- Time limit: 1.00 s
- Memory limit: 512 MB
Consider a xor pyramid where each number is the xor of lower-left and lower-right numbers. Here is an example pyramid:
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