Greatest Common Multiple

By Kay Akashi

Time: 1000 ms

Memory: 256000 kB

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Problem Statement

Given an integer $X$ and $n$ integers $a_{1}$ , …, $a_{n}$ , find the greatest common multiple of all the elements in $a$ which is smaller than or equal to $X$ . If there is no such answer, output $-1$ instead.

Note that, common multiple of $a$ is the number which can be divided by any element in $a$ . Your task is to find the greatest one amongst several possible (or zero) common multiples.

Constraints

$1 \leq n \leq 50$ , $1 \leq a_i \leq 100$ $(1 \leq i \leq n)$ , $1 \leq X \leq 10^{9}$ .

Input

The first line of input contains two integers, $n$ and $X$ . The second line contains $n$ integers separated by single spaces in between.

Output

Output the answer.

Examples

Input

3 100
2 3 5

Output

Explanation

In this example, common multiples of $a$ which are smaller than or equal to $X = 100$ are $(30, 60, 90)$ . The greatest common multiple of $a$ here is therefore $90$ .

Input

4 10
2 5 8 9

Output

-1

Explanation

In this example, the least common multiple is $360$ . This indicates that there's no common multiple that is smaller than or equal to $10$ . For this reason, output $-1$ .

Greatest Common Multiple

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