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 $a_1 + b_j, \ldots, a_n + b_j$.

Input

The first line contains two integers $n$ and $m$ ($1 \leq n, m \leq 2 \cdot 10^5$).

The second line contains $n$ integers $a_1, \ldots, a_n$ ($1 \leq a_i \leq 10^{18})$.

The third line contains $m$ integers $b_1, \ldots, b_m$ ($1 \leq b_j \leq 10^{18})$.

Output

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

见题面 Input 部分

见题面 Output 部分