Problem Description

There is a nonnegative integer sequence $a_{1...n}$ of length $n$. HazelFan wants to do a type of transformation called prefix-XOR, which means $a_{1...n}$ changes into $b_{1...n}$, where $b_i$ equals to the XOR value of $a_1,...,a_i$. He will repeat it for $m$ times, please tell him the final sequence.

Input

The first line contains a positive integer $T(1\leq T\leq5)$, denoting the number of test cases.
For each test case:
The first line contains two positive integers $n,m(1\leq n\leq2\times10^5,1\leq m\leq10^9)$.
The second line contains $n$ nonnegative integers $a_{1...n}(0\leq a_i\leq2^{30}-1)$.

Output

For each test case:
A single line contains $n$ nonnegative integers, denoting the final sequence.

2
1 1
1
3 3
1 2 3

1
1 3 1