SQL & PL/SQL

Hello, everyone.

I have a data like this:

with t as (select 1 id, null parent_id, 2 num from dual union all
           select 2, 1, 2 from dual union all
           select 3, 2, 3 from dual union all
           select 4, 1, 1 from dual union all
           select 3, 4, 2 from dual union all
           select 6, 3, 2 from dual union all
           select 7, 3, 1 from dual)

as you can see the node with id = 3 is met twice.
So the tree looks like (with "num" value in square brackets)

        1[2]
        /  \
      2[2]  4[1]
        \  /
         3[3;2]
        /   \
      6[2]  7[1]

Well, the idea is to find a query that will return the product
of "num" values of all the ancestors, including "num" value of the current node.
E.g. on the provided data the result would be:

        ID  PARENT_ID        NUM    PRODUCT
---------- ---------- ---------- ----------
         1                     2          2
         2          1          2          4
         3          2          3         12
         3          4          2          4
         4          1          1          2
         6          3          2         24
         6          3          2          8
         7          3          1         12
         7          3          1          4

Mention that nodes with id in (3,6,7) are returned twice because they have two different pathes to the root level.

Thanks beforehand.