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. lets 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*10^9

1<=arr[i]<=2*10^9 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.