php, 101 bytes

Result

AC

Duration

753ms

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                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
            A                                     
        AAAAA                                     

stderr

strace