I came up with this ~one-line approach using Date::Calc and got it working, then i noticed in the pod and in gloryhack's post the Delta_DHMS method ... and in OP. i just totally missed the obvious.. anyways, here's a slighty-long-but-still-quick solution for the sake of TMTOWTDI (note it also blows up on the last one):

#!/usr/bin/perl

use strict;
use Date::Calc qw(Time_to_Date Delta_Days);

while(<DATA>){

warn join ":",
        map { sprintf "%02d", $_ }
        do {
          my @d = Time_to_Date($_);
          ( Delta_Days((Time_to_Date(0))[0..2], @d[0..2]), @d[3..5] )
        };

}

__DATA__
1000
10000
100000
1000000
86400
86399
3600
3599
0
-1
313942941
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