The Equation

The laws of the universe can be represented by an array of N non-negative integers. The i-th of these integers is Ai.

The universe is good if there is a non-negative integer k such that the following equation is satisfied: (A1 xor k) + (A2 xor k) + ... (AN**** xor k) ≤ M, where xor denotes the bitwise exclusive or.

What is the largest value of k for which the universe is good?

The first line of the input gives the number of test cases, T. T test cases follow. Each test case begins with a line containing the two integers N and M, the number of integers in A and the limit on the equation, respectively.

The second line contains N integers, the i-th of which is Ai, the i-th integer in the array.

For each test case, output one line containing Case #x: y, where x is the test case number (starting from 1) and y is the largest value of k for which the universe is good, or -1 if there is no such k.

• 1 ≤ T ≤ 100.
• 1 ≤ N ≤ 1000.

In sample case #1, the array contains N = 3 integers and M = 27. The largest possible value of k that gives a good universe is 12 ((8 xor 12) + (2 xor 12) + (4 xor 12) = 26).

In sample case #2, the array contains N = 4 integers and M = 45. The largest possible value of k that gives a good universe is 14 ((30 xor 14) + (0 xor 14) + (4 xor 14) + (11 xor 14) = 45).

In sample case #3, the array contains N = 1 integer and M = 0. The largest possible value of k that gives a good universe is 100 (100 xor 100 = 0).

In sample case #4, there is no value of k that gives a good universe, so the answer is -1.