You are given two positive integer sequences $a_1,\ …,\ a_n$ and $b_1,\ …,\ b_m$. For each $j=1,\ …,\ m$ find the greatest common divisor of $a_1+b_j,\ …,\ a_n+b_j$.
给两个正整数序列 $a_1,\ …,\ a_n$ 和 $b_1,\ …,\ b_m$，求对于每个 $j=1,\ …,\ m$ 的 $a_1+b_j,\ …,\ a_n+b_j$ 最大公约数。

The first line contains two integers $n,\ m\ (1 ≤ n,\ m ≤ 2⋅10^5)$.
The second line contains $n$ integers $a_1,\ …,\ a_n\ (1 ≤ a_i ≤ 10^{18})$.
The third line contains $m$ integers $b_1,\ …,\ b_m\ (1 ≤ b_j ≤ 10^{18})$.

Print $m$ integers. The $j$-th of them should be equal to $\text{GCD}(a_1+b_j,\ …,\ a_n+b_j)$.