SOLVED (Scroll down for solution)

I have some zip files.

my @filelist = ('zip1.zip','zip2.zip','zip3.zip');
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Let's say that the contents of the zip files look like this:

zip1.zip
-->file1.txt
-->file2.txt

zip2.zip
-->directory1 (dir)
---->file1.txt
---->file3.txt
-->file4.txt

zip3.zp
-->file5.txt
-->file6.txt
-->file7.txt
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I wish to dynamically create a zip file called bigzip.zip that will include the contents of the zip files as a sub-directory in bigzip.zip. In other words, I want this:

bigzip.zip
-->zip1 (dir)
---->file1.txt
---->file2.txt
-->zip2 (dir)
---->directory1 (dir)
------>file1.txt
------>file3.txt
---->file4.txt
-->zip3 (dir)
---->file5.txt
---->file6.txt
---->file7.txt
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Here's the code I have so far:

my $zip = Archive::Zip->new();
foreach (@filelist) {
    my $file = Archive::Zip->new($_});

    foreach ($file->members()){
        $zip->addMember( $_ );
    }
}
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This successfully results in:

bigzip.zip
-->file1.txt
-->file2.txt
-->directory1 (dir)
---->file1.txt
---->file3.txt
-->file4.txt
-->file5.txt
-->file6.txt
-->file7.txt
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I can't figure out from the documentation if what I'm talking about is at all possible, and how to achieve it. I could, of course, extract the individual zips into the directories I want, then re-zip them, but that seems inelegant.

Any thoughts?

Solved: The following code works. I didn't realize that "directories" in zip files were simply a matter of specifying paths...

my $x=1;
my $zip = Archive::Zip->new();
foreach (@filelist) {
    my $file = Archive::Zip->new($_);
    my $directoryname = 'zip'.$x;

    foreach ($file->members()){
        my $m = $zip->addMember( $_ );
        $m->fileName($directoryname.'/'.$m->fileName());
    }

    $x++;
}
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