A13740 | 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 $(a_i, y)$ ; $0 = a_0 < a_1 < a_2 < \dots < a_{n - 1} < a_n = x$ .

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 $-1$ .

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 $a_0$ , $a_1$ , ..., $a_n$ ( $0 = a_0 < a_1 < a_2 < \dots < a_{n - 1} < a_n = x$ ).

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.

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.