awk, 67 bytes

Result

AC

Duration

818ms

Code [DL]

{sub(/ +$/,z);if($0){for(;length($0)<length(t);)$0=$0"K";t=$0}}$0=t

stdin

                               T                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
      K                                           

stdout

                               T
                               T
                               T
                               T
                               T
                               T
                               T
                               T
                               T
                               T
                               T
                               T
                               T
      KKKKKKKKKKKKKKKKKKKKKKKKKK

stderr

strace