is uniform, and give the time and space complexity.