Problem Statement

You are given an integer sequence of length $N$: $A=(A_1,A_2,\cdots,A_N)$, and an integer $M$.

For each $k=1,2,\cdots,M$, find the value of $A_N$ after doing the operation below $k$ times.

• For every $i$ ($1 \leq i \leq N$), simultaneously, replace the value of $A_i$ with $A_1 \oplus A_2 \oplus \cdots \oplus A_i$.

Here, $\oplus$ denotes bitwise $\mathrm{XOR}$.

What is bitwise $\mathrm{XOR}$? The bitwise $\mathrm{XOR}$ of non-negative integers $A$ and $B$, $A \oplus B$, is defined as follows: When $A \oplus B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if exactly one of $A$ and $B$ is $1$, and $0$ otherwise. For example, we have $3 \oplus 5 = 6$ (in base two: $011 \oplus 101 = 110$). Generally, the bitwise $\mathrm{XOR}$ of $k$ integers $p_1, p_2, p_3, \dots, p_k$ is defined as $(\dots ((p_1 \oplus p_2) \oplus p_3) \oplus \dots \oplus p_k)$. We can prove that this value does not depend on the order of $p_1, p_2, p_3, \dots p_k$.

Constraints

• $1 \leq N \leq 10^6$
• $1 \leq M \leq 10^6$
• $0 \leq A_i < 2^{30}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
A_1 A_2 \cdots A_N

Output

Print the answers for respective values of $k$, separated by spaces.