A sequence $S_n$ of whole numbers for natural $n$ is defined as

$S_1=1$

\[S_n = \begin{cases} S_{n-1} + n, & \text{if } S_{n-1} < n \\ S_{n-1} - n, & \text{if } S_{n-1} \geq n \end{cases}\]

For example, $S_2 = 3$ and $S_3 = 0$ .

Another sequence of increasing natural numbers $C_k$ for natural $k$ for which $S_{C_k} = 0$. Find $C_7$