<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 {
public:
    int findKthNumber(int n, int k) {
        int x = 1; 
        
        while (k > 1) {
            long count = 0;
            long cur = x, diff = 1;
            
            while (cur <= n) {
                count += min(n - cur + 1, diff);
                cur *= 10;
                diff *= 10;
            }
            
            if (k > count) {
                k -= count;
                x++;
            } else {
                k--;
                x *= 10;
            }
        }       
        return x;
    }
};

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