Migrated from Lutece 2848 Fatdog's True Love

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Description

There are $n$ numbers $a_1, a_2, ..., a_n$, which can make Fatdog happy. If a number $X$ is uniquely divisible by exactly one of these numbers, Fatdog will immediately love the number $X$.

Fatdog loves plenty of numbers, but he wants to find his true love number $Y$. However, he doesn't know the exact value of $Y$. He only knows that the true love number $Y$ is the $k$-th smallest number among all numbers he loves.

Could you help him find the exact value of $Y$?

Input

The first line contains two integers $n,k\ (1\leq n\leq 15, 1\leq k \leq 2^{31}-1)$.

The second line contains $n$ integers $a_1, a_2,\ldots , a_n\ (1\leq a_i \leq 2^{31}-1)$. It's guaranteed that there exists two integers $i,j\ (1\le i,j\le n,i\neq j)$ which satisfy $a_i\neq a_j$.

Output

One integer, which stands for the exact value of the true love number $Y$.

It's guaranteed that $Y \leq 10^{15}$.

Samples

5 100
196 226 219 186 45

2430

Resources

The 18th UESTC Programming Contest Preliminary