<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 steps(self, cur, n):
        first, last, step = cur, cur, 0
        while first <= n:
            step += min(last, n) - first + 1
            first *= 10
            last = last * 10 + 9
        return step

    def findKthNumber(self, n: int, k: int) -> int:
        cur = 1
        k -= 1
        while k:
            step = self.steps(cur, n)
            if step <= k:
                k -= step
                cur += 1
            else:
                k -= 1
                cur *= 10
        return cur
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