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.

Sample Input 1

3 2
2 1 3

Sample Output 1

0 1

Each operation changes $A$ as follows.

• Initially: $A=(2,1,3)$.
• After the first operation: $A=(2,3,0)$.
• After the second operation: $A=(2,1,1)$.

Sample Input 2

10 12
721939838 337089195 171851101 1069204754 348295925 77134863 839878205 89360649 838712948 918594427

Sample Output 2

716176219 480674244 678890528 642764255 259091950 663009497 942498522 584528336 364872846 145822575 392655861 844652404