Google maps says it is possible to go from Shanghai to Guilin using trains T99A→K21 or T99B→K21, with a layover in Zhuzhou. It leaves on T99A or B at 18:24, day 1, and arrives at Zhuzhou at 3:28, day 2. Then, we wait at that station until 5:32, when we take the K21 the remainder of the voyage to Guilin. It then arrives at 12:28, day 2. Is this truly a possibility? How would I go about doing this (getting tickets, etc.)

Thanks!
Colin Sorensen