E. Encryption of Orz Pandas
time limit per test
5 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

An Orz Panda agent has some data which should be encrypted. He has store the data into a list a with length n. To encrypt it, he'll run the following loop (wrote in Python) for $$$k$$$ times:

for i in range(1, n):
  a[i] ^= a[i-1]

Please output the content of the list a after the encryption.

Input

There is only one test case in the input file.

The first line contains two integers $$$n$$$ and $$$k$$$, seperated by a whitespace.

The second line contains $$$n$$$ integers $$$a_0, a_1, \cdots, a_{n-1}$$$, the elements in the list a. Each adjacent pair of integers are seperated by a whitespace.

It's guaranteed that $$$1 \leq n \leq 10^5$$$, $$$0 \leq a_i \lt 2^{17}$$$, and $$$1 \leq k \leq 10^{18}$$$.

Output

Output one line, containing $$$n$$$ integers in the encrypted list a. Each adjacent pair of integers should be seperated by a whitespace. There should be no trailing whitespaces.

Example
Input
6 5
1 0 5 1 5 5
Output
1 1 4 5 1 4
Note

For the example:

  • The list should become [1,1,4,5,0,5] after the first iteration
  • The list should become [1,0,4,1,1,4] after the second iteration
  • The list should become [1,1,5,4,5,1] after the third iteration
  • The list should become [1,0,5,1,4,5] after the fourth iteration
  • The list should become [1,1,4,5,1,4] after the fifth iteration, and you should output it