<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)
        {
            string ans = "";
            vector<int> numbers;
            int fact = 1;
            for (int i = 1; i <= n; i++)
            {
                fact = fact * i;
                numbers.push_back(i);
            }
            int blockSize = fact / n;
            k = k - 1;
            while (true)
            {
                ans += to_string(numbers[k / blockSize]);	
                numbers.erase(numbers.begin() + k / blockSize);
                if (numbers.size() == 0)
                {
                    break;
                }
                k = k % blockSize;
                blockSize = blockSize / numbers.size();
            }
            return ans;
        }
};
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