Appending standard C Time on each line out output

I have a command :

nawk 'BEGIN{print srand()}'

which gives the amount of seconds between January 1st 1970 00:00:00 (Unix Epoch) and the present time, to the closest second and I would want to append this time stamp every minute in a file which contains the data below which also has one row added every minute.

Current file output
1955 891
2270 1930
2173 1937

Required output:
1322123179 1955 891
1322123663 2270 1930

where the first column is the Unix Epoch time appended for the particular time the line of data was generated.

The file that gets appended, let's call it logfile, the new file: newlogfile

tail -f logfile | nawk '{ print srand(), $0}'  > newlogfile

You don't want the BEGIN{} function.