A super-d number is a positive, decimal (base ten) integer   n   such that   d × nd   has at least   d   consecutive digits   d   where

   2 ≤ d ≤ 9

For instance, 753 is a super-3 number because 3 × 7533 = 1280873331.


Super-d   numbers are also shown on   MathWorld™   as   super-d    or   super-d.



Task

 Write a function/procedure/routine to find super-d numbers.
 For   d=2   through   d=6,   use the routine to show the first   10   super-d numbers.


Extra credit

 Show the first   10   super-7, super-8, and/or super-9 numbers   (optional).


See also

   Wolfram MathWorld - Super-d Number.
   OEIS: A014569 - Super-3 Numbers.


sub super (\d) {
    my \run = d x d;
    ^∞ .hyper.grep: -> \n { (d * n ** d).Str.contains: run }
}
 
(2..9).race(:1batch).map: {
    my $now = now;
    put "\nFirst 10 super-$_ numbers:\n{.&super[^10]}\n{(now - $now).round(.1)} sec."
}