Chef has an array A of length N.

Chef wants to append a non-negative integer X to the array A such that the [bitwise OR] of the entire array becomes = Y i.e. (A_{1} \ | \ A_{2} \ | \ $\ldots$ \ | \ A_{N} \ | \ X) = Y. (Here, | denotes the bitwise OR operation)

Determine the minimum possible value of X. If no possible value of X exists, output -1.

------ Input Format ------

• The first line contains a single integer T — the number of test cases. Then the test cases follow.
• The first line of each test case contains two integers N and Y — the size of the array A and final bitwise OR of the array A.
• The second line of each test case contains $N space-separated integers A_{1}, A_{2}, \dots, A_{N}$ denoting the array A.

------ Output Format ------

For each test case, output the minimum possible value of X for which (A_{1} \ | \ A_{2} \ | \ $\ldots$ \ | \ A_{N} \ | \ X) = Y holds.

If no such value exists, output -1.

------ Constraints ------

$1 ≤ T ≤ 10^{5}$
$1 ≤ N ≤ 10^{5}$
$0 ≤A_{i} < 2^{20}$
$0 ≤Y < 2^{20}$
- Sum of $N$ over all test cases does not exceed $2 \cdot 10^{5}$

----- Sample Input 1 ------
4
4 15
3 5 6 2
3 8
1 2 1
1 1
0
5 7
1 2 4 2 1

----- Sample Output 1 ------
8
-1
1
0

----- explanation 1 ------
Test Case 1: $(3 \ | \ 5 \ | \ 6 \ | \ 2 \ | \ X) = 15$ holds for the following values of $X$: $\{8, 9, 10, 11, 12, 13, 14, 15\}$. The minimum among them is $8$.

Test Case 2: It can be proven that no valid value of $X$ exists.

Test Case 3: $(0 \ | \ X) = 1$ holds for only $X = 1$.

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