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 $p_1, p_2, p_3, \dots p_k$.
  

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.

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.

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

见题面 Input 部分

见题面 Output 部分