A13754. Boboniu and Bit Operations

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](https://en.wikipedia.org/wiki/Bitwise_operation#AND). 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](https://en.wikipedia.org/wiki/Bitwise_operation#AND).

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 $c_1 | c_2 | \ldots | c_n$ .

For the first example, we have $c_1=a_1\& b_2=0$ , $c_2=a_2\& b_1=2$ , $c_3=a_3\& b_1=0$ , $c_4 = a_4\& b_1=0$ .Thus $c_1 | c_2 | c_3 |c_4 =2$ , and this is the minimal answer we can get.