CF1398G.Running Competition

A running competition is going to be held soon. The stadium where the competition will be held can be represented by several segments on the coordinate plane:

• two horizontal segments: one connecting the points $(0, 0)$ and $(x, 0)$, the other connecting the points $(0, y)$ and $(x, y)$;
• $n + 1$ vertical segments, numbered from $0$ to $n$. The $i$-th segment connects the points $(a_i, 0)$ and $(a_i, y)$; $0 = a_0 \lt a_1 \lt a_2 \lt \dots \lt a_{n - 1} \lt a_n = x$.

For example, here is a picture of the stadium with $x = 10$, $y = 5$, $n = 3$ and $a = [0, 3, 5, 10]$:

A lap is a route that goes along the segments, starts and finishes at the same point, and never intersects itself (the only two points of a lap that coincide are its starting point and ending point). The length of a lap is a total distance travelled around it. For example, the red route in the picture representing the stadium is a lap of length $24$.

The competition will be held in $q$ stages. The $i$-th stage has length $l_i$, and the organizers want to choose a lap for each stage such that the length of the lap is a divisor of $l_i$. The organizers don't want to choose short laps for the stages, so for each stage, they want to find the maximum possible length of a suitable lap.

Help the organizers to calculate the maximum possible lengths of the laps for the stages! In other words, for every $l_i$, find the maximum possible integer $L$ such that $l_i \bmod L = 0$, and there exists a lap of length exactly $L$.

If it is impossible to choose such a lap then print $-1$.

一场跑步比赛即将举行。比赛场地可由坐标平面上的若干线段表示：

• 两条水平线段：一条连接点 $(0, 0)$ 与 $(x, 0)$，另一条连接点 $(0, y)$ 与 $(x, y)$；
• $n + 1$ 条垂直线段，编号从 $0$ 到 $n$。第 $i$ 条垂直线段连接点 $(a_i, 0)$ 与 $(a_i, y)$；其中满足 $0 = a_0 \lt a_1 \lt a_2 \lt \dots \lt a_{n - 1} \lt a_n = x$。

例如，下图展示了一个 $x = 10$、$y = 5$、$n = 3$ 且 $a = [0, 3, 5, 10]$ 的场地示意图：

一个“圈”（lap）是一条沿这些线段行进的闭合路径，起点与终点重合，且路径不自交（除起点/终点重合外，其余任意两点均不重合）。一个圈的长度即为其总行程距离。例如，图中用红色标出的路径即为一个长度为 $24$ 的圈。

比赛共分 $q$ 个阶段进行。第 $i$ 个阶段的指定长度为 $l_i$，主办方希望为每个阶段选择一个圈，使得该圈的长度能整除 $l_i$。主办方不希望为各阶段选择过短的圈，因此对每个阶段，他们希望找出满足条件的圈的最大可能长度。

请帮助主办方计算各阶段所能选择的圈的最大可能长度！换言之，对每个 $l_i$，求最大的正整数 $L$，使得 $l_i \bmod L = 0$，且存在一个长度恰好为 $L$ 的圈。

若不存在满足条件的圈，则输出 $-1$。

The first line contains three integers $n$, $x$ and $y$ ($1 \le n, x, y \le 2 \cdot 10^5$, $n \le x$).

The second line contains $n + 1$ integers $a_0$, $a_1$, ..., $a_n$ ($0 = a_0 \lt a_1 \lt a_2 \lt \dots \lt a_{n - 1} \lt a_n = x$).

The third line contains one integer $q$ ($1 \le q \le 2 \cdot 10^5$) — the number of stages.

The fourth line contains $q$ even integers $l_1$, $l_2$, ..., $l_q$ ($4 \le l_i \le 10^6$) — the lengths of the stages.

第一行包含三个整数 $n$、$x$ 和 $y$（$1 \le n, x, y \le 2 \cdot 10^5$，且 $n \le x$）。

第二行包含 $n + 1$ 个整数 $a_0$、$a_1$、...、$a_n$（满足 $0 = a_0 \lt a_1 \lt a_2 \lt \dots \lt a_{n - 1} \lt a_n = x$）。

第三行包含一个整数 $q$（$1 \le q \le 2 \cdot 10^5$）—— 阶段的数量。

第四行包含 $q$ 个偶数 $l_1$、$l_2$、...、$l_q$（$4 \le l_i \le 10^6$）—— 各阶段的长度。

Print $q$ numbers. The $i$-th number should be equal to the maximum possible length of a suitable lap for the $i$-th stage, or $-1$ if it is impossible to choose a lap for that stage.

输出 $q$ 个数。其中第 $i$ 个数应等于第 $i$ 个阶段的合适圈道的最大可能长度；若该阶段无法选择任何圈道，则输出 $-1$。