Given an array of n integers and a number x. Your task is very simple. You have to find the subarray (length > 0) whose xor is maximum with x. Let's say the subarray as maxsubarray. You have to print the xor value of maxsubarray.

Input

First line of input consists of t test cases.

Second line of input contains two integers n and x.

Third line contains n space separated integers denoting the elements of array.

Output

First and only line of output is xor value of maxsubarray.

Constraints

1 ≤ t ≤ 10

1 ≤ n ≤ 200000

1 ≤ x ≤ 2×10⁹

1 ≤ arr[i] ≤ 2×10⁹ where arr[i] is any integer of array.

Example

Input:
1
3 7
1 2 3
Output:
0

taking 1^2^3 is 0 when taken xor with 7 gives us the maximum xor value.