Finding the k-th Hamming Number
A positive integer is called a **Hamming number** (also known as a 3-smooth or ugly number) if its only prime factors are 2, 3, and 5. The sequence starts: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, ...
Given a positive integer $k$, return the $k$-th Hamming number in ascending order.
**Constraints:**
-
\leq k \leq 1{,}690$
- The
{,}690$-th Hamming number fits in a 32-bit integer
**Examples:**
- Input: $k = 1$ -- Output:
$ (by convention, 1 is the first Hamming number)
- Input: $k = 7$ -- Output: $8$ (the sequence is 1, 2, 3, 4, 5, 6, 8, so the 7th is 8)
- Input: $k = 12$ -- Output:
6$ (the sequence is 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16)
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