XOR

Aftandil has a sequence of integers a[1], a[2], ... , 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 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 a[1], a[2], ... , a[n] (0 ≤ a[i] ≤ 10^9).

Output

Print a single integer that denotes the minimum cost.

Examples