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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 ≥ 1,
followed by a number n, followed by n different prime numbers.
Assume 1 ≤ n ≤ 10^{4}.

Output

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

Public test cases

**Input**

1 1 2 2 1 2 3 1 2 5 4 2 5 7 3 11 4 2 5 7 3 19 4 2 5 7 3

**Output**

2 4 8 6 14 27

Information

- Author
- Albert Graells
- Language
- English
- Official solutions
- C++
- User solutions
- C++