Given a length-n array a and a number k, there are $\frac{n \times (n + 1)}{2}$ subarrays in total. For each subarray, we can compute the xor sum of its elements.

In this problem, we will sort all these xor-sums in non-increasing order. And we want to find the $k^{th}$ element.

$\textbf{Input}$

The first line contains two numbers n ($1 \le n \le 100 000$) and k ($1 \le k \le \frac{n \times(n + 1)}{2}$).

The second line contains n numbers - $a_1, a_2, a_3, \dots , a_n$ ($0 \le a_i < 2^{20}$).

$\textbf{Output}$

Output the $k^{th}$ element in the non-increasing order.