php, 100 bytes

Result

AC

Duration

818ms

Code [DL]

<?php
$b=0;for($d=1;$c=fread(STDIN,1);$d=($d+1)%51){$d*=$c!='T';$b=$c=='K'|$b*$d;echo!$d|$b?'A':$c;}

stdin

                                  T               
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
 K                                                

stdout

                                  A               
                                  A               
                                  A               
                                  A               
                                  A               
                                  A               
                                  A               
                                  A               
                                  A               
                                  A               
                                  A               
                                  A               
                                  A               
                                  A               
 AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA               

stderr

strace