Aftandil has a sequence of integers a1, a2, ... , an. 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 the sequence is bitwise or-sum of its parts' costs.

Help Aftandil to find the minimum cost of the given sequence.

Input

The first line contains two integers n and m (1 ≤ n ≤ 200000, 1 ≤ m ≤ n).

The second line contains n integers a1, a2, ... , an (0 ≤ ai ≤ 109).

Output

Print a single integer that denotes the minimum cost.