Bus Station

Ryan is the president of a planet. There is a large bus station on this planet and $M$ buses stop at this station every day. For each valid $i$, the $i$-th bus arrives at the station $t_i$ seconds after midnight (on Ryan's planet, each day lasts $10^{100}$ hours, not $24$ hours), waits at the station for some non-negative (not necessarily integer) amount of time and then leaves. Ryan knows that