python3, 98 bytes

Result

AC

Duration

2653ms

Code [DL]

i=input().find('T')
d=-1
while 1:
 print(' '*d+'*'*(i-d+1)if~d else' '*i+'*')
 d=input().find('K')

stdin

           T                                      
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
 K                                                

stdout

           *
           *
           *
           *
           *
           *
           *
           *
           *
           *
           *
           *
           *
           *
           *
           *
           *
           *
           *
           *
           *
           *
           *
           *
 ***********

stderr

Traceback (most recent call last):
  File "/volume/CODE", line 5, in <module>
    d=input().find('K')
EOFError: EOF when reading a line

strace