Awk: printing undetermined number of columns

I have a file that contains a number of fields separated by tab. I am trying to print all columns except the first one but want to print them all in only one column with AWK. The format of the file is

col 1   col 2   ... col n

There are at least 2 columns in one row.

Sample

2012029754      901749095
2012028240      901744459       258789
2012024782      901735922
2012026032      901738573       257784
2012027260      901742004
2003062290      901738925       257813  257822
2012026806      901741040
2012024252      901733947       257493
2012024365      901733700
2012030848      901751693       260720  260956  264843  264844

So I want to tell awk to print column 2 to column n for n greater than 2 without printing blank lines when there is no info in column n of that row, all in one column like the following.

This is the first time I am using awk, so bear with me. I wrote this from command line which works:

awk '{i=2; 
while ($i ~ /[0-9]+/)
{ 
    printf "%s\n", $i
    i++
}
}' bth.data

It is more of a seeking approval than asking a question whether it is the right way of doing something like this in AWK or is there a better/shorter way of doing it.

Note that the actual input file could be millions of lines.

Thanks

awk

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Awk: printing undetermined number of columns

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