There is an array $$$a_1, a_2, \ldots, a_n$$$ consisting of values $$$0$$$, $$$1$$$, and $$$2$$$, and an integer $$$s$$$. It is guaranteed that $$$a_1, a_2, \ldots, a_n$$$ contains at least one $$$0$$$, one $$$1$$$, and one $$$2$$$.

Alice wants to start from index $$$1$$$ and perform steps of length $$$1$$$ to the right or to the left, and reach index $$$n$$$ at the end. While Alice moves, she calculates the sum of the values she is visiting, and she wants the sum to be exactly $$$s$$$.

Formally, Alice wants to find a sequence $$$[i_1, i_2, \ldots, i_m]$$$ of indices, such that:

$$$i_1 = 1$$$, $$$i_m = n$$$.
$$$1 \leq i_j \leq n$$$ for all $$$1 \le j \le m$$$.
$$$|i_{j} - i_{j+1}| = 1$$$ for all $$$1 \leq j \lt m$$$.
$$$a_{i_1} + a_{i_2} + \ldots + a_{i_m} = s$$$.

However, Bob wants to rearrange $$$a_1, a_2, \ldots, a_n$$$ to prevent Alice from achieving her target. Determine whether it is possible to rearrange $$$a_1, a_2, \ldots, a_n$$$ such that Alice cannot find her target sequence (even if Alice is smart enough). If it is possible, you also need to output the rearranged array $$$a_1, a_2, \ldots, a_n$$$.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^3$$$). The description of the test cases follows.

The first line of each test case contains two integers $$$n$$$ and $$$s$$$ ($$$3 \le n \le 50$$$, $$$0 \le s \le 1000$$$).

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \le 2$$$).

It is guaranteed that $$$a$$$ contains at least one $$$0$$$, one $$$1$$$, and one $$$2$$$.

Output

For each test case, if it is possible to rearrange $$$a$$$ such that Alice cannot find her target sequence, output $$$n$$$ integers — such rearrangement of $$$a$$$. Otherwise, output $$$-1$$$ instead.

Note

In the first test case, any rearrangement of $$$a$$$ can prevent Alice from achieving her target.

In the second test case, regardless of rearranging $$$a$$$, Alice can always find the sequence $$$[1,2,3]$$$ as her target sequence.

In the third test case,there is no rearrangement of $$$a$$$ that can prevent Alice from achieving her target. For example, for $$$a=[0,2,1]$$$, Alice can find the sequence $$$[1,2,3,2,3]$$$ as her target sequence.

Pathless

Examples