Forever97 has two sequences of number. One of them consists of n positive integer numbers a₁, a₂, ..., a_n. And the other one consisted of m positive integer numbers b₁, b₂, …, b_n. Now Forever97 needs to get the maximum value of bitwise xor of one integer from the sequence a and one integer from the sequences b.

The input contains several test cases.

The first line contains two integer numbers n and m (1≤n, m≤10⁵).

The second line contains n integer numbers a₁, a₂, ..., a_n (1≤a_i≤10⁹).

The third line contains m integer numbers b₁, b₂, ..., b_m (1≤b_i≤10⁹).

For each test case, you should output the maximum number Forever97 can get.