<p>The set <code>[1, 2, 3, ...,&nbsp;n]</code> contains a total of <code>n!</code> unique permutations.</p>

<p>By listing and labeling all of the permutations in order, we get the following sequence for <code>n = 3</code>:</p>

<ol>
	<li><code>&quot;123&quot;</code></li>
	<li><code>&quot;132&quot;</code></li>
	<li><code>&quot;213&quot;</code></li>
	<li><code>&quot;231&quot;</code></li>
	<li><code>&quot;312&quot;</code></li>
	<li><code>&quot;321&quot;</code></li>
</ol>

<p>Given <code>n</code> and <code>k</code>, return the <code>k<sup>th</sup></code> permutation sequence.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> n = 3, k = 3
<strong>Output:</strong> "213"
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> n = 4, k = 9
<strong>Output:</strong> "2314"
</pre><p><strong class="example">Example 3:</strong></p>
<pre><strong>Input:</strong> n = 3, k = 1
<strong>Output:</strong> "123"
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 9</code></li>
	<li><code>1 &lt;= k &lt;= n!</code></li>
</ul>

class Solution:
    def getPermutation(self, n: int, k: int) -> str:
        if n == 1:
            return "1"
        ls = []
        ans = []
        total = 1
        tmp = n
        while tmp > 1:
            total *= tmp
            tmp -= 1
        sub = total // n
        index = math.ceil(k / sub) - 1
        for i in range(1, n+1):
            ls.append(i)
        ls[index], ls[0] = ls[0], ls[index]
        def check(ls, index, ans):
            if index == len(ls):
                ans.append("".join(str(c) for c in ls))
                return
            for i in range(index, len(ls)):
                ls[i], ls[index] = ls[index], ls[i]
                check(ls, index+1, ans)
                ls[i], ls[index] = ls[index], ls[i]
        check(ls, 1, ans)
        ans.sort()
        return ans[k % sub - 1]
        
        
19600