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 maxmimum xor value.