XOr

bobo has a sequence of integers $a_1, a_2, \dots, a_n$. He decides to divide the sequence into exactly $m$ consecutive parts.

The cost of each part is its xor sum (bitwise exclusive-or), while the cost of division is bitwise or-sum of its parts' costs.

Help bobo find the minimum cost.

The first line contains $2$ integers $n, m$ ($1 \leq n \leq 200000, 1 \leq m \leq n$).

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \leq a_i \leq 10^9$).

A single integer denotes the minimum cost.