<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 
{
public:
    string getPermutation(int n, int k) 
    {
       vector<int>tp;
       int fact = 1;
       for(int i=1;i<n;i++)
       {
        fact = fact*i;
        tp.push_back(i);
       } 
       tp.push_back(n);
       string ans = "";
       int f = k-1;
       while(true)
       {
        int num = f/fact;
        string t = to_string(tp[num]);
        ans = ans+t;
        tp.erase(tp.begin()+num);
        if(tp.size() == 0)
        {
            break;
        }
        f = f%fact;
        fact = fact/tp.size();
       }
       return ans;
    }
};
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