Score : $700$ points

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 $\mathrm{XOR}$.

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.

3 2
2 1 3

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: $A=(2,1,1)$.

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

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