Recursive Types — Deep Flatten & JSON Keys

TypeScript allows recursive type aliases to describe infinitely nested data:

// A deeply nested array of T at any depth:
type NestedArray<T> = T | NestedArray<T>[];

// A JSON-safe value (the canonical recursive type):
type JsonValue =
  | string | number | boolean | null
  | JsonValue[]
  | { [key: string]: JsonValue };

These types mirror recursive *algorithms* — and both must be implemented together.

Your Task

Implement two functions:

deepFlatten(arr)

Recursively flatten a nested array to a 1D array:

deepFlatten([1, [2, [3, [4]]]]) // → [1, 2, 3, 4]
deepFlatten([[1, 2], [3, [4, 5]]]) // → [1, 2, 3, 4, 5]

deepKeys(obj)

Return all leaf key paths in dot-notation from a nested object:

deepKeys({ a: { b: 1, c: { d: 2 } } }) // → ['a.b', 'a.c.d']
deepKeys({ x: 1, y: { z: 2 } })        // → ['x', 'y.z']