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 <= i <= n ), you're asked to choose a j ( 1 <= j <= 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 <= n,m <= 200 ). The next line contains n integers a_1,a_2, ldots,a_n ( 0 <= a_i < 2^9 ). The next line contains m integers b_1,b_2, ldots,b_m ( 0 <= 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.