Boboniu likes bit operations. He wants to play a game with you.

Boboniu gives you two sequences of non-negative integers $a_1,a_2,\ldots,a_n$ and $b_1,b_2,\ldots,b_m$.

For each $i$ ($1\le i\le n$), you're asked to choose a $j$ ($1\le j\le m$) and let $c_i=a_i\& b_j$, where $\&$ denotes the bitwise AND operation. Note that you can pick the same $j$ for different $i$'s.

Find the minimum possible $c_1 | c_2 | \ldots | c_n$, where $|$ denotes the bitwise OR operation.

The first line contains two integers $n$ and $m$ ($1\le n,m\le 200$).

The next line contains $n$ integers $a_1,a_2,\ldots,a_n$ ($0\le a_i < 2^9$).

The next line contains $m$ integers $b_1,b_2,\ldots,b_m$ ($0\le b_i < 2^9$).

Print one integer: the minimum possible $c_1 | c_2 | \ldots | c_n$.