You are given an array of $n$ integers. Consider the xors of all $2^n$ subsets of the array (including the empty subset with xor equal to zero).

Your task is to find the $k$ smallest subset xors.

Input

The first line has two integers $n$ and $k$: the size of the array and the number of subset xors $k$.

The next line has $n$ integers $x_1, x_2,\dots, x_n$: the contents of the array.

Output

Print $k$ integers: the $k$ smallest subset xors in increasing order.

Constraints

• $1 \le n \le 2 \cdot 10^5$
• $1 \le k \le \min(2^n, 2 \cdot 10^5)$
• $0 \le x_i \le 10^9$

Example

Input:

4 9
3 5 14 8

Output:

0 0 3 3 5 5 6 6 8