You are given two positive integer sequences a_1, ldots, a_n and b_1, ldots, b_m . For each j = 1, ldots, m find the greatest common divisor of a_1 + b_j, ldots, a_n + b_j . The first line contains two integers n and m ( 1 <= q n, m <= q 2 cdot 10^5 ). The second line contains n integers a_1, ldots, a_n ( 1 <= q a_i <= q 10^{18}) . The third line contains m integers b_1, ldots, b_m ( 1 <= q b_j <= q 10^{18}) . Print m integers. The j -th of them should be equal to GCD (a_1 + b_j, ldots, a_n + b_j) .