right justify each line?

Hi,

Assume each line in input.x has the same length.

$ cat input.x
99
    99
  9
  9 9
99999

I want to right justify each line, so output.x would be:

$ cat output.x
    99
    99
     9
   9 9
99999

What is simplest way to convert input.x to output.x?

I tried the following, but does not work, because of greedy evaluation, 
\2 always encompasses the entire line.

$ sed "s/^\(.*\)\( *\)$/\2\1/" input.x

Thanks,
Daniel