elixir, 461 bytes

Result

AC

Duration

1929ms

Code [DL]

defmodule A do
def b(t,h) do
c(t,String.length(Enum.at(String.split(IO.read(:line),"K"),0)),h)end
def c(t,51,h)do
b(t,h+1)end
def c(t,k,h)do
IO.puts String.duplicate(" ",t)<>"T"<>String.duplicate(" ",49-t)
Enum.each(1..h,fn(_)->IO.puts String.duplicate(" ",t)<>"*"<>String.duplicate(" ",49-t)end)
IO.puts String.duplicate(" ",k)<>"K"<>String.duplicate("*",t-k)<>String.duplicate(" ",49-t)end
end
A.b(String.length(Enum.at(String.split(IO.read(:line),"T"),0)),0)

stdin

                                         T        
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                              K                   

stdout

                                         T        
                                         *        
                                         *        
                                         *        
                                         *        
                                         *        
                                         *        
                                         *        
                                         *        
                                         *        
                                         *        
                                         *        
                                         *        
                                         *        
                                         *        
                                         *        
                                         *        
                                         *        
                                         *        
                              K***********        

stderr

strace