K-th Smallest in Lexicographical Order
<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>
Trie
class Solution {
    private int n;

    public int findKthNumber(int n, int k) {
        this.n = n;
        long curr = 1;
        --k;
        while (k > 0) {
            int cnt = count(curr);
            if (k >= cnt) {
                k -= cnt;
                ++curr;
            } else {
                --k;
                curr *= 10;
            }
        }
        return (int) curr;
    }

    public int count(long curr) {
        long next = curr + 1;
        long cnt = 0;
        while (curr <= n) {
            cnt += Math.min(n - curr + 1, next - curr);
            next *= 10;
            curr *= 10;
        }
        return (int) cnt;
    }
}