Consider a xor pyramid where each number is the xor of lower-left and lower-right numbers. Here is an example pyramid:

Given the bottom row of the pyramid, your task is to find the numbers on the $k$-th row from the top.

Input

The first line has two integers $n$ and $k$: the size of the pyramid and the given row.

The next line has $n$ integers $a_1,a_2,\dots,a_n$: the bottom row of the pyramid.

Output

Print $k$ integers: the numbers on the $k$-th row from the top.

Constraints

• $1 \le k \le n \le 2 \cdot 10^5$
• $1 \le a_i \le 10^9$

Example

Input:

8 5
2 10 5 12 9 5 1 5

Output:

1 10 5 1 8