#Perl 5, (33 Bytes+2) = 35

A regex-less solution.

    map{print$p=$_.$"if$_>=$p||!$p}@F

### Test

*Note that the @F array is populated because of the -a switch.*

    $ echo -7 -8 -5 0 -1 4 4 3 5|perl -na -e 'map{print$p=$_.$"if$_>=$p||!$p}@F'
    -7 -5 0 4 4 5