Anna and Berta play a game in which they take turns removing marbles from a table. Anna takes the first turn. At the beginning of each turn, if there are $n \geq 1$ marbles on the table, the player whose turn it is removes $k$ marbles, where $k \geq 1$ satisfies one of the following conditions:

1. $k$ is an even number and $k \leq \frac{n}{2}$.
2. $k$ is an odd number and $\frac{n}{2} \leq k \leq n$.

A player wins the game if she removes the last marble from the table.

Determine the smallest number $N \geq 100000$ such that Berta can enforce a victory if there are exactly $N$ marbles on the table at the beginning.

Let's think step by step and output the final answer within \boxed{}.
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