Peculiar Primes

Corruption has reached even the academic world. There are rumors that certain mathematicians have been pressured to favor some primes over others: they have stopped using a few "forbidden" primes entirely, and now build numbers only from a restricted set of allowed primes.

Reproduce such a restricted world. Given a set of allowed primes, a positive integer is constructible if it can be written as a product of powers of those primes and of no other prime. Equivalently, every prime factor of the number must belong to the given set.

For example, if the allowed primes are $\{2, 3\}$, then $1, 2, 3, 4, 6, 8, 9, 12, \dots$ are constructible, while $5, 7, 10, 14, \dots$ are not.

Note that the number $1$ needs no prime factors at all, so it is always constructible.

The input consists of several scenarios.

Each scenario is given on three lines:

• The first line contains a single integer $N$ ($1 \le N \le 10$), the number of allowed primes.
• The second line contains $N$ primes $2 \le P_1 < P_2 < \dots < P_N < 10000$, separated by single spaces. All of them are guaranteed to be prime.
• The third line contains two integers $X$ and $Y$ ($1 \le X \le Y < 2^{31}$), separated by a single space.

The list of scenarios ends with a line containing a single zero, which must not be processed.

For each scenario, print on its own line every integer in the closed interval $[X, Y]$ that is constructible from the given primes.

Print the qualifying numbers in strictly increasing order, without duplicates, separated by a single comma (,) and with no spaces. If no number in $[X, Y]$ is constructible, print the word none instead.