There is a circle with a circumference of 1 meter and a point marked on it. Two cockroaches start running in the same direction from the marked point at different speeds. 

- Whenever the faster cockroach catches up with the slower one, the slower one instantly turns around and starts running in the opposite direction with the same speed.
- Whenever they meet face-to-face, the faster one instantly turns around and starts running in the opposite direction with the same speed.

Determine how far from the marked point their 100th meeting could occur.

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