# ---
# title: 60. Permutation Sequence
# id: problem60
# author: Tian Jun
# date: 2020-10-31
# difficulty: Hard
# categories: Math, Backtracking
# link: <https://leetcode.com/problems/permutation-sequence/description/>
# hidden: true
# ---
# 
# 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!`
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
