There are T tokens arranged in a circle for some positive integer T. Moving clockwise around the circle, the tokens are labelled, in order, with the integers from 1 to T. Starting from the token labelled 1, Évariste:
- Removes the token at the current position.
- Moves clockwise to the next remaining token.
- Moves clockwise again to the next remaining token.
- Repeats steps (1) to (3) until only one token remains.
When T=337, the number on the last remaining token is L. There are other integers T for which the number on the last remaining token is also L. What are the rightmost two digits of the smallest possible value of T ?