awk, 73 bytes

Result

AC

Duration

738ms

Code [DL]

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

stdin

                    T                             
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
    K                                             

stdout

                    T
                    T
                    T
                    T
                    T
                    T
                    T
                    T
                    T
                    T
                    T
                    T
                    T
                    T
    KKKKKKKKKKKKKKKKK

stderr

strace