Replicants' IDs P73645

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Los Angeles. Dr. Eldon Tyrell from Tyrell Corporation has decided to identify each replicant with a number. He has chosen a set of prime numbers, and has given instructions to the workers at the factory to use as ID for a new replicant the smallest available number that can be obtained by multiplying the numbers of the set.

Given the set of prime numbers, can you compute the ID of the $m$-th replicant produced?

Input

Input consists of several cases. Every case begins with an integer number $m \ge 1$, followed by a number $n$, followed by $n$ different prime numbers. Assume $1 \le n \le 10^4$.

Output

For every case, print the ID of the $m$-th replicant. This number will be smaller than $2^{31}$.