node, 149 bytes

Result

AC

Duration

1065ms

Code [DL]

s=""+require("fs").readFileSync(0)
console.log(s.replace(RegExp(`
(.{${s.search(/T/)}}).`,"g"),`
$1#`).replace(/K *#/,m=>"K"+"#".repeat(m.length-1)))

stdin

                           T                      
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
                                                  
    K                                             

stdout

                           T                      
                           #                      
                           #                      
                           #                      
                           #                      
                           #                      
                           #                      
                           #                      
                           #                      
                           #                      
                           #                      
                           #                      
                           #                      
                           #                      
                           #                      
                           #                      
                           #                      
                           #                      
                           #                      
                           #                      
                           #                      
                           #                      
    K#######################                      

stderr

strace