How to get tickets for K24 to Beijing.

Hi there.

I found this forum after been searching the "nets" on how to buy a train ticket from Ulan Bator to Beijing and hope that you'll have the information I need.  I will spend a couple of weeks in Mongolia coming summer and after that I'll go to China. I been trying to find out how to purchase a ticket for the K24, which I think leaves Ulan Bator for Beijing on Thursday mornings. Is it advisable to buy a ticket a few days before at the train station? I'll Probably leave mongolia in mid-end of july.
Can't see that the Mongolian Railways got a website for online sales of tickets.

I prefer to stay clear of ticket monglers on the net...

Any help is very welcome,

/Andreas

Thanks in advance,