Yarik's birthday is coming soon, and Mark decided to give him an array $$$a$$$ of length $$$n$$$.

Mark knows that Yarik loves bitwise operations very much, and he also has a favorite number $$$x$$$, so Mark wants to find the maximum number $$$k$$$ such that it is possible to select pairs of numbers [$$$l_1, r_1$$$], [$$$l_2, r_2$$$], $$$\ldots$$$ [$$$l_k, r_k$$$], such that:

$$$l_1 = 1$$$.
$$$r_k = n$$$.
$$$l_i \le r_i$$$ for all $$$i$$$ from $$$1$$$ to $$$k$$$.
$$$r_i + 1 = l_{i + 1}$$$ for all $$$i$$$ from $$$1$$$ to $$$k - 1$$$.
$$$(a_{l_1} \oplus a_{l_1 + 1} \oplus \ldots \oplus a_{r_1}) | (a_{l_2} \oplus a_{l_2 + 1} \oplus \ldots \oplus a_{r_2}) | \ldots | (a_{l_k} \oplus a_{l_k + 1} \oplus \ldots \oplus a_{r_k}) \le x$$$, where $$$\oplus$$$ denotes the operation of bitwise XOR, and $$$|$$$ denotes the operation of bitwise OR.

If such $$$k$$$ does not exist, then output $$$-1$$$.

Input

Each test consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. The following lines contain the descriptions of the test cases.

The first line of each test case contains two integers $$$n$$$ and $$$x$$$ ($$$1 \le n \le 10^5, 0 \le x \lt 2^{30}$$$) — the length of the array $$$a$$$ and the number $$$x$$$ respectively.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i \lt 2^{30}$$$) — the array $$$a$$$ itself.

It is guaranteed that the sum of the values of $$$n$$$ across all test cases does not exceed $$$10^5$$$.

Output

For each test case, output a single integer on a separate line — the maximum suitable number $$$k$$$, and $$$-1$$$ if such $$$k$$$ does not exist.

Note

In the first test case, you can take $$$k$$$ equal to $$$2$$$ and choose two segments [$$$1, 1$$$] and [$$$2, 3$$$], $$$(1) | (2 \oplus 3) = 1$$$. It can be shown that $$$2$$$ is the maximum possible answer.

In the second test case, the segments [$$$1, 1$$$] and [$$$2, 2$$$] are suitable, $$$(1) | (1) = 1$$$. It is not possible to make more segments.

In the third test case, it is not possible to choose $$$2$$$ segments, as $$$(1) | (3) = 3 \gt 2$$$, so the optimal answer is $$$1$$$.

Birthday Gift

Examples