Finding all of the matching substrings, not only the "most extended" one

The code

String s = "y z a a a b c c z";
Pattern p = Pattern.compile("(a )+(b )+(c *)c");
Matcher m = p.matcher(s);
while (m.find()) {
    System.out.println(m.group());
}

prints

a a a b c c

which is right.

But logically, the substrings

a a a b c
a a b c c
a a b c
a b c c
a b c

match the regex too.

So, how can I make the code find those substrings too, i.e. not only the most extended one, but also its children?