<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 helper(string str,int k,string ans){
        int n=str.length();
        if(n==0){
            return ans;
        }
        int fact=1;
        for(int i=2;i<=n-1;i++){
            fact*=i;
        }
        int idx=k/fact;
        if(k%fact==0)idx--;
        char ch=str[idx];
        string left=str.substr(0,idx);
        string right =str.substr(idx+1);
        int q=1;
        if(k%fact==0)q=fact;
        else q=k%fact;
        return helper(left+right,q,ans+ch);
    }
    string getPermutation(int n, int k) {
        string str="";
        for(int i=1;i<=n;i++){
            str+=to_string(i);
        }
        string ans="";
        return helper(str,k,"");
    }
};
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