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.


   superD=: 1 e. #~@[ E. 10 #.inv ([ * ^~)&x:

   assert    3 superD 753
   assert -. 2 superD 753


   2 3 4 5 6 ,. _ 10 {. I. 2 3 4 5 6 superD&>/i.1e6
2    19     31     69     81    105    106    107    119    127    131
3   261    462    471    481    558    753   1036   1046   1471   1645
4  1168   4972   7423   7752   8431  10267  11317  11487  11549  11680
5  4602   5517   7539  12955  14555  20137  20379  26629  32767  35689
6 27257 272570 302693 323576 364509 502785 513675 537771 676657 678146
