siunitx: aligning infty in an S column

What’s the best way to align infty at the decimal point in an S column when using siunitx? Consider, if you will, the following contrived MWE:

documentclass{article}
usepackage{siunitx}
begin{document}
begin{tabular}{S}
    0.1111111 
    1         
    10        
    $infty$  
    1000
end{tabular}
end{document}

which produces

But that’s not particularly nice, and I’d prefer the following:

Is there a way to achieve this? FWIW I’m not hung up on using siunitx, so feel free to suggest other packages that provide column types for the automatic alignment and formatting of numbers in tabulars.

As always, thanks!

documentclass{article}
usepackage{siunitx}
begin{document}
sisetup{
  input-digits = 0123456789infty
}
begin{tabular}{S}
    0.1111111 
    1         
    10        
    infty  
    1000
end{tabular}
end{document}