Xor Pyramid Row

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