60\. Permutation Sequence

Hard

The set `[1, 2, 3, ..., n]` contains a total of `n!` unique permutations.

By listing and labeling all of the permutations in order, we get the following sequence for `n = 3`:

1.  `"123"`
2.  `"132"`
3.  `"213"`
4.  `"231"`
5.  `"312"`
6.  `"321"`

Given `n` and `k`, return the `kth` permutation sequence.

**Example 1:**

**Input:** n = 3, k = 3

**Output:** "213" 

**Example 2:**

**Input:** n = 4, k = 9

**Output:** "2314" 

**Example 3:**

**Input:** n = 3, k = 1

**Output:** "123" 

**Constraints:**

*   `1 <= n <= 9`
*   `1 <= k <= n!`