Boboniu likes bit operations. He wants to play a game with you.
Boboniu gives you two sequences of non-negative integers a1,a2,…,an and b1,b2,…,bm.
For each i (1≤i≤n), you're asked to choose a j (1≤j≤m) and let ci=ai&bj, where & denotes the bitwise AND operation. Note that you can pick the same j for different i's.
Find the minimum possible c1|c2|…|cn, where | denotes the bitwise OR operation.
The first line contains two integers n and m (1≤n,m≤200).
The next line contains n integers a1,a2,…,an (0≤ai<2^9).
The next line contains m integers b1,b2,…,bm (0≤bi<2^9).
Print one integer: the minimum possible c1|c2|…|cn
4 2 2 6 4 0 2 4
2
7 6 1 9 1 9 8 1 0 1 1 4 5 1 4
0
8 5 179 261 432 162 82 43 10 38 379 357 202 184 197
147
NoteFor the first example, we have c1=a1&b2=0, c2=a2&b1=2, c3=a3&b1=0, c4=a4&b1=0.Thus c1|c2|c3|c4=2, and this is the minimal answer we can get.