> For the complete documentation index, see [llms.txt](https://soumyajit4419.gitbook.io/ds-algo/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://soumyajit4419.gitbook.io/ds-algo/recursion-and-backtracking/15.-permutation-sequence.md).

# 15. Permutation Sequence

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"
```