We've carved those memories into ourselves... No matter how hard they were, they're the lives we carried out!

— Angel Beats!

In the afterlife school, Kanade studies a peculiar number game.

She gives you two integers $$$n$$$ and $$$k$$$, as well as an array $$$a$$$ consisting of $$$n$$$ integers, where $$$1 \le a_i \le k$$$ holds.

For an integer set $$$B = \{b_1, b_2, \ldots, b_m\}$$$ where $$$1\le b_i\le k$$$, we call it complete if and only if both of the following hold:

For each $$$1\le i\le n$$$, at least one divisor of $$$a_i$$$ is contained in $$$B$$$;
For each $$$1\le j\le m$$$, all positive multiples of $$$b_j$$$ which are less than or equal to $$$k$$$ appear in the array $$$a$$$ at least once.

You have to find a complete set $$$B$$$ with minimum possible size, or determine that no such set exists.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1\le n\le 2\cdot 10^5$$$, $$$1\le k\le 10^9$$$) — the length of $$$a$$$ and the upper bound of elements of $$$a$$$.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1\le a_i\le k$$$) — the elements of $$$a$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\cdot 10^5$$$.

Output

For each test case:

If no complete set $$$B$$$ exists, print a single integer $$$-1$$$ in the only line of output.
Otherwise:
- First print a single integer $$$m$$$ ($$$1\le m\le n$$$) in the first line of output — the size of $$$B$$$. Note that you have to minimize the size of $$$B$$$.
- Then output $$$m$$$ integers $$$b_1, b_2, \ldots, b_m$$$ ($$$1 \le b_i \le k$$$) in the second line — the set you constructed.

If there are multiple answers, you may print any of them.

Note

In the first test case, $$$B=\{2,3\}$$$ works. For $$$b=2$$$, all multiples $$$\{2,4,6\}$$$ (up to $$$k=6$$$) appear in $$$a$$$; for $$$b=3$$$, multiples $$$\{3,6\}$$$ appear. Every $$$a_i$$$ is divisible by $$$2$$$ or $$$3$$$. No single $$$b$$$ can satisfy both conditions, so $$$m=2$$$ is minimal.

In the second test case, $$$B=\{1\}$$$ satisfies both rules since every number is divisible by $$$1$$$ and all multiples of $$$1$$$ up to $$$k$$$ appear.

Kanade's Perfect Multiples

Examples