<p>Given two integers <code>n</code> and <code>k</code>, return <em>the</em> <code>k<sup>th</sup></code> <em>lexicographically smallest integer in the range</em> <code>[1, n]</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 13, k = 2
<strong>Output:</strong> 10
<strong>Explanation:</strong> The lexicographical order is [1, 10, 11, 12, 13, 2, 3, 4, 5, 6, 7, 8, 9], so the second smallest number is 10.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 1, k = 1
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= k &lt;= n &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution:
    def findKthNumber(self, n: int, k: int) -> int:
        cur = 1
        k-=1
        while k>0:
            step, first, last = 0, cur, cur+1
            while first <=n:
                step +=min(n+1, last) - first
                first *=10
                last *=10
            if step <=k:
                cur+=1
                k-=step
            else:
                cur*=10
                k-=1
        
        return cur
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