There is a nonnegative integer sequence a1...n of length n. HazelFan wants to do a type of transformation called prefix-XOR, which means a1...n changes into b1...n, where bi equals to the XOR value of a1,...,ai. He will repeat it for m times, please tell him the final sequence.
The first line contains a positive integer T(1≤T≤5), denoting the number of test cases.
For each test case:
The first line contains two positive integers n,m(1≤n≤2×10^5,1≤m≤10^9).
The second line contains n nonnegative integers a1...n(0≤ai≤2^30−1).
For each test case:
A single line contains n nonnegative integers, denoting the final sequence.