Given prime numbers $p_1, p_2, \dots, p_k$. Consider the set $A$ of positive integers whose prime factorization contains only these specified prime numbers. For example, if the given numbers are $2, 3, 7$, this set will be:
$A = \{1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 27, 28, 32, 36, 42, 48, 49, 54, 56, 63, 64, 72, 81, 84, 96, 98, \dots\}$.
Johnny wrote down on a piece of paper all such numbers not exceeding $N$. What is the largest number he wrote?
Input
The first line contains two integers $k, N$ ($k \geq 1, 1 \leq N \leq 10^{18}$), representing the size of the set of prime numbers and the limit for the problem, respectively. The second line of input contains a sequence of $k$ pairwise distinct prime numbers $p_1, \dots, p_k$ ($2 \leq p_i \leq 100$) — the numbers generating the set $A$.
Output
In the only line of output, print a single natural number — the largest number that is in the set $A$ and does not exceed $N$.
Examples
Input 1
3 30 2 3 7
Output 1
28