perl6, 54 bytes

Result

AC

Duration

1011ms

Code [DL]

lines».&{($=$_~|($ //=$_))~~{1 while s/k\s/kk/;.say}}

stdin

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   K                                              

stdout

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   kkkkkkkkkkkkkkkkkkkkt                          

stderr

WARNINGS for /volume/CODE:
Useless use of constant integer 1 in sink context (use Nil instead to suppress this warning) (line 1)

strace